Determination of the ATLAS jet energy measurement uncertainty using photon-jet events in proton-proton collisions at sqrt(s) = 7 TeV

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1 Haverford College Haverford Scholarshi Faculty Publications Physics Determination of the ALAS energy measurement uncertainty using hoton- events in roton-roton collisions at sqrt(s) = 7 ev Kerstin M. Perez Haverford College, kerez@haverford.edu Follow this and additional works at: htt://scholarshi.haverford.edu/hysics_facubs Reository Citation he ALAS Collaboration, Determination of the ALAS energy measurement un-certainty using hoton- events in rotonroton collisions at s = 7 ev, ALAS- CONF--, CERN (), For the 46th Rencontres de Moriond on QCD and High Energy Interactions, La huile, Italy, March. his Journal Article is brought to you for free and oen access by the Physics at Haverford Scholarshi. It has been acceted for inclusion in Faculty Publications by an authorized administrator of Haverford Scholarshi. For more information, lease contact nmedeiro@haverford.edu.

2 EPJ manuscrit No. (will be inserted by the editor) CERN-PH-EP--9 Submitted to Eur. Phys. J. C Jet energy measurement with the ALAS detector in roton-roton collisions at s=7 ev he ALAS Collaboration arxiv:.646v [he-ex] 9 Dec December, Abstract. he energy scale (JES) and its systematic uncertainty are determined for s measured with the ALAS detector at the LHC in roton-roton collision data at a centre-of-mass energy of s = 7 ev corresonding to an integrated luminosity of 8 b. Jets are reconstructed with the anti-k t algorithm with distance arameters R=.4 or R =.6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate s with transverse momenta GeV and seudoraidities η < 4.5. he JES systematic uncertainty is estimated using the single isolated hadron resonse measured in situ and in test-beams, exloiting the transverse momentum balance between central and forward s in events with di toologies and studying systematic variations in Monte Carlo simulations. he JES uncertainty is less than.5% in the central calorimeter region ( η <.8) for s with 6 < 8 GeV, and is maximally 4% for < GeV in the most forward region. η < 4.5. he uncertainty for additional energy from multile roton-roton collisions in the same bunch crossing is less than.5% er additional collision for s with > 5 GeV after a dedicated correction for this effect. he JES is validated for transverse momenta u to ev to the level of a few ercent using several in situ techniques by comaring a well-known reference such as the recoiling hoton, the sum of the transverse momenta of tracks associated to the, or a system of low- s recoiling against a high-. More sohisticated calibration schemes are resented based on calorimeter cell energy density weighting or hadronic roerties of s, roviding an imroved energy resolution and a reduced flavour deendence of the resonse. he JES systematic uncertainty determined from a combination of in situ techniques are consistent with the one derived from single hadron resonse measurements over a wide kinematic range. he nominal corrections and uncertainties are derived for isolated s in an inclusive samle of high- s. Secial cases such as event toologies with close-by s, or selections of samles with an enhanced content of s originating from light quarks, heavy quarks or gluons are also discussed and the corresonding uncertainties are determined.

3 ALAS collaboration: Jet measurement with the ALAS detector Contents Introduction he ALAS detector Introduction to energy calibration methods Monte Carlo simulation Event generators Simulation of the ALAS detector Nominal Monte Carlo simulation samles Simulated ile-u samles Data samle and event selection Data taking eriod and LHC conditions Event selection Data quality assessment Jet reconstruction Reconstructed calorimeter s Reconstructed track s Monte Carlo truth s and flavour association Jet quality selection Criteria to remove non-collision background Evaluation of the quality selection efficiency Summary of the quality selection Jet energy calibration in the EM+JES scheme Pile-u correction Jet origin correction Jet energy correction Jet seudoradity correction Jet energy scale uncertainties for the EM+JES scheme Jet resonse definition for the JES uncertainty evaluation 7 9. Uncertainty in the JES calibration Uncertainty on the calorimeter resonse Uncertainties due to the detector simulation Uncertainties due to the event modelling in Monte Carlo generators In situ intercalibration using events with di toologies 9.7 Uncertainties due to multile roton-roton collisions Summary of energy scale systematic uncertainties Discussion of secial cases Jet energy scale uncertainties validation with in situ techniques for the EM+JES scheme Comarison of transverse momentum balance of s from calorimeter and tracking Photon- transverse momentum balance Multi transverse momentum balance Summary of JES validation using in situ techniques JES uncertainty from combination of in situ techniques 48 Jet energy calibration based on global roerties Global sequential technique Proerties derived from the internal structure Derivation of the global sequential correction Jet energy scale uncertainties for calibrations based on global roerties Validation of the global sequential calibration using di events Sensitivity of the global sequential calibration to ile-u 58. Summary on the JES uncertainty for the global sequential calibration Jet calibration schemes based on cell energy weighting Global cell energy density weighting calibration Local cluster weighting calibration Jet energy calibration for s with calibrated constituents 6 4 Jet energy scale uncertainties for calibrations based on cell weighting Energy density as inut to the global cell weighting calibration Cluster roerties inside s as inut to the local cluster weighting calibration Jet energy scale uncertainty from in situ techniques for s based on cell weighting Summary of energy scale uncertainties of various calibration schemes Jet reconstruction efficiency Efficiency in the Monte Carlo simulation Efficiency in situ validation Summary of reconstruction efficiency Resonse uncertainty of non-isolated s Evaluation of close-by effects Non-isolated resonse Non-isolated energy scale uncertainty Summary of close-by uncertainty Light quark and gluon resonse and samle characterisation Data samles for flavour deendence studies Flavour deendence of the calorimeter resonse Systematic uncertainties due to flavour deendence Average flavour determination Systematic uncertainties of average flavour comosition Flavour comosition in a hoton- samle Flavour comosition in a multi samle Summary of resonse flavour deendence Global sequential calibrated resonse for a quark samle. 88 JES uncertainties for s with identified heavy quark comonents Selection of identified heavy quark s Calorimeter resonse uncertainty Uncertainties due to Monte Carlo modelling Final bottom quark JES uncertainty Validation of the heavy quark energy scale using tracks 9 Study of unch-through Event selection for unch-through analysis Energy deositions in the hadronic calorimeter Di balance as an indication of unch-through Summary of the unch-through study Summary

4 ALAS collaboration: Jet measurement with the ALAS detector Introduction Collimated srays of energetic hadrons, called s, are the dominant feature of high energy roton-roton interactions at the Large Hadron Collider (LHC) at CERN. In Quantum Chromodynamics (QCD) s are roduced via the fragmentation of quarks and gluons. hey are key ingredients for many hysics measurements and for searches for new henomena. During the year the ALAS detector collected rotonroton collision data at a centre-of-mass energy of s=7 ev corresonding to an integrated luminosity of 8 b. he uncertainty in the energy measurement is the dominant exerimental uncertainty for numerous hysics results, for examle the cross-section measurement of inclusive s, dis or multis [ 4], as well as of vector bosons accomanied by s [5], and new hysics searches with s in the final state [6]. Jets are observed as grous of toologically related energy deosits in the ALAS calorimeters. hey are reconstructed with the anti-k t algorithm [7]. Using a Monte Carlo (MC) simulation the observed s are calibrated such that, on average, the energy corresonds to that of the associated stable articles in the ALAS detector. he calibration of the energy scale (JES) should ensure the correct measurement of the average energy across the whole detector and needs to be indeendent of additional events roduced in roton-roton collisions at high luminosity comounding on the event of interest. In this document, the calibration strategies adoted by the ALAS exeriment are outlined and studies to evaluate the uncertainties in the energy measurement are resented. A first estimate of the JES uncertainty, described in Ref. [], was based on information available before the first LHC collisions. It also exloited transverse momentum balance in events with only two s at high transverse momenta ( ). A reduced uncertainty with resect to Ref. [] is resented that is based on the increased knowledge of the detector erformance obtained during the analysis of the first year of ALAS data taking. ALAS has develoed several calibration schemes [8] with different levels of comlexity and different sensitivity to systematic effects, which are comlementary in their contribution to the energy measurement. Each calibration scheme starts from the measured calorimeter energy at the electromagnetic (EM) energy scale, which correctly measures the energy deosited by electromagnetic showers. In the simlest scheme (EM+JES) the calibration is derived as a simle correction relating the calorimeter s resonse to the true energy. More sohisticated schemes exloit the toology of the calorimeter energy deositions to correct for calorimeter noncomensation (nuclear energy losses, etc.) and other reconstruction effects. For the simle EM+JES calibration scheme based only on the JES correction, the JES uncertainty can be determined from the single hadron resonse measurements in small data sets collected in situ or in test-beams. With a large data set available the JES uncertainty can also be determined using the ratio of the transverse momentum to the momentum of a reference object and by a comarison of the data to the Monte Carlo simulation. Several techniques have been develoed to directly determine the uncertainty on the energy measurement in situ. he JES uncertainty can be obtained by comaring the energy to a well calibrated reference object. A standard technique to robe the absolute energy scale, used also in earlier hadron collider exeriments, is to measure the balance between the and a well-measured object: a hoton or a Z boson. However, the currently limited data statistics imoses a limit on the range that can be tested with this technique. he JES uncertainty on higher transverse momenta u to the ev-scale can be assessed using the multi balance technique where a recoil system of well-calibrated s at lower is balanced against a single at higher. A comlementary technique uses the total momentum of the tracks associated to the s as reference objects. While the resolution of the energy measurement using tracks in s is rather oor, the mean energy can be determined to the recision of a few ercent. he standard calibration and the corresonding uncertainty on the energy measurement are determined for isolated s in an inclusive data samle. Additional uncertainties are evaluated for differences in the resonse of s induced by quarks or gluons and for secial toologies with close-by s. he outline of the aer is as follows. First the ALAS detector (Section ) is described. An overview of the calibration rocedures and the various calibration schemes is given in Section. he Monte Carlo simulation framework is introduced in Section 4. he data samles, data quality assessment and event selection are described in Section 5. hen, the reconstruction (Section 6), and the selection (Section 7) of s are discussed. he calibration method is outlined in Section 8 which includes a rescrition to correct for the extra energy due to multile roton-roton interactions (ile-u). Section 9 describes the sources of systematic uncertainties for the energy measurement and their estimation using Monte Carlo simulations and collision data. Section describes several in situ techniques used to validate these systematic uncertainties. Section resents a technique to imrove the resolution of the energy measurements and to reduce the flavour resonse differences by exloiting the toology of the s. he systematic uncertainties associated with this technique are described in Section. he calibration schemes based on calorimeter cell energy weighting in s are introduced in Section, and the associated JES uncertainties are estimated from the in situ techniques as described in Section 4. Section 5 summarises the systematic uncertainties for all studied calibration schemes. he reconstruction efficiency and its uncertainty is discussed in Section 6. he resonse uncertainty of non-isolated s is investigated in Section 7, while Section 8 and Section 9 discuss resonse difference for s originating from light quarks or gluons and resents a method to determine, on average, the flavour content in a given data samle. In Section JES uncertainties for s where a heavy quark is identified are investigated. Finally, ossible effects from lack of full calorimeter containment of s with high transverse momentum are studied in Section. he overall conclusion is given in Section.

5 4 ALAS collaboration: Jet measurement with the ALAS detector ile Ext ile Bar EMB EMEC FCAL HEC Fig. : Dislay of the central art of the ALAS detector in the x-z view showing the highest mass central di event collected during the data taking eriod. he two leading s have =. ev with y=.68 and =. ev with y=.64, resectively. he two leading s have an invariant mass of aroximately. ev. he missing transverse energy in the event is 46 GeV. he lines in the inner detector indicate the reconstructed article trajectories. he energy deosition in the calorimeter cells are dislayed as light rectangles. he size of the rectangles is roortional to the energy deosits. he histograms attached to thelar and theile calorimeter illustrate the amount of deosited energy. he ALAS detector he ALAS detector is a multi-urose detector designed to observe articles roduced in roton-roton and heavy ion collisions. A detailed descrition can be found in Ref. [9]. he detector consists of an inner detector, samling electromagnetic and hadronic calorimeters and muon chambers. Figure shows a sketch of the detector outline together with an event with two s at high transverse momenta. he inner detector (ID) is a tracking system immersed in a magnetic field of rovided by a solenoid and covers a seudoraidity η.5. heid barrel region η consists of three layers of ixel detectors (Pixel) close to the beam-ie, four layers of double-sided silicon micro-stri detectors (SC) he ALAS coordinate system is a right-handed system with the x-axis ointing to the centre of the LHC ring and the y-axis ointing uwards. he olar angle θ is measured with resect to the LHC beam-line. he azimuthal angle φ is measured with resect to the x-axis. he seudoraidity η is an aroximation for raidity y in the high energy limit, and it is related to the olar angle θ as η = lntan θ. he raidity is defined as y=.5 ln[(e+ z)/(e z )], where E denotes the energy and z is the comonent of the momentum along the beam direction. ransverse momentum and energy are defined as = sin θ and E = E sinθ, resectively. roviding eight hits er track at intermediate radii, and a transition radiation tracker (R) comosed of straw tubes in the outer art roviding 5 hits er track. At η > the ID endca regions each rovide three Pixel discs and nine SC discs erendicular to the beam direction. he liquid argon (LAr) calorimeter is comosed of samling detectors with full azimuthal symmetry, housed in one barrel and two endca cryostats. A highly granular electromagnetic (EM) calorimeter with accordion-shaed electrodes and lead absorbers in liquid argon covers the seudoraidity range η <.. It contains a barrel art (EMB, η <.475) and an endca art (EMEC,.75 η <.) each with three layers in deth (from innermost to outermost EMB, EMB, EMB and EMEC, EMEC, EMEC). he middle layer has a.5.5 granularity in η φ sace. he innermost layer (stris) consists of cells with eight times finer granularity in the η-direction and with -times coarser granularity in the φ direction. For η <.8, a resamler (Presamler), consisting of an active LAr layer is installed directly in front of the EM calorimeters, and rovides a measurement of the energy lost before the calorimeter. A coer-liquid argon hadronic endca calorimeter (HEC,.5 η <.) is located behind theemec. A coer/tungstenliquid argon forward calorimeter (FCal) covers the region clos-

6 ALAS collaboration: Jet measurement with the ALAS detector 5 η <.7. he muon sectrometer measures muon tracks with three layers of recision tracking chambers and is instrumented with searate trigger chambers. he trigger system for the ALAS detector consists of a hardware-based Level (L) and a software-based higher level trigger (HL) []. Jets are first identified at L using a sliding window algorithm from coarse granularity calorimeter towers. his is refined using s reconstructed from calorimeter cells in the HL. he lowest threshold inclusive trigger is fully efficient for s with 6 GeV. Events with lower s are triggered by the minimum bias trigger scintillators (MBS) mounted at each end of the detector in front of thelar endca calorimeter cryostats at z = ±.56 m. Introduction to energy calibration methods Fig. : Zoom of the x-y view of the ALAS detector showing one of the high- s of the event shown in Figure. he energy deositions in the calorimeter cells are dislayed as light rectangles. he size of the rectangles is roortional to the energy deosits. he dark histograms attached to the LAr (ile) calorimeter illustrates the amount of deosited energy. he lines in theid dislay the reconstructed tracks originating from the interaction vertex. est to the beam at. η <4.9. hehec has four layers and the FCAL has three layers. From innermost to outermost these are:hec,hec,hec,hec andfcal,fcal,fcal. Altogether, the LAr calorimeters corresond to a total of 8, 468 readout cells, i.e. 97.% of the full ALAS calorimeter readout. he hadronic ile calorimeter ( η <.7) surrounding the LAr cryostats comletes the ALAS calorimetry. It consists of lastic scintillator tiles and steel absorbers covering η <.8 for the barrel and.8 η <.7 for the extended barrel. Radially, the hadronic ile calorimeter is segmented into three layers, aroximately.4,.9 and.8 interaction lengths thick at η = ; the η φ segmentation is.. (.. in the last radial layer). he last layer is used to catch the tails of the longitudinal shower develoment. he three radial layers of the ile calorimeter will be referred to (from innermost to outermost) asile,ile,ile. Between the barrel and the extended barrels there is a ga of about 6 cm, which is needed for the ID and the LAr services. Ga scintillators (Ga) covering the region. η <. are installed on the inner radial surface of the extended barrel modules in the region between the ile barrel and the extended barrel. Crack scintillators (Scint) are located on the front of thelar endca and cover the region. η <.6. he muon sectrometer surrounds the ALAS calorimeter. A system of three large air-core toroids, a barrel and two endcas, generates a magnetic field in the seudoraidity range of In the barrel, theile layers will be calledilebar,ilebar, ilebar and in the extended barrel ileext, ileext and ileext. Hadronic s used for ALAS hysics analyses are reconstructed by a algorithm starting from the energy deositions of electromagnetic and hadronic showers in the calorimeters. An examle of a recorded by the ALAS detector and dislayed in the lane transverse to the beam line is shown in Figure. he Lorentz four-momentum is reconstructed from the corrected energy and angles with resect to the rimary event vertex. For systematic studies and calibration uroses track s are built from charged articles using their momenta measured in the inner detector. Reference s in Monte Carlo simulations (truth s) are formed from simulated stable articles using the same algorithm. he energy calibration relates the energy measured with the ALAS calorimeter to the true energy of the corresonding of stable articles entering the ALAS detector. he calibration corrects for the following detector effects that affect the energy measurement:. Calorimeter non-comensation: artial measurement of the energy deosited by hadrons.. Dead material: energy losses in inactive regions of the detector.. Leakage: energy of articles reaching outside the calorimeters. 4. Out of calorimeter cone: energy deosits of articles inside the truth entering the detector that are not included in the reconstructed. 5. Noise thresholds and article reconstruction efficiency: signal losses in the calorimeter clustering and reconstruction. Jets reconstructed in the calorimeter system are formed from calorimeter energy deositions reconstructed at the electromagnetic energy scale (EM) or from energy deositions that are corrected for the lower detector resonse to hadrons. he EM scale correctly reconstructs the energy deosited by articles in an electromagnetic shower in the calorimeter. his energy scale is established using test-beam measurements for electrons in the barrel [ 4] and the endca calorimeters [5, 6]. he absolute calorimeter resonse to energy deosited via electromagnetic rocesses was validated in the hadronic calorimeters using muons, both from test-beams [4, 7] and ro-

7 6 ALAS collaboration: Jet measurement with the ALAS detector duced in situ by cosmic rays [8]. he energy scale of the electromagnetic calorimeters is corrected using the invariant mass of Z bosons roduced in roton-roton collisions (Z e + e events) [9]. he correction for the lower resonse to hadrons is solely based on the toology of the energy deositions observed in the calorimeter. In the simlest case the measured energy is corrected, on average, using Monte Carlo simulations, as follows: E calib = E meas /F calib(emeas ), with E meas = E EM O(N PV). () he variable E EM is the calorimeter energy measured at the electromagnetic scale, E is the calibrated energy and calib F calib is the calibration function that deends on the measured energy and is evaluated in small seudoraidity regions. he variable O(N PV ) denotes the correction for additional energy from multile roton-roton interactions deending on the number of rimary vertices (N PV ). he simlest calibration scheme (called EM+JES) alies the JES corrections to s reconstructed at the electromagnetic scale. his calibration scheme allows a simle evaluation of the systematic uncertainty from single hadron resonse measurements and systematic Monte Carlo variations. his can be achieved with small data sets and is therefore suitable for early hysics analyses. Other calibration schemes use additional cluster-by-cluster and/or -by- information to reduce some of the sources of fluctuations in the energy resonse, thereby imroving the energy resolution. For these calibration schemes the same calibration rocedure is alied as for the EM+JES calibration scheme, but the energy corrections are numerically smaller. he global calorimeter cell weighting (GCW) calibration exloits the observation that electromagnetic showers in the calorimeter leave more comact energy deositions than hadronic showers with the same energy. Energy corrections are derived for each calorimeter cell within a, with the constraint that the energy resolution is minimised. he cell corrections account for all energy losses of a in the ALAS detector. Since these corrections are only alicable to s and not to energy deositions in general, they are called global corrections. he local cluster weighting (LCW) calibration method first clusters together toologically connected calorimeter cells and classifies these clusters as either electromagnetic or hadronic. Based on this classification energy corrections are derived from single ion Monte Carlo simulations. Dedicated corrections are derived for the effects of non-comensation, signal losses due to noise threshold effects, and energy lost in non-instrumented regions. hey are alied to calorimeter clusters and are defined without reference to a definition. hey are therefore called local corrections. Jets are then built from these calibrated clusters using a algorithm. he final energy calibration (see Equation ) can be alied to EM scale s, with the resulting calibrated s referred to as EM+JES, or to GCW and LCW calibrated s, with the resulting s referred to as GCW+JES and LCW+JES s. A further calibration scheme, called global sequential (GS) calibration, starts from s calibrated with the EM+JES calibration and exloits the toology of the energy deosits in the calorimeter to characterise fluctuations in the article content of the hadronic shower develoment. Correcting for such fluctuations can imrove the energy resolution. he corrections are alied such that the mean energy is left unchanged. he correction uses several roerties and each correction is alied sequentially. In articular, the longitudinal and transverse structure of the hadronic shower in the calorimeter is exloited. he simle EM+JES calibration scheme does not rovide the best erformance, but allows in the central detector region the most direct evaluation of the systematic uncertainties from the calorimeter resonse to single isolated hadron measured in situ and in test-beams and from systematic variations of the Monte Carlo simulation. For the GS the systematic uncertainty is obtained by studying the resonse after alying the GS calibration with resect to the EM+JES calibration. For the GCW+JES and LCW+JES calibration schemes the JES uncertainty is determined from in situ techniques. For all calibration schemes the JES uncertainty in the forward detector regions is derived from the uncertainty in the central region using the transverse momentum balance in events where only two s are roduced. In the following, the calibrated calorimeter transverse momentum will be denoted as, and the seudoraidity as η. 4 Monte Carlo simulation 4. Event generators he energy and direction of articles roduced in roton-roton collisions are simulated using various event generators. An overview of Monte Carlo event generators for LHC hysics can be found in Ref. []. he samles using different event generators and theoretical models used are described below:. PYHIA with the MC or AMB tune: he event generator PYHIA [] simulates non-diffractive roton-roton collisions using a matrix element at leading order in the strong couling to model the hard subrocess, and uses -ordered arton showers to model additional radiation in the leading-logarithmic aroximation []. Multile arton interactions [], as well as fragmentation and hadronisation based on the Lund string model [4] are also simulated. he roton arton distribution function (PDF) set used is the modified leading-order PDF set MRS LO* [5]. he arameters used for tuning multile arton interactions include charged article sectra measured by A- LAS in minimum bias collisions [6], and are denoted as the ALAS MC tune [7].. he PERUGIA tune is an indeendent tune of PYH- IA with increased final state radiation to better reroduce the shaes and hadronic event shaes using LEP and EVARON data [8]. In addition, arameters sensitive to the roduction of articles with strangeness and related to fragmentation have been adjusted.. HERWIG+JIMMY uses a leading order matrix element sulemented with angular-ordered arton showers

8 ALAS collaboration: Jet measurement with the ALAS detector 7 in the leading-logarithm aroximation [9]. he cluster model is used for the hadronisation []. Multile arton interactions are modelled using JIMMY []. he model arameters of HERWIG/JIMMY have been tuned to ALAS data (AUE tune) []. he MRS LO* PDF set [5] is used. 4. HERWIG++ [] is based on the event generator HERWIG, but redesigned in the C++ rogramming language. he generator contains a few modelling imrovements. It also uses angular-ordered arton showers, but with an udated evolution variable and a better hase sace treatment. Hadronisation is erformed using the cluster model. he underlying event and soft inclusive interactions are described using a hard and soft multile artonic interactions model [4]. he MRS LO* PDF set [5] is used. 5. ALPGEN is a tree level matrix-element generator for hard multi-arton rocesses ( n) in hadronic collisions [5]. It is interfaced to HERWIG to roduce arton showers in the leading-logarithmic aroximation. Parton showers are matched to the matrix element with the MLM matching scheme [6]. For the hadronisation, HERWIG is used and soft multile arton interactions are modelled using JIMMY [] (with the ALAS MC9 tune [7]). he PDF set used is CEQ6L [8]. 4. Simulation of the ALAS detector he GEAN4 software toolkit [9] within the ALAS simulation framework [4] roagates the generated articles through the ALAS detector and simulates their interactions with the detector material. he energy deosited by articles in the active detector material is converted into detector signals with the same format as the ALAS detector read-out. he simulated detector signals are in turn reconstructed with the same reconstruction software as used for the data. In GEAN4 the model for the interaction of hadrons with the detector material can be secified for various article tyes and for various energy ranges. For the simulation of hadronic interactions in the detector, the GEAN4 set of rocesses called QGSP BER is chosen [4]. In this set of rocesses, the Quark Gluon String model [4] is used for the fragmentation of the nucleus, and the Bertini cascade model [4] for the descrition of the interactions of hadrons in the nuclear medium. he GEAN4 simulation and in articular the hadronic interaction model for ions and rotons, has been validated with test-beam measurements for the barrel [4, 44 46] and endca [5,6,47] calorimeters. Agreement within a few ercent is found between simulation and data for ion momenta between GeV and 5 GeV. Further tests have been carried out in situ comaring the single hadron resonse, measured using isolated tracks and identified single articles. Agreement within a few ercent is found for the inclusive measurement [48, 49] and for identified ions and rotons from the decay roducts of kaon and lambda articles roduced in roton-roton collisions at 7 ev [5]. With this method article momenta of ions and rotons in the range from a few hundred MeV to 6 GeV can be reached. Good agreement between Monte Carlo simulation and data is found. 4. Nominal Monte Carlo simulation samles he baseline (nominal) Monte Carlo samle used to derive the energy scale and to estimate the sources of its systematic uncertainty is a samle containing high- s roduced via strong interactions. It is generated with the PYHIA event generator with the MC tune (see Section 4.), assed through the full ALAS detector simulation and is reconstructed as the data. he ALAS detector geometry used in the simulation of the nominal samle reflects the geometry of the detector as best known at the time of these studies. Studies of the material of the inner detector in front of the calorimeters have been erformed using secondary hadronic interactions [5]. Additional information is obtained from studying hoton conversions [5] and the energy flow in minimum bias events [5]. 4.4 Simulated ile-u samles For the study of multile roton-roton interactions, two samles have been used, one for in-time and one for out-of-time ile-u. he first simulates additional roton-roton interactions er bunch crossing, while the second one also contains ile-u arising from bunches before or after the bunch where the event of interest was triggered (for more details see Section 5 and Section 8.). he bunch configuration of LHC (organised in bunch trains) is also simulated. he additional number of rimary vertices in the in-time (bunch-train) ile-u samle is.7 (.9) on average. 5 Data samle and event selection 5. Data taking eriod and LHC conditions Proton-roton collisions at a centre-of-mass energy of s = 7 ev, recorded from March to October are analysed. Only data with a fully functioning calorimeter and inner detector are used. he data set corresonds to an integrated luminosity of 8 b. Due to different data quality requirements the integrated luminosity can differ for the various selections used in the in situ technique analyses. Several distinct eriods of machine configuration and detector oeration were resent during the data taking. As the LHC commissioning rogressed, changes in the beam otics and roton bunch arameters resulted in changes in the number of ile-u interactions er bunch crossing. he sacing between the bunches was no less than 5 ns. Figure shows the evolution of the maximum of the distribution of the number of interactions (eak) derived from the online luminosity measurement and assuming an inelastic rotonroton scattering cross section of 7.5 mb [54]. he very first data were essentially devoid of multile rotonroton interactions until the otics of the accelerator beam (secifically β ) were changed in order to decrease the transverse size of the beam and increase the luminosity. his change alone he arameter β is the value of the β-function (the enveloe of all trajectories of the beam articles) at the collision oint and smaller values of β imly a smaller hysical size of the beams and thus a higher instantaneous luminosity.

9 8 ALAS collaboration: Jet measurement with the ALAS detector he γ- samle is selected using a hoton trigger [] that is fully efficient for hotons assing offline selections. he higher threshold for the hoton is 4 GeV and this trigger was not re-scaled; the lower threshold is GeV and this trigger was re-scaled at high luminosity. 5. Data quality assessment Fig. : he eak number of interactions er bunch crossing ( BX ) as measured online by the ALAS luminosity detectors [54]. raised the fraction of events with at least two observed interactions from less than % to between 8% and % (May-June ). A further increase in the number of interactions occurred when the number of rotons er bunch (b) was increased from aroximately 5 9 to.5 b. Since the number of roton-roton collisions er bunch crossing is roortional to the square of the bunch intensity, the fraction of events with ile-u increased to more than 5% for runs between June and Setember. Finally, further increasing the beam intensity slowly raised the average number of interactions er bunch crossing to more than three by the end of the roton-roton run in November. 5. Event selection Different triggers are used to select the data samles, in order to be maximally efficient over the entire -range of interest. he di samle is selected using the hardware-based calorimeter triggers [, 55], which are fully efficient for s with > 6 GeV. For lower a trigger based on the minimum bias trigger scintillators is used. he multi samle uses either the inclusive trigger or a trigger that requires at least two, three or more s with > GeV at the EM scale. hese triggers are fully efficient for s with > 8 GeV. Each event is required to have a rimary hard scattering vertex. A rimary vertex is required to have at least five tracks (N tracks ) with a transverse momentum of track > 5 MeV. he rimary vertex associated to the event of interest (hard scattering vertex) is the one with the highest associated transverse track momentum squared used in the vertex fit Σ( track ), where the sum runs over all tracks used in the vertex fit. his renders the contribution from fake vertices due to beam backgrounds to be negligible. he ALAS data quality (DQ) selection is based uon insection of a standard set of distributions that leads to a data quality assessment for each subdetector, usually segmented into barrel, forward and endca regions, as well as for the trigger and for each tye of reconstructed hysics object (s, electrons, muons, etc.). Each subsystem sets its own DQ flags, which are recorded in a conditions database. Each analysis alies DQ selection criteria, and defines a set of luminosity blocks (each corresonds to aroximately two minutes of data taking). he good luminosity blocks used are those not flagged for having issues affecting a relevant subdetector. Events with minimum bias and calorimeter triggers were required to belong to secific runs and run eriods in which the detector, trigger and reconstructed hysics objects have assed a data quality assessment and are deemed suitable for hysics analysis. he rimary systems of interest for this study are the electromagnetic and hadronic calorimeters, and the inner tracking detector for studies of the roerties of tracks associated with s. 6 Jet reconstruction In data and Monte Carlo simulation s are reconstructed using the anti-k t algorithm [7] with distance arameters R =.4 or R =.6 using the FASJE software [56]. he four-momentum recombination scheme is used. Jet finding is done in y-φ coordinates, while corrections and erformance studies are often done in η-φ coordinates. he reconstruction threshold is > 7 GeV. In the following, only anti-k t s with distance arameter R=.6 are discussed in detail. he results for s with R=.4 are similar, if not stated otherwise. 6. Reconstructed calorimeter s he inut to calorimeter s can be toological calorimeter clusters (too-clusters) [6,57] or calorimeter towers. Only tooclusters or towers with a ositive energy are considered as inut to finding. 6.. oological calorimeter clusters oological clusters are grous of calorimeter cells that are designed to follow the shower develoment taking advantage of the fine segmentation of the ALAS calorimeters. he toocluster formation algorithm starts from a seed cell, whose signalto-noise (S/N) ratio is above a threshold of S/N= 4. he noise

10 ALAS collaboration: Jet measurement with the ALAS detector 9 Loose Medium HEC sikes ( f HEC >.5 and f HECquality >.5) Loose or or E neg > 6 GeV f HEC > f HECquality Coherent f EM > 5 and f quality >.8 Loose or EM noise and η <.8 f EM > and f quality >.8 and η <.8 Non-collision t > 5 ns or Loose or background ( f EM <.5 and f ch <.5 and η < ) t > ns or ( f EM <.5 and η ) or ( f EM <.5 and f ch <. and η < ) or ( f max > 9 and η < ) or ( f EM > 5 and f ch <.5 and η < ) able : Selection criteria used to reject fake s and non-collision background. is estimated as the absolute value of the energy deosited in the calorimeter cell divided by the RMS of the energy distribution measured in events triggered at random bunch crossings. Cells neighbouring the seed (or the cluster being formed) that have a signal-to-noise ratio of at least S/N = are included iteratively. Finally, all calorimeter cells neighbouring the formed too-cluster are added. he too-cluster algorithm efficiently suresses the calorimeter noise. he too-cluster algorithm also includes a slitting ste in order to otimise the searation of showers from different close-by articles: All cells in a too-cluster are searched for local maxima in terms of energy content with a threshold of 5 MeV. his means that the selected calorimeter cell has to be more energetic than any of its neighbours. he local maxima are then used as seeds for a new iteration of toological clustering, which slits the original cluster into more too-clusters. A too-cluster is defined to have an energy equal to the energy sum of all the included calorimeter cells, zero mass and a reconstructed direction calculated from the weighted averages of the seudoraidities and azimuthal angles of the constituent cells. he weight used is the absolute cell energy and the ositions of the cells are relative to the nominal ALAS coordinate system. 6.. Calorimeter towers Calorimeter towers are static, η φ =.., grid elements built directly from calorimeter cells 4. ALAS uses two tyes of calorimeter towers: with and without noise suression. Calorimeter towers based on all calorimeter cells are called non-noise-suressed calorimeter towers in the following. Noise-suressed towers make use of the tooclusters algorithm, i.e. only calorimeter cells that are included in too-clusters are used. herefore, for a fixed geometrical area, noise-suressed towers have the same energy content as the too-clusters. Both tyes of calorimeter towers have an energy equal to the energy sum of all included calorimeter cells. he formed Lorentz four-momentum has zero mass. 4 For the few calorimeter cells that are larger than the η φ =.. (like in the last ile calorimeter layer and the HEC inner wheel) or have a secial geometry (like in the FCAL), rojective tower grid geometrical weights are defined that secify the fraction of calorimeter cell energy to be attributed to a articular calorimeter tower. 6. Reconstructed track s Jets built from charged article tracks originating from the rimary hard scattering vertex (track s) are used to define s that are insensitive to the effects of ile-u and rovide a stable reference to study close-by effects. racks with track >.5 GeV and η <.5 are selected. hey are required to have at least one (six) hit(s) in the Pixel (SC) detector. he transverse (d ) and longitudinal (z ) imact arameters of the tracks measured with resect to the rimary vertex are also required to be d <.5 mm and z sinθ <.5 mm, resectively. he track s must have at least two constituent tracks and track a total transverse momentum of > GeV. Since the tracking system has a coverage u to η =.5, the erformance studies of calorimeter s is carried out in the range η <.9 for R=.6 and η <. for R= Monte Carlo truth s and flavour association Monte Carlo simulation truth s are built from stable articles defined to have roer lifetimes longer than s excluding muons and neutrinos. For certain studies, s in the Monte Carlo simulation are additionally identified as s initiated by light or heavy quarks or by gluons based on the generator event record. he highest energy arton that oints to the truth 5 determines the flavour of the. Using this method, only a small fraction of the s (< % at low and less at high ) could not be assigned a artonic flavour. his definition is sufficient to study the flavour deendence of the resonse. Any theoretical ambiguities of flavour assignment do not need to be addressed in the context of a erformance study. 5 With R<.6 for s with R=.6 and R<.4 for s with R=.4, where R= ( η) +( φ).

11 ALAS collaboration: Jet measurement with the ALAS detector 7 Jet quality selection Jets at high transverse momenta roduced in roton-roton collisions must be distinguished from background s not originating from hard scattering events. he main backgrounds are the following:. Beam-gas events, where one roton of the beam collided with the residual gas within the beam ie.. Beam-halo events, for examle caused by interactions in the tertiary collimators in the beam-line far away from the ALAS detector.. Cosmic ray muons overlaing in-time with collision events. 4. Large calorimeter noise. he criteria to efficiently reject s arising from background are only alied to data. hey are discussed in the following sections. 7. Criteria to remove non-collision background 7.. Noise in the calorimeters wo tyes of calorimeter noise are addressed:. Soradic noise bursts in the hadronic endca calorimeter (HEC), where a single noisy calorimeter cell contributes almost all of the energy. Jets reconstructed from these roblematic cells are characterised by a large energy fraction in thehec calorimeter ( f HEC ) as well as a large fraction of the energy in calorimeter cells with oor signal shae quality 6 ( f HECquality ). Due to the caacitive couling between channels, the neighbouring calorimeter cells will have an aarent negative energy (E neg ).. Rare coherent noise in the electromagnetic calorimeter. Similarly, fake s arising from this source are characterised by a large electromagnetic energy fraction ( f EM ) 7, and a large fraction of calorimeter cells with oor signal shae quality ( f quality ). 7.. Cosmic rays or non-collision background Cosmic rays or non-collision backgrounds can induce events where the candidates are not in-time with the beam collision. A cut on the time (t ) is alied to reject these backgrounds. he time is reconstructed from the energy deosition in the calorimeter by weighting the reconstructed time of calorimeter cells forming the with the square of the cell energy. he calorimeter time is defined with resect to the event time recorded by the trigger. A cut on the f EM is alied to make sure that the has some energy deosited in the calorimeter layer closest to the interaction region as exected for a originating from the nominal interaction oint. 6 he signal shae quality is obtained by comaring the measured ulse from the calorimeter cell to the exected ulse shae. 7 he EM fraction is defined as the ratio of the energy deosited in the EM calorimeter to the total energy. Since a real is exected to have tracks, the f EM cut is alied together with a cut on the minimal charged fraction ( f ch ), defined as the ratio of the scalar sum of the of the tracks associated to the divided by the, for s within the tracking accetance. A cut on the maximum energy fraction in any single calorimeter layer ( f max ) is alied to further reject non-collision background. 7.. Jet quality selections wo quality selections are rovided:. A loose selection is designed with an efficiency above 99%, that can be used in most of the ALAS hysics analyses.. A medium selection is designed for analyses that select s at high transverse momentum, such as for crosssection measurements []. A tight quality selection has been develoed for the measurement of the quality selection efficiency described in Section 7., but is not used in hysics analyses, since the medium quality selection is sufficient for removing fake s. he quality selection criteria used to identify and reject fake s are listed in able. 7. Evaluation of the quality selection efficiency he criteria for the quality selection are otimised by studying samles with good and fake s classified by their amount of missing transverse momentum significance 8 :. Good s belong to events where the two leading s have > GeV, and are back-to-back ( φ j j>.6 radian) in the lane transverse to the beam, and with a small missing transverse momentum significance E miss / ΣE <.. Fake s belong to events with a high transverse momentum significance E miss / ΣE > and with a reconstructed back-to-back to the missing transverse momentum direction ( φ E miss j >.6 radian). As the quality selection criteria are only alied to data an efficiency correction for data is determined. his efficiency is measured using a tag-and-robe method in events with two s at high transverse momentum. he reference ( ref ) is required to ass the tightened version of the quality selections, and to be back-to-back and well-balanced with the robe ( robe ): ( robe ref /avg <.4),with avg =(robe + ref )/. () he quality selection criteria were then alied to the robe s, measuring the fraction of s assing as a function of η and. he resulting efficiencies for s with R =.6 for loose and medium selections alied to the robe s are shown in 8 he missing transverse momentum (E miss ) significance is defined as E miss / ΣE, where ΣE is the scalar sum of the transverse energies of all energy deosits in the calorimeter.

12 ALAS collaboration: Jet measurement with the ALAS detector Jet quality selection efficiency ALAS s = 7 ev, Data anti-k t R=.6 η <. Loose selection Medium selection (a) η <. Jet quality selection efficiency ALAS s = 7 ev, Data anti-k t R=.6. η <.8 Loose selection Medium selection (b). η <.8 Jet quality selection efficiency ALAS s = 7 ev, Data anti-k t R=.6.8 η <. Loose selection Medium selection (c).8 η <. Jet quality selection efficiency ALAS s = 7 ev, Data anti-k t R=.6. η <. Loose selection Medium selection (d). η <. Jet quality selection efficiency ALAS s = 7 ev, Data anti-k t R=.6. η <.8 Loose selection Medium selection (e). η <.8 Jet quality selection efficiency ALAS s = 7 ev, Data anti-k t R=.6.8 η <.6 Loose selection Medium selection (f).8 η <.6 Jet quality selection efficiency ALAS s = 7 ev, Data anti-k t R=.6.6 η < 4.4 Loose selection Medium selection (g).6 η <4.4 Fig. 4: Jet quality selection efficiency for anti-k t s with R=.6 measured with a tag-and-robe technique as a function of in bins of η, for loose and medium selection criteria (see able ). Only statistical uncertainties are shown. In (e), (f), (g) the loose and medium results overla.

13 ALAS collaboration: Jet measurement with the ALAS detector Figure 4. he tight selection of the reference was varied to study the systematic uncertainty. he loose selection criteria are close to % efficient. In the forward region the medium selection criteria are also close to fully efficient. In the central region they have an efficiency of 99% for > 5 GeV. For lower s of about 5 GeV an inefficiency of u to 4% is observed. 7. Summary of the quality selection Quality selections used to reject fake s with the ALAS detector have been develoed. Simle variables allow the removal of fake s due to soradic noise in the calorimeter or noncollision background at the analysis level, with an efficiency greater than 99% over a wide kinematic range. 8 Jet energy calibration in the EM+JES scheme he simle EM+JES calibration scheme alies corrections as a function of the energy and seudoraidity to s reconstructed at the electromagnetic scale. he additional energy due to multile roton-roton collisions within the same bunch crossing (ile-u) is corrected before the hadronic energy scale is restored, such that the derivation of the energy scale calibration is factorised and does not deend on the number of additional interactions measured. he EM+JES calibration scheme consists of three subsequent stes as outlined below and detailed in the following subsections:. Pile-u correction: he average additional energy due to additional roton-roton interactions is subtracted from the energy measured in the calorimeters using correction constants obtained from in situ measurements.. Vertex correction: he direction of the is corrected such that the originates from the rimary vertex of the interaction instead of the geometrical centre of the detector.. Jet energy and direction correction: he energy and direction as reconstructed in the calorimeters are corrected using constants derived from the comarison of the kinematic observables of reconstructed s and those from truth s in Monte Carlo simulation. 8. Pile-u correction 8.. Correction strategy he measured energy of reconstructed s can be affected by contributions that do not originate from the hard scattering event of interest, but are instead roduced by additional roton-roton collisions within the same bunch crossing. An offset correction for ile-u is derived from minimum bias data as a function of the number of reconstructed rimary vertices, N PV, the seudoraidity, η, and the bunch sacing. Constituent tower multilicity ALAS η 5 4 Fig. 5: Distribution of the number constituent calorimeter towers as a function of the seudoraidity for anti-k t s with R=.6 and > 7 GeV. he black dots indicate the average number of tower constituents. his offset correction alied to the transverse energy (E ) at the EM scale as the first ste of calibration can be written generically as: E corrected = E uncorrected O(η,N PV,τ bunch ), () where O(η,N PV,τ bunch ) corrects for the offset due to ileu. Due to the varying underlying article sectrum and the variation in the calorimeter geometry the offset is derived as a function of the seudoraidity. he amount of in-time ile-u is arameterised by N PV. he sacing between consecutive bunches, τ bunch, is considered, because it can imact the amount by which collisions in revious bunch crossings affect the energy measurement 9. he offset correction is roortional to the number of constituent towers in a as a measure of the area. For s built directly from dynamically-sized toological clusters, for which no clear geometric definition is available, a model is used that describes the average area of a in terms of the equivalent number of constituent towers. 8.. Constituent tower multilicity of s he multilicity of calorimeter towers in s deends on the internal comosition and on the resence of ile-u. he average tower multilicity can be measured in situ. 9 he deendence on τ bunch is exlicitly allowed for due to the ossibility of ile-u contributions from revious roton-roton bunch crossings for closely saced bunches. his will be an imortant consideration for the - LHC run as the number of bunches is increased and the sacing between consecutive bunches is reduced.

14 ALAS collaboration: Jet measurement with the ALAS detector [MeV] EM E 7 ALAS 6 Data 5 EM energy scale = N PV = N PV = N PV = 4 N PV EM E ALAS Data EM energy scale = N PV = N PV = N PV = 4 N PV ower offset: 4 = 5 N PV Jet offset: 4 = 5 N PV η tower η (a) ower offset (b) Jet offset Fig. 6: ower offset (a) and offset (b) at the EM scale as a function of the tower or seudoraidity in bins of the number of reconstructed rimary vertices. he offset is shown for anti-k t s with R=.6. Only statistical uncertainties are shown. hey are tyically smaller than the marker size. Figure 5 deicts the distribution of the constituent tower multilicity for s based on towers with > 7 GeV as a function of the seudoraidity. he average number of constituent towers is also indicated. his distribution is governed by the change in hysical size of calorimeter towers for a constant interval in seudoraidity, as well as by differences in the noise sectrum for the various calorimeters and samling regions. 8.. Pile-u offset for towers and s he calorimeter tower offset at the EM scale is derived by measuring the average tower transverse energy for all towers in events with N PV =,,...N and comaring directly to events with N PV = NPV ref = : O tower (η,n PV )= E tower (η,n PV ) E tower (η,npv ref ), (4) where the angled brackets denote a statistical average over all events. he average is comuted for events at each rimary vertex multilicity. For this measurement non-noise-suressed calorimeter towers are used (see Section 6..) in order to remain sensitive to low energy deositions that may not rise above noise threshold excet inside of a. he calorimeter tower offset is shown in Figure 6a for N PV 5. he tower offset can be extraolated to an EM scale offset using: O tower (η,n PV )=O tower (η,n PV ) A, (5) where A is the area that, for s built from calorimeter towers, can be estimated from the constituent tower multilicity, A = Ntowers. For s built from too-clusters, the mean equivalent constituent tower multilicity (A = N towers ) is used. he small deendencies of the constituent multilicity on and N PV are neglected in the correction, but incororated as systematic uncertainties (see Section 9.7). he offset for s with R=.6 is shown in Figure 6b rack based validation and offset correction rack s constructed from charged articles originating from the rimary hard-scattering vertex matched to the calorimeter s rovide a stable reference that can be used to measure the variation of the calorimeter E as a function of N PV. It is therefore ossible to validate the tower-based offset correction and also to directly estimate the ile-u energy contribution to s. As this method is only alicable to s within the inner detector accetance, it serves rimarily as a cross-check for the tower-based method discussed above. It can also be used, however, to derive a dedicated offset correction that can be alied to s at energy scales other than the electromagnetic energy he equivalent constituent tower multilicity for s based on too-clusters is calculated from the location of the calorimeter cells of the constituent too-clusters in the.

15 4 ALAS collaboration: Jet measurement with the ALAS detector,em Landau+Gauss fit (MPV) E ALAS Data ower s EM energy scale η <.9 4 Number of rimary vertices (N ) PV,EM Landau+Gauss fit (MPV) E ALAS Data oo-cluster s EM energy scale η <.9 track < < 5 GeV track 5 < < GeV track < < 5 GeV track 5 < < 4 GeV track 4 < < 45 GeV track 45 < < 5 GeV 4 Number of rimary vertices (N ) PV (a) ower s (b) oo-cluster s Fig. 7: ransverse energy E for calorimeter s associated to track s measured at the EM scale using a Landau-Gauss fit track as a function of the reconstructed vertex multilicity, N PV, in bins of. Calorimeter s are reconstructed at the EM scale with calorimeter towers (a) and too-clusters (b) as inuts. Systematic uncertainties are not shown. he statistical uncertainties from the fit results are smaller than the marker size. scale. Studying the variation of the offset correction as a function of can establish the systematic uncertainty of the track ile-u correction. he criterion to match a track to a calorimeter with R=.6 is R(, track) <.4, (6) where R= ( η) +( φ). he offset is calculated by measuring the average calorimeter E as a function of N PV and track the transverse momentum of the matched track, O track = E (N PV track ) E (Nref PV : track ). (7) he reference NPV ref = is used. Figure 7 shows the E as a function of N PV for several track bins in. Both tower and too-cluster s at the electromagnetic scale are used. he most robable value (MPV) of the calorimeter E is determined from a fit using a Landau distribution convolved with a Gaussian for each range of. track A consistent offset of nearly O =.5 GeV er vertex is found for η <.9. No systematic trend of the offset as a function of track is observed. Figure 8 resents the -based offset correction as a function of N PV derived with resect to NPV ref = for tower and too-cluster based using the EM and the EM+JES scale. As exected, the magnitude of the offset is higher after EM+JES calibration (see Figure 8c and Figure 8d), and the increase corresonds to the average energy correction (see Section 8.). 8. Jet origin correction Calorimeter s are reconstructed using the geometrical centre of the ALAS detector as reference to calculate the direction of s and their constituents (see Section 6). he fourmomentum is corrected for each event such that the direction of each too-cluster oints back to the rimary hard-scattering vertex. he kinematic observables of each too-cluster are recalculated using the vector from the rimary hard-scattering vertex to the too-cluster centroid as its direction. he raw four-momentum is thereafter redefined as the vector sum of the too-cluster four-momenta. he origin-corrected seudoraidity is called η origin. his correction imroves the angular resolution and results in a small imrovement (< %) in the resonse. he energy is unaffected. 8. Jet energy correction he final ste of the EM+JES calibration restores the reconstructed energy to the energy of the Monte Carlo truth. Since ile-u effects have already been corrected for, the Monte Carlo samles used to derive the calibration do not include multile roton-roton interactions.

16 ALAS collaboration: Jet measurement with the ALAS detector 5 Jet offset ALAS Data ower s EM energy scale η <.9 < 5 < < 5 < 4 < 45 < track track track track track track < 5 GeV < GeV < 5 GeV < 4 GeV < 45 GeV < 5 GeV Jet offset ALAS Data oo-cluster s EM energy scale η < Number of rimary vertices (N ) PV Number of rimary vertices (N ) PV (a) ower offset (EM scale) (b) oo-cluster offset (EM scale) Jet offset ALAS Data ower s EM+JES energy scale η <.9 4 Number of rimary vertices (N ) PV (c) ower offset (EM+JES scale) Jet offset ALAS Data oo-cluster s EM+JES energy scale η <.9 4 Number of rimary vertices (N ) PV (d) oo-cluster offset (EM+JES scale) track Fig. 8: Jet offset as a function of the number of rimary vertices for several ranges of values. he track offset is derived for calorimeter tower s at the EM scale (a), too-cluster s at the EM scale (b), calorimeter tower s at the EM+JES scale (c), and too-cluster s at the EM+JES scale (d). Only statistical uncertainties from the fit results are shown.

17 6 ALAS collaboration: Jet measurement with the ALAS detector Average JES correction ALAS simulation. η <.8. η <.8.6 η < 4.4 Jet resonse at EM scale ALAS simulation Barrel Barrel-Endca ransition Endca Endca-Forward ransition Forward. R =.6, EM+JES Anti-k t.5.4 R =.6, EM+JES Anti-k t E = GeV E = 6 GeV E = GeV E = 4 GeV E = GeV η det Fig. 9: Average energy scale correction as a function of the calibrated transverse momentum for three reresentative η- intervals obtained from the nominal Monte Carlo simulation samle. he correction is only shown over the accessible kinematic range. he calibration is derived using all isolated calorimeter s that have a matching isolated truth within R=.. Here, an isolated is defined as a having no other with > 7 GeV within R =.5R, where R is the distance arameter of the algorithm. A is defined to be isolated, if it is isolated with resect to the same tye, i.e. either a calorimeter or a truth. he final energy scale calibration is first arametrised as a function of uncalibrated energy and η. Here the detector seudoraidity is used rather than the origin-corrected η (used by default in hysics analyses), since it more directly corresond to a region of the calorimeter. Energy is used rather than, since the calorimeter resonds to energy, and the resonse curves can be directly comared to exectation and between η bins. he method to derive this calibration is detailed below. he EM-scale energy resonse R EM = E EM /E truth (8) for each air of calorimeter and truth s is measured in bins of the truth energy E truth and the calorimeter detector seudoraidity η det. For each (E truth,η det)-bin, the averaged resonse R EM is defined as the eak osition of a Gaussian fit to the E EM /E truth distribution. In the same (E truth,η det)-bin, in addition, the average energy resonse ( ) is derived E EM from the mean of the E EM distribution. For a given η det-bin k, the resonse calibration function F calib,k (E EM ) is obtained using a fit of the( E EM, R EM ) values for each E j j truth -bin j. Here, seudoraidity refers to the original reconstructed before the origin correction. Fig. : Average simulated resonse (R EM ) at the electromagnetic scale in bins of EM+JES calibrated energy and as a function of the detector seudoraidity η det. Also shown are the η-intervals used to evaluate the JES uncertainty (see able ). he inverse of the resonse shown in each bin is equal to the average energy scale correction. origin - η truth η ALAS simulation -.4 E = GeV E = 4 GeV E = 6 GeV E = GeV Anti-k t R =.6, EM+JES E = GeV η det Fig. : Difference between the seudoraidity calculated using an origin correction and the true seudoraidity in bins of the calorimeter energy calibrated with the EM+JES scheme as a function of the detector seudoraidity η det. he fitting function is arameterised as: F calib,k (E N max ( i, EM )= a i lneem) (9) i= where a i are free arameters, and N max is chosen between and 6 deending on the goodness of the fit. he final energy scale correction that relates the measured calorimeter energy to the true energy is then defined as /F calib (EEM calo ) in the following: E EM+JES = E EM F calib (E EM ), () η det

18 ALAS collaboration: Jet measurement with the ALAS detector 7 where F calib (E EM ) η det is the resonse calibration function for the relevant η det -bin k. he average energy scale correction /F calib,k (Ecalo EM) is shown as a function of calibrated transverse momentum for three η-intervals in Figure 9. In this and the following figures the correction is only shown over the accessible kinematic range, i.e. values for s above the kinematic limit are not shown. he calorimeter resonse R EM is shown for various energy- and η det -bins in Figure. he values of the energy correction factors range from about. at low energies in the central region to less than. for high energy s in the most forward region. 8.4 Jet seudoradity correction After the origin and energy corrections the origin-corrected η is further corrected for a bias due to oorly instrumented regions of the calorimeter. In these regions too-clusters are reconstructed with a lower energy with resect to better instrumented regions (see Figure ). his causes the direction to be biased towards the better instrumented calorimeter regions. he η-correction is derived as the average difference η = η truth η origin in (E truth,η det )-bins, and is arameterised as a function of the calibrated energy EEM+JES calo and the uncorrected η det. he correction is very small ( η <.) for most regions of the calorimeter but larger in the transition regions. he size of the bias is illustrated as a function of the detector seudoraidity η det and EM+JES calibrated energy in Figure. 9 Jet energy scale uncertainties for the EM+JES scheme he JES systematic uncertainty is derived combining information from the single hadron resonse measured in situ and single ion test-beam measurements, uncertainties on the amount of material of the ALAS detector, the descrition of the electronic noise, and the Monte Carlo modelling used in the event generation. Dedicated Monte Carlo simulation test samles are generated with different conditions with resect to the nominal Monte Carlo samle described in Section 4.. hese variations are exected to rovide an estimate of the systematic effects contributing to the JES uncertainty. he seudoraidity bins used for the estimate of the JES uncertainty divide the ALAS detector in the eight η-regions secified in able and Figure. he JES systematic uncertainty for all s with seudoraidity η >.8 is determined using the JES uncertainty for the central barrel region (. η <.8) as a baseline, with a contribution from the relative calibration of the s with resect to the central barrel region. his choice is motivated by the good knowledge of the detector geometry in the central region, and by the use of ion resonse measurements in the ALAS combined test-beam, which used a full slice of the ALAS barrel detector, for the estimate of the calorimeter resonse uncertainties. he region. η <.8 is the largest fully instrumented η region ALAS detector regions η <. Central Barrel. η <.8.8 η <. Barrel-Endca ransition. η <.. η <.8 Endca.8 η <. Endca-Forward ransition. η <.6.6 η <4.5 Forward able : Detector regions used for the JES uncertainty estimate. η region considered where combined test-beam results, used to estimate the calorimeter uncertainty, are available for the entire seudoraidity range. his section describes the sources of systematic uncertainties and their effect on the resonse of EM+JES calibrated s. In Section 9., the selection of s used to derive Monte Carlo based comonents of the JES systematic uncertainty is discussed. he contributions to the JES systematics due to the following effects are then described:. JES calibration method (Section 9.).. Calorimeter resonse (Section 9.).. Detector simulation (Section 9.4). 4. Physics model and arameters emloyed in the Monte Carlo event generator (Section 9.5). 5. Relative calibration for s with η >.8 (Section 9.6). 6. Additional roton-roton collisions (ile-u) (Section 9.7). Section 9.8 discusses how the final uncertainties are calculated. Additional uncertainties such as those for close-by s are mentioned in Section 9.9 and discussed in more detail in Section Jet resonse definition for the JES uncertainty evaluation he comonents of the JES uncertainty derived from Monte Carlo samles are obtained by studying the average calorimeter energy resonse of calibrated s. he average energy or resonse, defined as R = E /E truth or R( = ) /truth, () is obtained as the eak osition from a Gaussian fit to the distribution of the ratio of the kinematic quantities for reconstructed and truth s by matching isolated calorimeter s to Monte Carlo truth s as described in Section 8., but without the isolation cut for truth s. his is done searately for the nominal and each of the alternative Monte Carlo samles. Only MC truth s with truth > 5 GeV, and calorimeter s with > 7 GeV after calibration, are considered. he calibrated he isolation cut for truth s on the average resonse has a negligible imact on the average resonse given that truth s are matched to isolated reconstructed s.

19 8 ALAS collaboration: Jet measurement with the ALAS detector resonse R is studied in bins of the truth transverse momentum truth. For each truth -bin, an associated calibrated value is calculated by multilying the bin centre with the average resonse. he shifts between the Monte Carlo truth level truth bin centres and the reconstructed bin centres are negligible with resect to the chosen bin widths. Hence the average resonse can be obtained to a good aroximation as a function of. 9. Uncertainty in the JES calibration After the s in the nominal Monte Carlo simulation samle are calibrated (see Section 8), the energy and resonse still show slight deviations from unity at low (non-closure). his can be seen in Figure, showing the resonse for and energy as a function of for the nominal Monte Carlo samle in the barrel (a) and endca (b) and the most forward (c) regions for anti-k t s with R=.6. Any deviation from unity in the energy or resonse after the alication of the JES to the nominal Monte Carlo samle imlies that the kinematic observables of the calibrated calorimeter are not restored to that of the corresonding truth (non-closure). Besides aroximations made when deriving the calibration (fit quality, arametrisation of calibration curve), the non-closure is due to the alication of the same correction factor for energy and transverse momentum. Closure can therefore only be achieved if the reconstructed mass is close to the true mass. If this is not the case, such as for low s, restoring only the energy and seudoraidity will lead to a bias in the calibration. he non-closure is also affected by resolution and by details how the Monte Carlo samles are roduced in order to cover the large kinematic range in transverse momentum. he systematic uncertainty due to the non-closure of the nominal JES calibration is taken as the larger deviation of the resonse in either energy or from unity. In the barrel region (. η <.8) this contribution amounts to about % at low and less than % for > GeV. In the endca and forward regions, the closure is less than % for > GeV, and the energy resonse is within % for s with transverse momentum above GeV. he deviation of the resonse from unity after calibration is taken as a source of systematic uncertainty. For hysics analysis the non-closure uncertainty only needs to be considered when an absolute energy or transverse momentum is needed. For analyses where only the descrition of the data by the Monte Carlo simulation is imortant, this uncertainty does not need to be considered. 9. Uncertainty on the calorimeter resonse Average resonse Average resonse Average resonse Anti-k t R=.6, EM+JES,. η <.8 ALAS simulation 4 5 PYHIA MC (nominal), E resonse PYHIA MC (nominal), (a). η <.8 Anti-k t R=.6, EM+JES,. η <.8 ALAS simulation resonse PYHIA MC (nominal), E resonse PYHIA MC (nominal), (b). η <.8 Anti-k t R=.6, EM+JES,.6 η < 4.5 ALAS simulation PYHIA MC, E resonse PYHIA MC (nominal), (c).6 η <4.5 resonse resonse Fig. : Average simulated resonse (oen squares) after the EM+JES calibration and energy resonse (full circles) as a function of for the nominal Monte Carlo samle for s in the central (a), endca (b) and most forward (c) calorimeter regions. Systematic uncertainties are not shown. Statistical uncertainties are smaller than the marker size. he resonse and corresonding uncertainties for single articles interacting in the ALAS calorimeters can be used to derive the energy scale uncertainty in the central calorimeter region as detailed in Ref. [49, 58].

20 ALAS collaboration: Jet measurement with the ALAS detector 9 > truth /E <E..8.6 Anti-k t R=.6, EM+JES,. η <.8 PYHIA MC (nominal) Additional Dead Material Additional Dead Material (ID only) > truth /E <E..8.6 Anti-k t R=.6, EM+JES,. η <.8 PYHIA MC ALPGEN + HERWIG + JIMMY PYHIA PERUGIA ALAS simulation 4 (a) Energy resonse 6 4 ALAS simulation 4 (a) Energy resonse > truth / <..8.6 Anti-k t R=.6, EM+JES,. η <.8 PYHIA MC (nominal) Additional Dead Material Additional Dead Material (ID only) > truth / <..8.6 Anti-k t R=.6, EM+JES,. η <.8 PYHIA MC ALPGEN + HERWIG + JIMMY PYHIA PERUGIA ALAS simulation ALAS simulation 4 (b) ransverse momentum resonse (b) ransverse momentum resonse Fig. : Average simulated resonse in energy (a) and in (b) as a function of in the central region (. η <.8) in the case of additional dead material in the inner detector (full triangles) and in both the inner detector and the calorimeters (oen squares). he resonse within the nominal Monte Carlo samle is shown for comarison (full circles). Only statistical uncertainties are shown. In the ALAS simulation infrastructure the true calorimeter energy deosits in each calorimeter cell can be traced to the articles generated in the collision. he uncertainty in the calorimeter resonse to s can then be obtained from the resonse uncertainty in the individual articles constituting the. he in situ measurement of the single article resonse detailed in Ref. [49] significantly reduces the uncertainty due to the limited knowledge of the exact detector geometry, in articular that due to the resence of additional dead material, and the modelling of the exact way articles interact in the detector. he following single article resonse measurements are used:. he single hadron energy measured in a cone around an isolated track with resect to the track momentum (E/) in the momentum range from.5 track < GeV.. he ion resonse measurements erformed in the 4 combined test-beam, where a full slice of the ALAS de- Fig. 4: Average simulated resonse in energy (a) and in (b) as a function of in the central region (. η <.8) for ALPGEN+HERWIG+JIMMY (oen squares) and PYHIA with the PERUGIA tune (full triangles). he resonse of the nominal Monte Carlo simulation samle is shown for comarison (full circles). Only statistical uncertainties are shown. tector was exosed to ion beams with momenta between GeV and 5 GeV [45]. Uncertainties for charged hadrons are estimated from these measurements as detailed in Ref. [49]. Additional uncertainties are related to:. he calorimeter accetance for low articles that do not reach the calorimeter or are not reconstructed in a toocluster due to the noise thresholds.. Calorimeter resonse to articles with > 4 GeV for which the uncertainty is conservatively estimated as %, to account for ossible calorimeter non-linearities and longitudinal leakage.. he baseline absolute electromagnetic scale for the hadronic and electromagnetic calorimeters for articles in the kinematic range not measured in situ. 4. he calorimeter resonse to neutral hadrons is estimated by comaring various models in GEAN4. An uncertainty of % for articles with an energy E < GeV and 5% for higher energies is obtained.

21 ALAS collaboration: Jet measurement with the ALAS detector At high transverse momentum, the dominant contribution to the calorimeter resonse uncertainties is due to articles with momenta covered by the test-beam. In the seudoraidity range η <.8 the shift of the relative energy scale exected from the single hadron resonse measurements in the test-beam is u to %, and the uncertainty on the shift is from % to %. he total enveloe (the shift added linearly to the uncertainty) of about.5 4%, deending on the transverse momentum, is taken as the relative JES calorimeter uncertainty. he calorimeter uncertainty is shown in Figure. 9.4 Uncertainties due to the detector simulation 9.4. Calorimeter cell noise thresholds As described in Section 6.., too-clusters are constructed based on the signal-to-noise ratio of calorimeter cells, where the noise is defined as the RMS of the measured cell energy distribution in events with no energy deositions from collision events. Discreancies between the simulated noise and the real noise in data can lead to differences in the cluster shaes and to the resence of fake too-clusters. For data, the noise can change over time, while the noise RMS used in the simulation is fixed at the time of the roduction of the simulated data sets. hese effects can lead to biases in the reconstruction and calibration, if the electronic noise injected in the Monte Carlo simulation does not reflect that data. he effect of the calorimeter cell noise mis-modelling on the resonse is estimated by reconstructing too-clusters, and thereafter s, in Monte Carlo using the noise RMS measured from data. he actual energy and noise simulated in the Monte Carlo are left unchanged, but the values of the thresholds used to include a given calorimeter cell in a too-cluster are shifted according to the cell noise RMS measured in data. he resonse for s reconstructed with the modified noise thresholds are comared with the resonse for s reconstructed in exactly the same samle using the default Monte Carlo noise thresholds. o further understand the effect of the noise thresholds on the resonse, the noise thresholds were shifted. An increase of each calorimeter cell threshold by 7% in the Monte Carlo simulation is found to give a similar shift in the resonse as using the noise RMS from data. Raising and lowering the cell thresholds by 7% shows that the effect on the resonse from varying the cell noise thresholds is symmetric. his allows the use of the calorimeter cell noise thresholds derived from data as a reresentative samle to determine the energy scale uncertainty and covers the cases when the data have either more or less noise than the simulation. he maximal observed change in resonse is used to estimate the uncertainty on the energy measurement due to the calorimeter cell noise modelling. It is found to be below % for the whole seudoraidity range, and negligible for s with transverse momenta above 45 GeV. he uncertainties assigned to s with transverse momenta below 45 GeV are: ime-deendent noise changes for single cells in data are accounted for using regular measurements. % and % for < GeV for anti-k t s with R=.4 and R=.6 s, resectively, % for < 45 GeV for both R values Additional detector material he energy scale is affected by ossible deviations in the material descrition as the energy scale calibration has been derived to restore the energy lost assuming a geometry as simulated in the nominal Monte Carlo samle. Simulated detector geometries that include systematic variations of the amount of material have been designed using test-beam measurements [], in addition to 9 GeV and 7 ev data [5, 5, 59]. he ossible additional material amount is estimated from these in situ measurements and the a riori knowledge of the detector construction. Secific Monte Carlo simulation samles have been roduced using these distorted geometries. In the case of uncertainties derived with in situ techniques, such as those coming from the single hadron resonse measurements detailed in Section 9., most of the effects on the resonse due to additional dead material do not aly, because in situ measurements do not rely on any simulation where the material could be misreresented. However, the quality criteria of the track selection for the single hadron resonse measurement effectively only allow articles that have not interacted in the Pixel and SC layers of the inner detector to be included in the measurement. herefore the effect of dead material in these inner detector layers on the resonse needs to be taken into account for articles in the momentum range of the single hadron resonse measurement. his is achieved using a secific Monte Carlo samle where the amount of material is systematically varied by adding 5% of material to the existing inner detector services [9]. he resonse in the two cases is shown in Figure. Electrons, hotons, and hadrons with momenta > GeV are not included in the single hadron resonse measurements and therefore there is no estimate based on in situ techniques for the effect of any additional material in front of the calorimeters. his uncertainty is estimated using a dedicated Monte Carlo simulation samle where the overall detector material is systematically varied within the current uncertainties [9] on the detector geometry. he overall changes in the detector geometry include:. he increase in the inner detector material mentioned above.. An extra. radiation length (X ) in the cryostat in front of the barrel of the electromagnetic calorimeter ( η <.5).. An extra.5 X between the resamler and the first layer of the electromagnetic calorimeter. 4. An extra. X in the cryostat after the barrel of the electromagnetic calorimeter. 5. Extra material in the barrel-endca transition region in the electromagnetic calorimeter (.7 < η <.5). he uncertainty contribution due to the overall additional detector material is estimated by comaring the EM+JES resonse in the nominal Monte Carlo simulation samle with the resonse in a Monte Carlo simulation samle with a distorted geometry (see Figure ), and scaled by the average energy fraction of electrons, hotons and high transverse momentum hadrons within a as a function of.

22 ALAS collaboration: Jet measurement with the ALAS detector 9.5 Uncertainties due to the event modelling in Monte Carlo generators he contributions to the JES uncertainty from the modelling of the fragmentation, the underlying event and other choices in the event modelling of the Monte Carlo event generator are obtained from samles based on ALPGEN+HERWIG+JIMMY and the PYHIA PERUGIA tune discussed in Section 4. By comaring the baseline PYHIA Monte Carlo samle to the PYHIA PERUGIA tune, the effects of soft hysics modelling are tested. he PERUGIA tune rovides, in articular, a better descrition of the internal structure recently measured with ALAS []. he ALPGEN Monte Carlo uses different theoretical models for all stes of the event generation and therefore gives a reasonable estimate of the systematic variations. However, the ossible comensation of modelling effects that shift the resonse in oosite directions cannot be excluded. Figure 4 shows the calibrated kinematic resonse for the two Monte Carlo generators and tunes used to estimate the effect of the Monte Carlo theoretical model on the energy scale uncertainty. he kinematic resonse for the nominal samle is shown for comarison. he ratio of the nominal resonse to that for each of the two samles is used to estimate the systematic uncertainty to the energy scale, and the rocedure is further detailed in Section In situ intercalibration using events with di toologies he resonse of the ALAS calorimeters to s deends on the direction, due to the different calorimeter technology and to the varying amounts of dead material in front of the calorimeters. A calibration is therefore needed to ensure a uniform calorimeter resonse to s. his can be achieved by alying correction factors derived from Monte Carlo simulations. Such corrections need to be validated in situ given the non-comensating nature of the calorimeters in conjunction with the comlex calorimeter geometry and material distribution. he relative calorimeter resonse and its uncertainty is studied by comaring the transverse momenta of a well-calibrated central and a in the forward region in events with only two s at high transverse momenta (dis). Such techniques have been alied in revious hadron collider exeriments [6, 6] Intercalibration method using a fixed central reference region he traditional aroach for η-intercalibration with di events is to use a fixed central region of the calorimeters as the reference region. he relative calorimeter resonse to s in other calorimeter regions is then quantified by the balance between the reference and the robe, exloiting the fact that these s are exected to have equal due to transverse momentum conservation. he balance can be characterised by the asymmetry A, defined as A= robe avg ref, () with avg =(robe + ref )/. he reference region is chosen as the central region of the barrel: η <.8. If both s fall into the reference region, each is used, in turn, as the reference. As a consequence, the average asymmetry in the reference region will be zero by construction. he asymmetry is then used to measure an η-intercalibration factor c for the robe, or its resonse relative to the reference /c, using the relation robe ref = +A = /c. () A he asymmetry distribution is calculated in bins of η det and avg : he bins are labeled i for each robe η det and k for each avg -bin. Intercalibration factors are calculated for each bin according to Equation (): c ik = A ik + A ik, (4) where the A ik is the mean value of the asymmetry distribution in each bin. he uncertainty on A ik is taken to be the RMS/ N of each distribution, where N is the number of events er bin Intercalibration using the matrix method A disadvantage with the method outlined above is that all events are required to have a in the central reference region. his results in a significant loss of event statistics, esecially in the forward region, where the di cross section dros steely as the raidity interval between the s increases. In order to use the full event statistics, the default method can be extended by relacing the robe and reference s by left and right s defined as η left < η right. Equations () and () then become: A= left right avg and R lr = left right = cright c left = +A A, (5) where the term R denotes the ratio of the resonses, and c left and c right are the η-intercalibration factors for the left and right s, resectively. In this aroach there is a resonse ratio distribution, R i jk, whose average value R i jk is evaluated for each η left -bin i, η right -bin j and avg -bin k. he relative correction factor c ik for a given η-bin i and for a fixed avg -bin k, is obtained by minimising a matrix of linear equations: S(c k,...,c Nk )= ( N j= j i= ( ) c ik Ri jk c jk R i jk ) + X(c ik), (6)

23 ALAS collaboration: Jet measurement with the ALAS detector where N denotes the number of η-bins, R i jk is the statistical uncertainty of R i jk and the function X(cik ) is used to quadratically suress deviations from unity of the average corrections 4. Note that if the resonse does not vary with η, then the relative resonse will be unity for each (η left,η right )- bin combination (see Equation 5). A erfect minimization S = is achieved when all correction factors equal unity. he minimisation of Equation 6 is done searately for each avg -bin k, and the resulting calibration factors c ik (for each η-bin i) are scaled such that the average calibration factor in the reference region η <.8 equals unity Selection of di events Events are retained if there were at least two s above the reconstruction threshold of > 7 GeV. he event is rejected if either of the two leading s did not satisfy the standard selection criteria (see Section 7). Events are required to satisfy a secific logic using one central and one forward trigger, which select events based on activity in the central ( η <.) and forward ( η >.) trigger regions, resectively []. he requirements are chosen such that the trigger efficiency, for a secific region of avg, was greater than 99% and aroximately flat as a function of the seudoraidity of the robe. o cover the region avg < 45 GeV, events triggered by the minimum bias trigger scintillators were used. o enhance events which have only two s at high, the following selection criteria are alied; avg > GeV, φ(j,j )>.6 rad, (7) (j )<max(.5 avg,7 GeV), (8) where j i denotes the i th highest in the event and φ(j,j ) is the azimuthal angle between the two leading s. he lowest avg -bins are likely to suffer from biases. At very low avg, it is exected that this technique may not measure accurately the relative resonse to s, because the assumtion of di balance at hadron level may start to fail. First, there are residual low- effects since the selection criterion on the third, which is used to suress the unbalancing effects of soft QCD radiation, is not as efficient due to the reconstruction threshold of 7 GeV. Second, the reconstruction efficiency is worse for low- s Comarison of intercalibration methods he relative resonse obtained with the matrix method is comared to the relative resonse obtained using the method with a fixed reference region. Figure 5 shows the resonse relative to central s (/c) for two avg -bins, avg < ( 4 X(c ik ) = K Nbins N bins i= c ik ) is defined with K being a constant and N bins being the number of η-bins (number of indices i). his term revents the minimisation from choosing the trivial solution: all c ik equal to zero. he value of the constant K does not imact the solution as long as it is sufficiently large (K 6 ). Relative resonse Ratio Relative resonse Ratio ALAS Data avg < 4 GeV R=.6, EM+JES Anti-k t Fixed central reference region method Matrix method η det ALAS Data 6 avg (a) avg < 8 GeV < 4 GeV R=.6, EM+JES Anti-k t Fixed central reference region method Matrix method η det (b) 6 avg < 8 GeV Fig. 5: Relative resonse of anti-k t s with R=.6 calibrated with the EM+JES scheme, /c, as a function of the seudoraidity measured using the matrix and fixed central reference region η-intercalibration methods. Results are resented for two bins of avg : avg < 4 GeV measured in minimum bias data (a), and 6 avg < 8 GeV measured in data collected using triggers (b). he lower art of the figures shows the ratio of the two methods. he central reference region is. η <.6. Only statistical uncertainties are shown. 4 GeV and 6 avg < 8 GeV. hese results are obtained for a reference region. η <.6 and therefore not directly comarable to the results discussed below where. η <.8 is used. he resonse observed using the fixed reference region method is comatible with those obtained using the matrix method 5. hese results are reresentative of all the hase sace regions studied in this analysis and the matrix method is therefore 5 As discussed in Section 9.6., even for an ideal detector the asymmetry, and hence the relative resonse, is not exected to be exactly flat due to the effects of soft QCD radiation and other soft article activities.

24 ALAS collaboration: Jet measurement with the ALAS detector Relative resonse MC / Data ALAS avg < GeV Data, PYHIA MC HERWIG++ s = 7 ev R=.6, EM+JES Anti-k t PYHIA PERUGIA η det (a) avg < GeV Relative resonse MC / Data ALAS avg < 45 GeV Data, PYHIA MC HERWIG++ s = 7 ev R=.6, EM+JES Anti-k t PYHIA PERUGIA ALPGEN η det (b) avg < 45 GeV Relative resonse MC / Data ALAS 6 avg < 8 GeV Data, PYHIA MC HERWIG++ s = 7 ev R=.6, EM+JES Anti-k t PYHIA PERUGIA ALPGEN η det (c) 6 avg < 8 GeV Relative resonse MC / Data ALAS 8 avg < GeV Data, PYHIA MC HERWIG++ s = 7 ev R=.6, EM+JES Anti-k t PYHIA PERUGIA ALPGEN η det (d) 8 avg < GeV Fig. 6: Relative resonse, /c, of anti-k t s with R=.6 as a function of the seudoraidity measured using the matrix η-intercalibration method in bins of the average of the two leading s (a) avg < GeV, (b) avg < 45 GeV, (c) 6 avg < 8 GeV and 8 avg < GeV. he lower art of each figure shows the ratio of Monte Carlo simulation to data. Only statistical uncertainties are shown. used to give the final uncertainty on the in situ η-intercalibration due to its higher statistical recision Comarison of data with Monte Carlo simulation Figure 6 shows the relative resonse obtained with the matrix method as a function of the seudoraidity for data and Monte Carlo simulations in four avg regions. he resonse in data is reasonably well reroduced by the Monte Carlo simulations for > 6 GeV, with the Monte Carlo simulation and data agreeing tyically better than % in the central region ( η <.8) and 5 % (deending on avg ) in the forward region ( η >.8). At lower values of, the data do not agree as well with the Monte Carlo simulations and the Monte Carlo simulations themselves show a large sread around the data. For avg < GeV, the Monte Carlo simulation deviates from the data by about % for η >.8, with the different Monte Carlo simulations redicting both higher and lower relative resonses than that observed in the data. he main differences, due to residual low- effects (see Section 9.6.), occur between PYHIA with the MC or the PERUGIA tune on one side and ALPGEN/HERWIG++ on the other. he differences therefore aarently reflect a difference in hysics modelling between the event generators. Figure 7 shows the relative resonse as a function of avg. he distributions are shown for s in the region. η <. and also for those in the region.6 η < 4.5. Again, the resonse is reasonably well described by the Monte Carlo simulation for all calorimeter regions at high and the more central region at low.

25 4 ALAS collaboration: Jet measurement with the ALAS detector Relative resonse MC / Data.. Data, PYHIA MC HERWIG++ s = 7 ev ALPGEN PYHIA PERUGIA ALAS R=.6, EM+JES Anti-k t Minimum. η <. Jet trigger.8 bias trigger avg (a). η <. Relative resonse MC / Data.. Data, PYHIA MC HERWIG++ s = 7 ev ALPGEN PYHIA PERUGIA ALAS R=.6, EM+JES Anti-k t Minimum.6 η < 4.5 Jet trigger.8 bias trigger avg (b).6 η <4.5 Fig. 7: Relative resonse, /c, of anti-k t s with R =.6 as a function of avg found using the matrix η-intercalibration method for (a). η <. and (b).6 η <4.5. For avg < 45 GeV, the data are collected using the minimum bias trigger stream. For avg > 45 GeV, the data are collected using the calorimeter trigger stream. he lower art of each figure shows the ratio of Monte Carlo simulation to data. Only statistical uncertainties are shown otal uncertainties in the forward region he Monte Carlo simulation redictions for the relative resonse diverge at low values of avg. he data themselves lie between the different redictions. he uncertainty on the relative resonse must reflect this disagreement because there is no a riori reason to believe one theoretical rediction over another. he uncertainty on the relative resonse is taken to be the RMS deviation of the Monte Carlo redictions from the data. At high, where the sread of Monte Carlo simulation redictions is small, the uncertainty mainly reflects the true difference between the resonse in data and simulation. At low and large η, the uncertainty mainly reflects the hysics modelling uncertainty, although the detector-based differences between data and simulation are also accounted for. Other uncertainty sources, such as trigger selection or the QCD radiation suression using the third, are either negligible, or included in the total uncertainty assigned from the sread of Monte Carlo redictions around the data. Figure 8 shows the uncertainty in the resonse, relative to s in the central region η <.8, as a function of the and η. he JES uncertainty, determined in the central detector region using the single article resonse and systematic variations of the Monte Carlo simulations, is transferred to the forward regions using the results from the di balance. hese uncertainties are included in the final uncertainty as follows:. he total JES uncertainty in the central region. η <.8 is ket as a baseline.. he uncertainty from the relative intercalibration is taken as the RMS deviation of the MC redictions from the data and is added in quadrature to the baseline uncertainty. he measurements are erformed for transverse momenta in the range avg < GeV. he uncertainty for s with > GeV is taken as the uncertainty of the last available -bin 6. he uncertainties are evaluated searately for s reconstructed with distance arameters R=.4 and R=.6, and are in general found to be slightly larger for R =.4. Figure 9 shows the relative resonse, and the associated intercalibration uncertainty calculated as detailed above, as a function of η for two reresentative avg -bins. 9.7 Uncertainties due to multile roton-roton collisions he offset to the transverse energy due to ile-u interactions can be measured at the EM scale from the average energy in calorimeter towers in minimum bias events. he uncertainty in the ile-u corrections can be obtained by varying certain analysis choices and by studying the resonse with resect to the transverse momentum of track s as a function of the number of rimary vertices ower-based offset closure test using track s he systematic uncertainty in the offset correction can be evaluated using track s. Figure 8 shows the variation of the track offset among the various ranges of. he result indicates a systematic uncertainty on the correction of aroximately δ(o EM track )< MeV er additional vertex at the EM scale and δ(o EM+JES track ) < MeV er additional vertex at the EM+JES scale. Since the ile-u offset was about 5 MeV 6 his is justified by the decrease of the intercalibration uncertainty with, but cannot comletely exclude the resence of calorimeter non-linearities for energies above those used for the intercalibration.

26 ALAS collaboration: Jet measurement with the ALAS detector 5 Fractional uncertainty from di balance.4 ALAS Data.8 η < η <.. η <.8.8 η <.6.6 η < 4.5 R=.6, EM+JES Anti-k t (a) ransverse momentum Fractional uncertainty from di balance.4 avg < GeV avg avg avg avg < 45 GeV < 6 GeV < 8 GeV < GeV R=.6, EM+JES Anti-k t ALAS Data (b) Pseudoraidity η det Fig. 8: Fractional resonse uncertainty for anti-k t s with R=.6 calibrated with the EM+JES scheme as obtained from the di balance in situ technique as a function of for various η -regions of the calorimeter (a) and as a function of η in various bins (b). Relative resonse MC / Data.. ALAS avg Data, < 45 GeV PYHIA MC s = 7 ev PYHIA PERUGIA R=.6, EM+JES Anti-k t.8 HERWIG++ ALPGEN Intercalibration uncertainty η det (a) avg < 45 GeV Relative resonse MC / Data.. ALAS 8 avg Data, < GeV PYHIA MC s = 7 ev PYHIA PERUGIA R=.6, EM+JES Anti-k t.8 HERWIG++ ALPGEN Intercalibration uncertainty η det (b) 8 avg < GeV Fig. 9: Average resonse for anti-k t s with R =.6 calibrated with the EM+JES scheme measured relative to a central reference within η <.8 in data and various Monte Carlo generator samles as a function of η for avg in the ranges 45 GeV (a) and 8 GeV (b). he resulting systematic uncertainty comonent is shown as a shaded band around the data oints. he errors bars on the data oints only show the statistical uncertainties. Systematic ower-based offset Jet-based offset Comments rigger selection 6% 6% MBS vs Jet triggers ower multilicity variation % Ntowers vs track and N PV track variation % % Variation of MeV/vertex otal (quadrature sum) 6% 4% Assumes uncorrelated errors Result from closure test % 5% Determined from average able : Summary of systematic uncertainties associated with the offset correction for both the tower-based offset alied -by to tower s and the -level offset alied to too-cluster s. he uncertainty is exressed as a ercentage of the average offset correction, shown in able 4.

27 6 ALAS collaboration: Jet measurement with the ALAS detector Jet offset ALAS Data ower s Corrected EM energy scale ower-based offset correction η <.9 Jet offset ALAS Data ower s Corrected EM energy scale Jet-based offset correction η < Number of rimary vertices (N ) PV Number of rimary vertices (N ) PV (a) ower s (tower-based correction) (b) ower s (-based correction) Jet offset ALAS Data oo-cluster s Corrected EM energy scale Jet-based offset correction η <.9 4 Number of rimary vertices (N ) PV (c) oo-cluster s (-based correction) < 5 < < 5 < 4 < 45 < track track track track track track < 5 GeV < GeV < 5 GeV < 4 GeV < 45 GeV < 5 GeV Fig. : Jet residual offset measured at the EM scale after ile-u correction using the most robable value E obtained from a track fit to a Landau+Gauss distribution for various bins in track transverse momentum ( ) as a function of the rimary vertex multilicity: tower s corrected with tower-based offset correction (using the actual number constituent towers) (a), tower s corrected with the -based offset correction (using the average number of constituent towers) (b) and too-cluster s corrected with the -based offset correction (using the average number of equivalent constituent towers) (c). he axis ranges are identical to Figure 8 for ease of comarison. he offset is given for anti-k t s at the EM scale with R =.6. Only the statistical uncertainties of the fit results are shown.

28 ALAS collaboration: Jet measurement with the ALAS detector 7 ower s [GeV/vertex] oo-cluster s [GeV/vertex] rack Before After Before After - 5 GeV.55 ±..6 ±..5 ±. ±. 5 - GeV.47 ±.. ±..47 ±..6 ±. - 5 GeV.49 ±.. ±..47 ±..7 ±. 5-4 GeV.4 ±..8 ±..4 ±.. ± GeV.5 ±.5. ±.5.48 ±.5.8 ± GeV.4 ±.6.7 ±.6.4 ±.6. ±.6 Average.48 ±.. ±..46 ±..6 ±. able 4: Variation of the calorimeter E with ile-u for several bins in track. Sloes are given in GeV/vertex at the electromagnetic scale for each rimary vertex from additional roton-roton collisions in the event, and reresent the sloe of the offset before and after the tower-based offset correction. ower-based corrections are alied to tower s and -based corrections are alied to too-cluster s. he reorted uncertainties are urely statistical. Relative ile-u uncertainty R=.6, EM+JES, NPV = Anti-k t. η <.8. η <.8.6 η <4.5 ALAS 4 Fig. : Relative JES uncertainty from ile-u for anti-k t s with R =.6 in the case of two measured rimary vertices, N PV =, for central (. η <.8, full circles), endca (. η <.8, oen squares) and forward (.6 η < 4.5, full triangles) s as a function of. before correction, even with this conservative estimate the alication of the offset correction reresents an imrovement of a factor of five obtained over the systematic bias associated with ile-u effects on the calorimeter transverse momentum. he full offset correction shows reasonable closure when using the actual constituent tower multilicity directly (towerbased) and a slight under-correction using the average constituent multilicity in the (-based). Figure a shows the tower-based correction alied to tower s at the EM scale as a function of the reconstructed vertex multilicity. he towerbased correction exhibits a closure consistent with zero sloe in E as a function of N PV. Figure b and Figure c show the -based correction alied to both tower s and toocluster s, resectively. he use of the -based offset correction slightly under-corrects for the effect of ile-u for s constructed from both towers and too-clusters. he imlication of this observation is two-fold:. here is no significant difference in the sensitivity of toocluster s to ile-u as comared to tower s.. here is a systematic underestimation of the average tower multilicity in s due to the effect of ile-u or due to differences in the transverse energy distribution in the derivation and the validation of the ile-u correction Jet offset correction uncertainties he contributions to the offset correction uncertainty are estimated from studies that account for:. he effect of variations of the trigger selection on the measured non-noise-suressed tower energy distribution that is inut to the offset correction.. he variation with and N PV of the tower multilicity in s based on too-clusters 7.. he variation of the offset correction derived from track s as a function of the number of rimary vertices for various values of track. 4. he non-closure of the tower-based offset correction as evaluated by the deendence of the corrected calorimeter energy for calorimeter s matched to track s as a function of the number of rimary vertices. he JES uncertainty is estimated by adding all uncertainties in quadrature, including the one from the non-closure of the correction. he track method can be used only u to η =.9, if a full coverage of the area by the tracking accetance is needed. Beyond η =.9, the di balance method detailed in Section 9.6 is used. his aroach comares the relative resonse in events with only one reconstructed vertex with the resonse measured in events with several reconstructed vertices. he di balance method yields uncertainties similar to those intrinsic to the method also in the case of η <.9. Each source of systematic uncertainty is summarised in able and the resulting effects exressed as a ercentage of the average offset correction, shown in able 4. For s based on towers the total systematic uncertainty is significantly larger than the validation of the correction using 7 his is determined from the variation in tower multilicity for N PV = in s matched to track s with 5 < GeV as comared to N PV = 4 in track s with 5 < 4 GeV.

29 8 ALAS collaboration: Jet measurement with the ALAS detector track s indicate. he larger of the two individual uncertainties (%) is therefore adoted. his results in δ(o tower based )= MeV er vertex 8. he resulting total uncertainty is a factor of five smaller than the bias attributable to ile-u ( 5 MeV er vertex) even with this conservative systematic uncertainty estimation. he offset correction for s based on too-clusters receives an additional uncertainty due to the average tower multilicity aroximation. his contribution is estimated to introduce a % uncertainty in the constituent tower multilicity by comaring s in events with N PV = and for the five highest track -bins. his estimation translates directly into a % uncertainty on the -based offset. he resulting systematic uncertainty on s corrected by the offset correction is estimated to be δ(o based ) 6 MeV er vertex; a factor of three smaller than the bias due to ile-u. Figure shows the relative uncertainty due to ile-u in the case of two measured rimary vertices. In this case, the uncertainty due to ile-u for central s with = GeV and seudoraidity η.8 is about %, while it amounts to about % for s with seudoraidity. η <.8 and to less than.5% for all s with η 4.5. In the case of three rimary vertices, N PV =, the ile-u uncertainty is aroximately twice that of N PV =, and with four rimary vertices the uncertainty for central, endca and forward s is less than %, 6% and 8%, resectively. he relative uncertainty due to ile-u for events with u to five additional collisions becomes less than % for all s with > GeV. he ile-u uncertainty needs to be added searately to the estimate of the total energy scale uncertainty detailed in Section Out-of-time ile-u he effect of additional roton-roton collisions from revious bunch crossings within trains of consecutive bunches (out-oftime ile-u) has been studied searately. he effect is found to be negligible in the data Pile-u corrections alied to shae measurements he measurement of internal roerties like the energy flow inside s can be made considerably more difficult in the resence of additional roton-roton collisions. he alicability of the tower-based offset resented in Section 9.7 to correct the mean energy can also be tested on the internal shae measurements. he offset correction is alied to the measurement of the differential shae for R =.6 tower s, as described in Ref. []. he shae variable used, ρ a (r), is defined as: ρ a (r) =) =) / (N Ratio: (N ρ a (r) =) =) / (N Ratio: (N PV PV PV PV ALAS Data One-Vertex Events wo-vertex Events wo-vertex Events, corrected. y <., 6 <8 GeV (a) Comarison of N PV = and N PV = ALAS Data One-Vertex Events hree-vertex Events hree-vertex Events, corrected. y <., 6 <8 GeV r (b) Comarison of N PV = and N PV = Fig. : Measured sum in annuli around the axis, divided by the total around the within R =.7 of the axis and normalised by the area of each annulus as a function of the distance of the constituent to the axis. he shaes of s in the raidity range. y <. are comared, before and after the offset corrections, in events with one and two reconstructed vertices (a), and one and three reconstructed vertices (b). he corrected distribution is also shown (full triangles). Note that the single vertex data (full circles) are artially hidden behind the corrected multi-vertex data. Anti-k t s with R =.6 reconstructed from calorimeter towers are used and calibrated with the EM+JES scheme. where r= (dη) +(dφ) is the distance of the constituents to the four-momentum vector and the angled brackets denote an average over all s, (b,c) is the sum of the of all towers with an oening angle b R < c with resect to the ) ρ a (r δr δr axis, and δr=.. (r)= π [(r+δr/) ],r+, his definition differs from the canonical shae variable (r δr/) (,.7) ρ(r) in two imortant ways. First, by normalising to area, the variable measures an energy density. herefore, ρ (9) a (r) will aroach an asymtotic value far from the axis. he level of 8 Using twice the RMS of the variation in the closure test yields a the asymtote is related to the energy density in the calorimeter and is measurably higher in events with ile-u. Second, similar value. all r

30 ALAS collaboration: Jet measurement with the ALAS detector 9 towers are included in the definition. his allows an examination of energy outside of the cone, in some sense measuring energy flow around the axis. Figure deicts ρ a (r) with and without a correction of the tower constituent energy for the mean energy induced by ile-u interactions. In events with two (three) reconstructed vertices, differences in this articular shae variable of u to 5% (7%) just outside the (r >.6) and % (4%) near the nominal radius (r=.6) are observed. he bulk of the shae (. r<.6) is restored to that observed in events with only a single interaction, in both the core (r<.) and the erihery (r >.6) of the. he results demonstrate that the tower-based offset correction can be alied on a fine scale granularity and is valid both inside and near s. 9.8 Summary of energy scale systematic uncertainties he total energy scale uncertainty is derived by considering all the individual contributions described in the revious sections. In the central region ( η <.8), the estimate roceeds as follows:. For each and η bin, the uncertainty due to the calibration rocedure is calculated as described in Section 9. for both energy and resonse. For each bin, the maximum deviation from unity between the energy and resonse is taken as the final non-closure uncertainty.. he calorimeter resonse uncertainty is estimated as a function of η and from the roagation of single article uncertainties to the s, as detailed in Section 9... Sources of uncertainties estimated using Monte Carlo samles with a systematic variation are accounted as follows: (a) the resonse in the test samle R var and the resonse in the nominal samle R nom is considered as a starting oint for the estimate of the JES uncertainty. he deviation of this ratio from unity is defined as: JES (,η)= R var(,η) R nom (,η). () his deviation is calculated from both the energy and resonse, leading to JES E (,η) for the deviation in the energy resonse, and to JES (,η) for the deviation in the transverse momentum resonse. (b) he larger JES in each bin derived from the energy or transverse momentum resonse is considered as the contribution to the final JES systematic uncertainty due to the secific systematic effect: JES (, η )=max( JES( E,η), JES (,η)). () 4. he estimate of the uncertainty contributions due to additional material in the inner detector and overall additional dead material are estimated as described in the revious ste. hese uncertainties are then scaled by the average fraction of articles forming the that have < GeV (for the inner detector distorted geometry) and by the average fraction of articles outside the kinematic range of the single hadron resonse in situ measurements (for the overall distorted geometry). For each (, η)-bin, the uncertainty contributions from the calorimeter, the calibration non-closure, and systematic Monte Carlo simulation variations are added in quadrature. For seudoraidities beyond η >.8, the η-intercalibration contribution is estimated for each seudoraidity bin in the endca region as detailed in Section he seudoraidity intercalibration contribution is added in quadrature to the total JES uncertainty determined in the. η <.8 region to estimate the JES uncertainty for s with η >.8, with the excetion of the non-closure term that is taken from the secific η-region. For low, this choice leads to artially double counting the contribution from the dead material uncertainty, but it leads to a conservative estimate in a region where it is difficult to estimate the accuracy of the material descrition. he contribution to the uncertainty due to additional rotonroton interactions described in Section 9.7 is added searately, deending on the number of rimary vertices in the event. In the remainder of the section only the uncertainty for a single roton-roton interaction is shown in detail. Figure shows the final fractional energy scale systematic uncertainty and its individual contributions as a function of for three selected η regions. he fractional JES uncertainty in the central region amounts to % to 4% for < 6 GeV, and it is between % and.5% for 6 < 8 GeV. For s with > 8 GeV, the uncertainty ranges from.5% to 4%. he uncertainty amounts to u to 7% and %, resectively, for < 6 GeV and > 6 GeV in the endca region, where the central uncertainty is taken as a baseline and the uncertainty due to the intercalibration is added. In the forward region, a % uncertainty is assigned for = GeV. he increase in the uncertainty is dominated by the modelling of the soft hysics in the forward region that is accounted for in the η-intercalibration contribution. his uncertainty contribution is estimated conservatively. able 5 resents a summary of the maximum uncertainties in the different η regions for anti-k t s with R=.6 and with of GeV, GeV and.5 ev as examles. he same study has been reeated for anti-k t s with distance arameter R =.4, and the estimate of the JES uncertainty is comarable to that obtained for anti-k t s with R =.6. he JES uncertainty for anti-k t s with R=.4 is between 4% (8%, 4%) at low and.5% % (.5%.5%, 5%) for s with > 6 GeV in the central (endca, forward) region, and is summarised in able Discussion of secial cases he energy scale is derived using the simulated samle of inclusive s described in Section 4., with a articular mixture of quark and gluon initiated s and with a articular selection of isolated s. he differences in fragmentation between quark and gluon initiated s and the effect of close-by s give

31 ALAS collaboration: Jet measurement with the ALAS detector Fractional JES systematic uncertainty Anti-k t R=.6, EM+JES,. η <.8, Data + Monte Carlo incl s 4 ALPGEN+HERWIG+JIMMY JES calibration non-closure Single article (calorimeter) otal JES uncertainty ALAS (a). η <.8 Noise thresholds PYHIA PERUGIA Additional dead material η region Maximum fractional JES Uncertainty = GeV GeV.5 ev η <. 4.6%.%.%. η <.8 4.5%.%.%.8 η <. 4.4%.%.%. η <. 5.4%.4%.4%. η <.8 6.5%.5%.8 η <. 7.9%.%. η <.6 8.%.%.6 η <4.5.9%.9% able 5: Summary of the maximum EM+JES energy scale systematic uncertainties for different and η regions from Monte Carlo simulation based study for anti-k t s with R =.6. Fractional JES systematic uncertainty Fractional JES systematic uncertainty R=.6, EM+JES,. η <.8, Data + Monte Carlo incl s Anti-k t ALPGEN+HERWIG+JIMMY JES calibration non-closure Single article (calorimeter) Intercalibration 4 ALAS (b). η < ALAS Noise thresholds PYHIA PERUGIA Additional dead material otal JES uncertainty Anti-k t R=.6, EM+JES,.6 η < 4.5, Data + Monte Carlo incl s ALPGEN+HERWIG+JIMMY JES calibration non-closure Single article (calorimeter) Intercalibration (c).6 η <4.5 Noise thresholds PYHIA PERUGIA Additional dead material otal JES uncertainty Fig. : Fractional energy scale systematic uncertainty as a function of for s in the seudoraidity region. η <.8 in the calorimeter barrel (a),. η <.8 in the calorimeter endca (b), and in the forward seudoraidity region.6 η <4.5. he total uncertainty is shown as the solid light shaded area. he individual sources are also shown together with uncertainties from the fitting rocedure if alicable. η region Maximum fractional JES Uncertainty = GeV GeV.5 ev η <. 4.%.%.%. η <.8 4.%.4%.%.8 η <. 4.4%.5%.4%. η <. 5.%.6%.5%. η <.8 7.4%.7%.8 η <. 9.%.%. η <.6 9.%.5%.6 η <4.5.4% 4.9% able 6: Summary of the maximum EM+JES energy scale systematic uncertainties for different and η regions from Monte Carlo simulation based study for anti-k t s with R =.4. rise to a toology and flavour deendence of the energy scale. Since the event toology and flavour comosition (quark and gluon fractions) may be different in final states other than the considered inclusive samle, the deendence of the energy resonse on flavour and toology has to be accounted for in hysics analyses. he flavour deendence is discussed in more detail in Section 8 and an additional uncertainty secific to s with heavy quark comonents is discussed in Section. he JES systematic uncertainty is derived for isolated s 9. he resonse of s as a function of the distance to the closest reconstructed needs to be studied and corrected for searately if the measurement relies on the absolute energy scale. he contribution to the JES uncertainty from close-by s also needs to be estimated searately, since the resonse deends on the angular distance to the closest. his additional uncertainty can be estimated from the Monte Carlo simulation to data comarison of the -ratio between calorimeter s and matched track s in inclusive events as a function of the isolation radius. his is discussed in more detail in Section 7. 9 his choice is motivated by the minor differences observed in the average kinematic resonse of isolated and non-isolated s in the nominal inclusive Monte Carlo samle and by the need to factorise the toology deendence of the close-by energy scale uncertainty for final states other than the inclusive s considered.

32 ALAS collaboration: Jet measurement with the ALAS detector Jet energy scale uncertainties validation with in situ techniques for the EM+JES scheme he energy calibration can be tested in situ using a wellcalibrated object as reference and comaring data to the nominal PYHIA Monte Carlo simulation. he following in situ techniques have been used by ALAS:. Comarison to the momentum carried by tracks associated to a : he mean transverse momentum sum of tracks that are within a cone with size R rovides an indeendent test of the calorimeter energy scale over the entire measured range within the tracking accetance. he comarison is done in the η range η <... Direct balance between a hoton and a : Events with a hoton and one at high transverse momentum are used to comare the transverse momentum of the to that of the hoton. o account for effects like soft QCD radiation and energy migrating out of the area the data are comared to the Monte Carlo simulation. he comarison is done in the η range η <. and for hoton transverse momenta 5 γ < 5 GeV.. Photon balance to hadronic recoil: he hoton transverse momentum is balanced against the full hadronic recoil using the rojection of the missing transverse momentum onto the hoton direction (MPF). his method does not exlicitly involve a algorithm. he comarison is done in the same kinematic region as the direct hoton balance method. 4. Balance between a high- and low- system: If s at low transverse momentum are well-calibrated, s at high transverse momentum can be balanced against a recoil system of low transverse momentum s. his method can robe the energy scale u to the ev-regime. he η range used for the comarison is η <.8. All methods are alied to data and Monte Carlo simulation. he in situ techniques usually rely on assumtions that are only aroximately fulfilled. An examle is the assumtion that the to be calibrated and the reference object are balanced in transverse momentum. his balance can be altered by the resence of additional high- articles. For the determination of the JES uncertainties the modelling of hysics effects has to be disentangled from detector effects. his can be studied by systematically varying the event selection criteria. he ability of the Monte Carlo simulation to describe extreme variations of the selection criteria determines the systematic uncertainty in the in situ methods, since hysics effects can be suressed or amlified by these variations. So far the in situ techniques are used to validate the systematic uncertainty in the energy measurement. However, they can also be used to obtain energy corrections. his is an interesting ossibility when the statistical and systematic uncertainties in the samles studied become smaller than the standard JES uncertainty from the single hadron resonse. he results of the in situ techniques are discussed in the following sections.. Comarison of transverse momentum balance of s from calorimeter and tracking he transverse momentum of each can be comared with the total transverse momentum of tracks associated with the by means of a geometrical selection and the charged-to-totalmomentum ratio: r trk = track () can be used to test the calibration. If all roduced articles were ions, the symmetry of QCD under isosin transformation would require that this ratio be / once the energy is high enough so that the total article multilicity is large and the initial isosin of the roton-roton system can be ignored. Production of other articles such as kaons, η mesons, and baryons gives different fractions, but their contributions can be calculated using a roerly tuned event generator. Since the tracking system rovides a measurement that is indeendent of the calorimeter, the ratio r trk can be used to determine the calorimeter energy scale. he r trk distribution is broad but a meaningful calibration does not require very many events, since the statistical uncertainty on the mean scales as / N. his calibration can be used for s confined within the tracking detector coverage. Dominant systematic uncertainties result from the knowledge of the tracking efficiency, variations in the redicted value of r trk for various generator tunes and loss of tracking efficiency in the dense core of high- s. o test the deendence of the energy measurement, the double ratio of charged-to-total momentum observed in data to that obtained in Monte Carlo simulation is studied:.. Jet and track selection R rtrk [ r trk ] Data [ r trk ] MC. () o ensure that the majority of tracks associated with the s found in the calorimeter are within the inner detector fiducial volume, s are required to have η <. and > GeV. o reduce the influence of nearby s on the measurement, if two s are searated by a distance R<R then the softer of these two s is rejected from the analysis. racks with track > GeV are selected using the criteria detailed in Section 6.. he track > GeV requirement is intended to select mainly tracks from fragmentation rather than those arising from soft and diffuse interactions. racks are associated with s using a geometric algorithm. If the distance R track, between the track and the is less than the distance arameter used in the reconstruction (R=.4 or R=.6), the track is associated to the. rack arameters are evaluated at the distance of closest aroach to the Section 9.7 discusses track s obtained by running the antik t algorithm using tracks as inut. hose studies are restricted to η <.9 to avoid bias in the osition of the centre of the due to tracking inefficiencies. Since the s in this section are found using calorimeter information, no such bias is resent and it is therefore ossible to extend the seudoraidity coverage to η <..

33 ALAS collaboration: Jet measurement with the ALAS detector trk (/N)dN/dr ALAS = 4-6 GeV Anti-k t R=.6 EM+JES s = 7 ev, L dt = 6 b - Minimum bias data Jet rigger data PYHIA MC Data trk (/N)dN/dr ALAS = 6-8 GeV Anti-k t R=.6 EM+JES s = 7 ev, L dt = 6 b - Jet rigger data PYHIA MC Data (a) track r trk = Σ / (b) track r trk = Σ / > / track <r trk > = <Σ ALAS η <. R=.6 EM+JES Anti-k t s = 7 ev, L dt = 6 b - Minimum bias data Jet rigger data PYHIA MC Data R rtrk ALAS η <. R=.6 EM+JES Anti-k t s = 7 ev, L dt = 6 b - Minimum bias data Jet rigger data Data (c) (d) Fig. 4: he distribution of the charged-to-total momentum ratio r trk for 4 < 6 GeV (a) and for 6 < 8 GeV (c) and the ratio (b), the average charged-to-total momentum ratio r trk for data and Monte Carlo simulation as a function of of r trk for data and Monte Carlo simulation (R rtrk ) as a function of for the seudoraidity range η <. (d) for anti-k t s with R=.6 calibrated using the EM+JES scheme. he data measured with the (minimum bias) trigger are shown as closed (oen) circles. Only statistical uncertainties are shown.

34 ALAS collaboration: Jet measurement with the ALAS detector rimary hard-scattering vertex and are not extraolated to the calorimeter. his simle association algorithm facilitates comarison with charged articles from truth s whose arameters corresond to those measured at the origin... Systematic uncertainties he systematic uncertainties associated with the method using the total track momentum to test the JES are discussed below... Comarison of data and Monte Carlo simulation he resonse validation using the total momentum measured in tracks deends on a comarison of the mean value of r trk observed in the data to that redicted in the Monte Carlo simulation. It is therefore imortant to demonstrate that the baseline Monte Carlo generator and simulation rovide a reasonable descrition of the data. ALAS has measured the charged article fragmentation function for s with 5 < 5 GeV and η <. and has comared the measurement with the redictions of several Monte Carlo generators and generator tunes [6]. he fragmentation function and the transverse rofile are comared to various Monte Carlo event generators and tunes. he fragmentation function is measured using charged articles with momentum fraction z with resect to the momentum F(z, )=/N dn ch /dz. he growth of the mean charged article multilicity with is well modelled by the Monte Carlo simulation. he measured fragmentation function agrees well with the PYHIA MC and the PERUGIA tunes within the measurement uncertainties. he fragmentation function is described by the PYHIA tunes. he HERWIG++ Monte Carlo generator is not consistent with the data. For observables related to roerties in the direction transverse to the axis the Monte Carlo generators (HER- WIG and the various PYHIA tunes) show reasonable agreement with data, but none of the generators agrees within the exerimental uncertainties over the full kinematic range. For instance, the PYHIA MC tune shows an excess of about % in the transverse charged article distributions close to the axis. hese measurements indicate that the PYHIA MC and PERUGIA tunes san the range of fragmentation functions that are consistent with the data. he studies resented here use the MC tune to obtain the central values of the Monte Carlo redictions. Systematic uncertainties are assessed from the difference between the MC and PERUGIA PYHIA tunes. he r trk distributions used to validate the JES are shown for data and simulation for two tyical bins of in Figure 4a and Figure 4b. Agreement between data and simulation is good, although the data distribution is somewhat wider than the Monte Carlo simulation. Figure 4c and Figure 4d show r trk for data and simulation and the average double ratio R rtrk, resectively, as a function of. Figure 4d demonstrates that the measured JES calibration agrees with that redicted by the Monte Carlo simulation to better than % for > 5 GeV. Measurements using the minimum bias and triggers are consistent for those bins where both triggers are accessible. Generator model deendence While basic isosin arguments constrain the mean fraction of the momentum observed in charged tracks, the rediction for r trk does deend on details of the hysics model used in the Monte Carlo generator. Systematic uncertainties arise from:. he arametrisation of the fragmentation function and of the underlying event (which mainly affect the fraction of the momentum carried by articles below the = GeV cut used for this analysis).. he model of colour reconnection (which can change the distribution of articles with low momenta).. he robability of roducing strange quarks and baryons (which are iso-doublets rather than iso-trilets like the ion) and of roducing iso-scalars such as the η. he size of these uncertainties has been estimated by studying a wide range of PYHIA tunes. A list of the PYHIA tunes studied is given in able 7. hese studies have been done at the generator level and have been cross-checked using simulated samles when the aroriate tunes were available with full simulation. he data have also been comared to default tunes of HER- WIG++ and HERWIG+JIMMY. PYHIA tune 7, and the default HERWIG++ and HERWIG+JIMMY tunes are not consistent with the measured f(z) distributions.since these generators do not described the fragmentation functions measured by ALAS [6] they are excluded from consideration when determining the systematic uncertainty on the JES measurement. At low, the variations between tunes arise mainly from differences in the hardness of the fragmentation, which affects the fraction of charged articles falling below the GeV cut on track. In general, PYHIA tunes that include the colour annealing model of colour reconnection exhibit harder fragmentation than similar tunes without colour annealing. At high, differences among tunes are rimarily associated with the strangeness and baryon content of the truth s. Versions of PYHIA tuned to LEP data (including flavour-deendent fragmentation measurements) using the tuning software PROFES- SOR [6] in general show a charged fraction about % higher than the other tunes considered here. Using a conservative aroach, the value of systematic uncertainty has been symmetrised around the baseline tune using the absolute value of the largest deviation of the tunes considered from the baseline. Inner detector material descrition he dominant systematic uncertainty on the reconstruction efficiency for isolated tracks is derived from the uncertainty on the simulation s descrition of material in the inner detector. he systematic uncertainty on the efficiency is indeendent of track for tracks with track > 5 MeV but is η-deendent, ranging from % Additional information about the PYHIA tunes can be found in Ref. [8].

35 4 ALAS collaboration: Jet measurement with the ALAS detector Relative systematic uncertainties ALAS Anti-k t R=.6 EM+JES s = 7 ev Data η <. Jet resolution Generator tune Material descrition Efficiency in core otal Relative systematic uncertainties ALAS Anti-k t R=.6 EM+JES s = 7 ev Data. η <.8 Jet resolution Generator tune Material descrition Efficiency in core otal (a) η <. (b). η <.8 Relative systematic uncertainties ALAS Anti-k t R=.6 EM+JES s = 7 ev Data.8 η <. Jet resolution Generator tune Material descrition Efficiency in core otal Relative systematic uncertainties ALAS Anti-k t R=.6 EM+JES s = 7 ev Data. η <.7 Jet resolution Generator tune Material descrition Efficiency in core otal (c).8 η <. (d). η <.7 Relative systematic uncertainties ALAS Anti-k t R=.6 EM+JES s = 7 ev Data.7 η <. Jet resolution Generator tune Material descrition Efficiency in core otal (e).7 η <. Fig. 5: Relative systematic uncertainty on the JES obtained by comaring the total momentum of tracks associated to s to the calorimeter measurements for different η regions for anti-k t s with R=.6 calibrated with the EM+JES scheme as a function of. he total and the individual systematic uncertainties, as evaluated from the inclusive Monte Carlo simulation, are shown.

36 ALAS collaboration: Jet measurement with the ALAS detector 5 une Name PYUNE Value Comments MC ALAS default ( ordered showering) MC9 ALAS default for Summer ( ordered showering) RFA Rick Field une A Q ordered showering 7 une A with colour annealing colour reconnection une A with LEP tune from Professor 7 une with colour annealing colour reconnection 9 une of Q ordered showering and UE with Professor PERUGIA ( ordered showering) PERUGIA 7 PERUGIA with udated fragmentation and more arton radiation able 7: PYHIA generator tunes used to study the systematic uncertainty on the rediction for r trk. unes secified by number (e.g. ) refer to the value of the PYUNE arameter [8]. A dash in the table indicates that the articular tune has no PYUNE value. for η track <. to 7% for. η track <.5 [64]. Convolving these uncertainties with the aroriate η track distributions results in systematic uncertainties on r trk that range from % for seudoraidities η <. to.5% for seudoraidities.7 η <.. Uncertainties in the material distributions also affect the robability that hoton conversions roduce charged articles that can be included in the r trk measurement. he track selection used here requires at least one Pixel hit and most of the material in the ID is at a larger radius than the Pixel detector, resulting in a small systematic uncertainties associated with rate of conversions. racking efficiency in the core here are several effects that change the tracking efficiency and resolution inside a comared to those for isolated tracks:. When two tracks are close together, their hits may overla. While the attern recognition software allows tracks to share hits, the resolution is degraded since the calculated osition of the hit is affected by the resence of the other track. he robability of not assigning hits to tracks increases.. When the hit density becomes high in the core of the, failures in the attern recognition may result in the creation of tracks by combining hits that in fact came from several articles. Such tracks are called fake tracks.. When two high- tracks are close together in sace, they will share hits over many layers. In this case, one of the two tracks may be lost. his effect, referred to as loss of efficiency, becomes more imortant as the increases. he reliability of the simulation to redict the size of these effects deends on whether the software roerly models merging of ID hits. Detailed comarisons of the data and Monte Carlo simulation indicate that the simulation accurately reroduces the degradation of resonse in the core and models the degradation in resolution well. Comarison of the fraction of tracks with z > in data and Monte Carlo simulation constrains the size of the non-gaussian tails in the track resolution. Any residual difference in resolution between data and simulation is absorbed in the quoted uncertainty due toid alignment. Fake tracks and loss of efficiency are studied in the simulation using a hit-based matching algorithm using truth s. hese studies indicate that the rate for reconstructing fake tracks remains at.% for the full range considered here, but that there is loss of tracking efficiency near the core of high- s. his effect has a negligible effect on r trk for s with < 5 GeV, but increases with such that on average 7.5% of the charged track momentum is lost for s in the range 8 < GeV. A relative uncertainty of 5% is assigned to the value of the inefficiency that is caused by merged hits. While this effect gives the largest systematic uncertainty on the JES for > 6 GeV (.9% for 6 < 8 GeV and.7% for 8 < GeV), it is still smaller than the resent statistical uncertainty at these values of. Inner detector alignment For high tracks, the momentum resolution achieved in theid is worse than that of the simulation. his degradation in resolution is attributed to an imerfect alignment of the ID. he systematic uncertainty on r trk is obtained by degrading the tracking resolution in the simulation. he size of this additional resolution smearing is determined by studying the width of the measured mass distribution for Z-decays Z µ + µ. his rocedure results in a systematic uncertainty of less than.% for all and η. Calorimeter resolution he systematic uncertainty due to transverse momentum resolution [65] is determined by smearing the four-momentum (without changing η or φ) in Monte Carlo simulation. he relative uncertainty on the resolution is 5% for η <.8 and % for.8 η <.. he effect of this variation is largest for low values of and high values of η; for < 4 GeV and.8 < η <. the uncertainty on R rtrk is %. Combined systematic uncertainty he above uncertainties are assumed to be uncorrelated and are combined in quadrature. he resulting total uncertainties are shown in Figure 5 as a function of for several regions of η.

37 6 ALAS collaboration: Jet measurement with the ALAS detector ALAS η <. Anti-k t R=.6 EM+JES - L dt = 6 b s = 7 ev Data ALAS. η <.8 Anti-k t R=.6 EM+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (a) η <. (b). η < ALAS.8 η <. Anti-k t R=.6 EM+JES - L dt = 6 b s = 7 ev Data ALAS. η <.7 Anti-k t R=.6 EM+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (c).8 η <. (d). η < ALAS.7 η <. Anti-k t R=.6 EM+JES - L dt = 6 b s = 7 ev Data ALAS η <. Anti-k t R=.6 EM+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (e).7 η <. (f) η <. Fig. 6: Double ratio of the mean track to calorimeter resonse ratio in data and Monte Carlo simulation R rtrk =[r trk ] Data /[r trk ] MC for anti-k t s with R =.6 calibrated with the EM+JES scheme as a function of for various η bins. Systematic (total) uncertainties are shown as a light (dark) band.

38 ALAS collaboration: Jet measurement with the ALAS detector 7 [/GeV] γ dn/d 4 ALAS s= 7 ev Data PYHIA MC - Ldt = 8 b the electromagnetic calorimeter, is used as a reference. Such a toology can be used to validate the energy measurement. Any discreancy between data and simulation may be taken as an uncertainty on the energy calibration. wo methods of balancing the hoton and the recoiling transverse momentum with different sensitivities and systematic uncertainties are used: the direct balance technique and the missing transverse momentum rojection fraction technique γ Fig. 7: Distribution of the hoton transverse momentum for events assing the hoton selection criteria described in Section..4. A correction is made in the first γ bin for the rescale alied to the trigger in this γ range. he Monte Carlo simulation is normalised to the observed number of events observed in data and corrected for the trigger re-scale. Uncertainties are statistical only... Direct transverse momentum balance technique he direct balance technique exloits the aroximate transverse momentum balance in events with only one hoton and one with high. he ratio of the to the hoton ( /γ ) is used to estimate the resonse. Since the hoton is well-measured and well-described by the simulation, the quality of the calibration can be assessed by comaring data and Monte Carlo simulation using the ratio /γ. his technique was used at the CDF exeriment [6]...4 Summary of JES uncertainty from tracks Final results for anti-k t s with R=.6 and EM+JES corrections are shown in Figure 6 for five bins in η with the derived systematic uncertainties. o facilitate comarisons at high, where the statistical uncertainties are large, the combined data from the three bins with η <. are also dislayed. Averaging all data with > 5 GeV and η <. yields a value of r trk that agrees with the simulation to better than %. his small discreancy is well within the quoted systematic uncertainty, which is highly correlated between bins in. No significant variation of R rtrk with is observed. For η >., the statistical uncertainties are large for > 5 GeV. For < 5 GeV, the level of agreement between data and simulation is similar to that obtained at low η. In summary, r trk, the ratio of track to calorimeter transverse momentum, is used to validate the JES for anti-k t s with R =.4 and R =.6 calibrated with the EM+JES calibration scheme. Systematic uncertainties associated with modelling and track reconstruction are assessed and the method is shown to rovide a JES uncertainty evaluation indeendent of the modelling of the calorimeter resonse. Systematic uncertainties are below % for η <.8 and rise to 4% for.7 η <. for 4 < 8 GeV. he results agree within systematic uncertainties with those redicted using the ALAS calorimeter simulation and rovide an indeendent estimate of the overall energy scale and its uncertainty.. Photon- transverse momentum balance In γ- events, a recoils against a hoton at high transverse momentum. he hoton energy, being accurately measured in.. Missing transverse momentum rojection fraction technique he missing transverse momentum (E miss ) rojection fraction (MPF) technique exloits the momentum balance, in the transverse lane, of the hoton and the hadronic recoil to derive the detector resonse to s. his technique has been used in the ast for the D exeriment [6]. he missing transverse momentum vector (E miss ) is defined as the oosite of the vector sum of the transverse rojections of calorimeter energy deosits. he missing transverse momentum is calculated from the energy deosits in the calorimeter cells that are included in too-clusters. he calorimeter cell energy is comuted using the same calibration as the one used in the calibration scheme to be tested. he missing transverse momentum is corrected for the hoton four-momentum. he reconstructed four-momentum is not directly used in the missing transverse momentum calculation. he MPF technique is based on the assumtion that the only missing transverse momentum in a γ- event arises from calorimeter non-comensation, signal losses due to noise suression and energy losses in the non-active regions of the detector by the hadronic. he transverse momentum balance can be written as: γ + =, (4) where γ and is the hoton and transverse momentum vector. he articles roduced by the hard scatter and their interaction in the calorimeter can be exressed in terms of the observables: R γ γ +R = Emiss, (5) where R γ is the calorimeter resonse to hotons. Since the calorimeter is well calibrated for hotons, R γ =. he variabler denotes the calorimeter resonse to s. By using the

39 8 ALAS collaboration: Jet measurement with the ALAS detector / EM γ.8 ALAS simulation s = 7 ev R MPF PYHIA γ- PYHIA di.7.6 ALAS simulation s = 7 ev PYHIA γ - PYHIA di γ -.5. γ R γ- / R.5 - R γ- / R.5 di R 5 5 γ di R 5 5 γ (a) Direct balance technique (b) MPF technique Fig. 8: Average resonse measured at the EM scale as a function of γ as determined by the direct balance technique for anti-k t s with R=.6 (a) and by the MPF technique (b) for γ- events and di events where one has been reconstructed as a hoton, as derived in the Monte Carlo simulation. he lower art of the figures shows the absolute resonse difference between the di and γ- events with resect to the resonse of γ- events. Only statistical uncertainties are shown. Variable hreshold η <. γ > 5 GeV η γ <.7 E γisolation < GeV φ -γ > π. rad /γ < % able 8: Criteria used to select events with a hoton and a with high transverse momentum. above two equations and rojecting the E miss in the direction of the hoton the resonse can be written as: R MPF = + γ Emiss γ, (6) which is defined as the MPF resonse. Note that the MPF technique measures the calorimeter resonse by relying only on the hoton and E miss quantities and does not use the energy directly. herefore the MPF resonse is indeendent of the algorithm... Photon- Monte Carlo simulation samle he γ- samle is simulated with the event generator PYHIA using the ALAS MC tune [7]. he systematic uncertainty from s which are identified as hotons (fakes) are studied with an inclusive PYHIA samle using the MC9 tune [7]. o efficiently roduce this samle a generated event is only fully simulated if it contains at least one generated article with > 7 GeV. hese s are comuted from the sum of the four-momenta of all stable generated articles within a.8.8 region in η φ. Events in the di samle with romt hotons, e.g. that are roduced by radiation are removed...4 Selection of the hoton- data samle he leading hoton in each event must have γ > 5 GeV and lie in the seudoraidity range η γ <.7. In this range the hoton is fully contained within the electromagnetic barrel calorimeter. Furthermore, events in which the leading hoton is in a calorimeter region where an accurate energy measurement is not ossible are rejected. In each event only the leading hoton is considered. he leading hoton candidate must also satisfy strict hoton identification criteria [66], meaning that the attern of energy deosition in the calorimeter is consistent with the exected hoton showering behaviour. he hoton candidate must be isolated from other activity in the calorimeter (E γ Isolation ) with an isolation cone of size R =.4. If the leading hoton does not meet all of these criteria, the event is rejected. Only events are retained that fired an online trigger requiring a hoton candidate with γ > GeV or γ > 4 GeV. At the trigger level the hoton identification requirements are less strict than those of the off-line selection. Since a large event statistics is needed for this samle, only a samle with an older tune was available.

40 ALAS collaboration: Jet measurement with the ALAS detector 9 /.5.4. γ ALAS Point / D Point D Point i.. ALAS EM Data 45 GeV < < 6 GeV γ.. Point 9 - L dt = 8 b s = 7 ev φ (-γ) [rad] Point (a) (b) Fig. 9: he values of radiation-suressing cut thresholds (oints) used to robe the soft QCD radiation systematic uncertainty, as a function of φ -γ and /γ overlaid with the number of events observed in data (a). he nominal selection is the bottomrightmost oint labelled Point. Relative change in the MPF resonse between data and Monte Carlo simulation (b), defined as D=[R MPF ] Data /[R MPF ] MC from the oint given on the x-axis to oint, when relaxing the soft QCD radiation suression as indicated in (a). Only statistical uncertainties are shown. he distribution of hotons in events selected with the above criteria is shown in Figure 7. he small discreancies between the γ sectrum in data and Monte Carlo simulation do not affect the comarison of the resonse in data and Monte Carlo simulation. he leading must be in the fiducial region η <.. Soft QCD radiation can affect the balance between the and hoton. he following two selection cuts are alied to suress this effect. o select events in which the hoton and the leading are back-to-back, φ -γ > π. radians is required. he resence of sub-leading s is suressed by requiring that the sub-leading has less than % of the of the leading hoton. A summary of the event selection criteria can be found in able Systematic uncertainties of the hoton- in situ validation technique Uncertainties due to background from s identified as hotons (fakes), soft QCD radiation, in-time ile-u, non-functional calorimeter read-out regions and the hoton energy scale are studied. Background in the hoton- samle he systematic uncertainty from s which are identified as hotons (fakes) his cut is not alied, if it would be below the reconstruction threshold of = 7 GeV. If in this case a sub-leading with 7 GeV is resent, the event is rejected. Direct balance [%] MPF [%] γ range Background ±. ±.4 ±.6 ±. Soft QCD radiation ±.8 ± ±.7 ±.4 In-time ile-u ±.8 ±.8 ± ± Photon scale otal systematics able 9: Individual systematic uncertainties in the energy scale from both the direct balance and the MPF techniques at two values of γ. are studied with the inclusive Monte Carlo simulation samle described in Section... Di events in which one of the s is misidentified as a hoton contribute to the data samle but not to Monte Carlo simulation signal samle. he rate of di events faking hotons is sensitive to the detailed modelling of the fragmentation and the detector simulation, and is therefore subject to large uncertainties. he systematic uncertainty from this background is determined in two stes. First the difference in the detector resonse between the γ- (R γ- ) and the filtered di samle (R di ) is determined in the Monte Carlo simulation as seen in Figure 8. Also shown is the absolute resonse difference R di R γ- relative to the resonse of the γ- samle-. A resonse difference of maximally 5% is estimated. o estimate the contribution from background in the signal region the distribution of hoton candidates observed in the sidebands of a two-dimensional distribution is used. he

41 4 ALAS collaboration: Jet measurement with the ALAS detector / γ ALAS s = 7 ev. L dt = 8 b Data. - R=.6, EM+JES Anti-k t Data Point PYHIA Point Data Point PYHIA Point Arbitrary units.4 ALAS - L dt = 8 b s = 7 ev Data N PV = N PV > Data / MC γ γ Fig. : Average resonse as determined by the direct balance technique with the nominal selection (Point ) and with a set of relaxed radiation suression cuts (Point ), for anti-k t s with R=.6 calibrated with the EM+JES scheme as a function of the hoton transverse momentum for data and Monte Carlo simulation. Only statistical uncertainties are shown. transverse isolation energy, E γisolation, and the hoton identification of the hoton candidate are used for this estimate. On the isolation axis, the signal region contains hoton candidates with E γisolation < GeV, while the sideband contains hoton candidates with E γisolation > 5 GeV. On the other axis, hoton candidates assing the identification criteria belong to the signal region, while those that fail the tight identification criteria but ass a background-enriching selection belong to the hoton identification sideband. Further details are found in Ref. [66]. he urity P measured in the signal samle is about.6 at = 5 GeV and rises to about 5 at higher 4. he systematic uncertainty is then calculated as ( ) Rdi R γ- ε = ( P). (7) R γ- he systematic uncertainty is below % for the direct balance technique and below.6% for the MPF technique. he effect of background contamination in the γ- samle has been further validated by relaxing the hoton identification criteria. Both data and Monte Carlo simulation show a % variation in resonse for the direct balance technique, mostly at low. his is consistent with the systematic uncertainty comuted with the urity method using Equation 7, e.g. for the lowest bin 4% of the events are exected to be di background giving a resonse that is 5% higher than the resonse of γ- events. 4 his is similar to the urity measured in Ref. [66] and small differences are due to the different data samles Missing ransverse Momentum Fraction Fig. : he missing transverse momentum fraction (MF) distribution for data with exactly one reconstructed rimary vertex N PV, and with more than one reconstructed rimary vertex. Only statistical uncertainties are shown. Soft QCD radiation suression cuts he stability of the resonse ratio of the data to the Monte Carlo simulation is exlored by varying the radiation suression cuts. Figure 9a shows the thresholds for the /γ and φ -γ cuts for sets of cuts. Figure 9b illustrates the change in the ratio of the data to the Monte Carlo simulation of the MPF resonse for each of these sets of cuts, for one tyical γ bin. he result demonstrates that the ratio of the data resonse to the Monte Carlo resonse is not sensitive to the exact values of the radiation cuts, within the % level. he systematic uncertainty is taken as the difference in the data to Monte Carlo ratio between the nominal cuts defining the signal samle, and the loosest cuts in all -bins, labelled as Point in Figure 9a. he MPF-determined resonse changes slightly between the data and the Monte Carlo simulation, the systematic uncertainty is.7% at γ = 5 GeV and falls to.4% at γ = 5 GeV. he quoted values are determined from linear fits to the oints analogous to those shown in Figure 9b. he stability of the ratio of the data to the Monte Carlo simulation for the resonse measured with the direct balance technique is shown in Figure. he resonse measured in either data or in Monte Carlo simulation varies by u to % due to differing radiation suression cuts. However, the data to Monte Carlo ratio with and without the radiation suression cuts is stable within %. In-time ile-u he average number of roton-roton collisions in each bunch crossing grew significantly during the data-taking eriod. hus, there is a non-negligible fraction of events containing in-time ile-u (see Section 8.). he additional collisions roduce extra articles which can overla with

42 ALAS collaboration: Jet measurement with the ALAS detector 4 γ / ALAS anti-k t R=.6, EM s = 7 ev Data N PV - PYHIA N PV L dt = 8 b Data N PV =.8 PYHIA N PV = Data one vertex and for events with more than one vertex is consistent with a variation of.8%. his is taken as a systematic uncertainty. No effect due to the offset correction for in-time ile-u is seen (see Section 8.), and no systematic uncertainty is attributed to the offset correction for in-time ile-u. Data / MC γ γ Imact of missing calorimeter read-out regions For a small subset of the calorimeter channels the calorimeter readout is not functioning roerly. he energy of these calorimeter cells is evaluated using the trigger tower information, which has larger granularity and less accurate resolution. While hotons reconstructed in or near such a region are not considered in the analysis, there is no such rejection alied to s. A subsamle of events with no containing such a cell has been used to evaluate a ossible systematic uncertainty between data and simulation. Within the statistical uncertainty, no bias is observed for the MPF γ- technique or the direct balance technique, therefore no systematic uncertainty is assigned. Fig. : Average resonse for anti-k t s with R=.6 at the EM scale as determined by the direct balance technique in events with any number of reconstructed rimary vertices and in events with exactly one reconstructed vertex as a function of the hoton transverse momentum for both data and Monte Carlo simulation. he lower art of the figure shows the data to Monte Carlo simulation ratio. Only statistical uncertainties are shown. the hard interaction of interest in the ALAS detector. he increased energy is about.5 GeV er additional reconstructed rimary vertex (see Section 8..4). he MPF technique is exected to be insensitive to in-time ile-u events. Because in-time ile-u is random and symmetric in φ, the mean of the quantity γ Emiss should be robust against in-time ile-u. he missing transverse fraction (MF) is defined as: MF= (γ Emiss ) z γ = Emiss γ sin(φ E miss φ γ ), (8) where ( γ Emiss ) z is the z-comonent of the vector resulting from the cross roduct. he MF measures the activity in the lane erendicular to the hoton. he mean of the MF is zero, if there is no bias due to in-time ile-u. Figure shows the MF distribution for data with and without in-time ile-u. For both these distributions the means are comatible with zero. From the study of the MF distribution and other checks, such as the deendence of the MPF on N PV, it can be justified that in-time ile-u can be neglected and no systematic uncertainty is attributed to the MPF method. In the case of the direct balance technique the imact of in-time ile-u is exlored by comaring the balance between events with exactly one identified rimary vertex and events with any number of vertices. As seen in Figure the ratio of the resonse in data to the resonse in Monte Carlo simulation for events with exactly Photon energy scale Both the direct balance and the MPF techniques are sensitive to the hoton energy scale. he absolute electron energy scale has been measured in situ using the invariant mass constraint in Z e + e for electrons. he uncertainty on the hoton energy scale results in a systematic uncertainty smaller than %, deending on and η. he direct balance technique and the MPF technique find a systematic uncertainty which is aroximately oosite in sign. his sign difference is caused by the uwards shift in hoton energy leading to an equivalent downwards shift in, and vice versa. he resonse measured with both the MPF and the direct balance techniques has been studied for converted and nonconverted hotons. he results of both samles agree within the statistical uncertainties. No additional systematic uncertainty has been considered for this effect, which is already accounted for in the hoton energy scale and the hoton background systematic uncertainty. E miss otal systematic uncertainty able 9 shows a summary of the systematic uncertainties studied for the direct balance and MPF techniques. he total systematic uncertainties for each method are similar, although each method is sensitive to different effects. otal systematic uncertainties are found on the data to Monte Carlo simulation resonse ratio of smaller than % for the MPF method and of smaller than.6% for direct balance method...6 Results from the hoton- balance he direct balance and MPF techniques are used to validate the resonse in situ by comaring data and Monte Carlo simulation. he resonse in data and Monte Carlo simulation for the EM scale energy is shown in Figure. he resonse in data and Monte Carlo simulation agrees within uncertainties in the range γ > 45 GeV. In the range 5 γ < 45 GeV there

43 4 ALAS collaboration: Jet measurement with the ALAS detector / γ ALAS anti-k t R=.6, EM s = 7 ev - Data L dt = 8 b.8 PYHIA MC R MPF.8 MPF EM scale, all algorithms Data PYHIA MC.7.7 Data / MC (a) Direct balance technique γ γ Data / MC ALAS L dt = 8 b s = 7 ev (b) MPF technique - γ Fig. : Average resonse as determined by the direct balance for anti-k t s with R=.6 (a) and the MPF technique (b) using the EM scale for both data and Monte Carlo simulation as a function of the hoton transverse momentum. he lower art of the figure shows the data to Monte Carlo simulation ratio. Only statistical uncertainties are shown. γ / Data / MC ALAS s = 7 ev L dt = 8 b - R=.6, EM+JES anti-k t Data PYHIA MC γ γ Fig. 4: Average resonse as determined by the direct balance technique for anti-k t s with R=.6 calibrated with the EM+JES scheme as a function of the hoton transverse momentum for both data and Monte Carlo simulation. he lower art of the figure shows the data to Monte Carlo simulation ratio. Only statistical uncertainties are shown. Since the EM+JES calibration deends only on the and η of the, it is ossible to validate the EM+JES calibration scheme by using the EM scale as a function of γ and η. Figure 4 shows the resonse measured in both data and Monte Carlo simulation using the direct balance technique with the anti-k t algorithm with R=.6 for the EM+JES calibration scheme. he data to Monte Carlo simulation agreement is within±5%. Figure 5 shows the ratio of /γ between data and Monte Carlo simulation together with the total uncertainty on the determination of the data to Monte Carlo simulation ratio, for anti-k t s with R =.6. Similarly, Figure 6 shows the resonse ratio of data to Monte Carlo simulation, as determined using the MPF technique together with the total uncertainty on the determination of the data to Monte Carlo simulation ratio. For γ > 45 GeV, the resonse in data and Monte Carlo simulation agree to within % for both MPF and direct balance techniques u to about GeV. In the range 5 γ < 45 GeV there is an observed shift of 5% for the direct balance technique and % for the MPF technique. he lower resonse at the highest γ is further discussed in Section.5.. he size of these shifts is consistent with the systematic uncertainty on the EM+JES energy calibration (see Section 9). At high γ the dominant uncertainty is statistical while the systematic uncertainty dominates at low γ...7 Summary of the hoton- balance is a shift in the data to Monte Carlo ratio of 5% for the direct balance technique and % for the MPF technique. he validation of the EM+JES calibration scheme for s with the anti-k t algorithm reconstructed from too-clusters using in situ methods is resented. Agreement between the resonse

44 ALAS collaboration: Jet measurement with the ALAS detector 4 / ) MC / ( / ) Data.5 γ γ..5 s = 7 ev L dt = 8 b Data - anti-k t R=.6, EM Uncertainty Statistical Systematic otal / ) MC / ( ( / ) Data.5 γ γ..5 s = 7 ev L dt = 8 b Data - anti-k t R=.6, EM+JES Uncertainty Statistical Systematic otal ( ALAS ALAS (a) EM γ (b) EM+JES γ Fig. 5: Average resonse ratio of data to Monte Carlo simulation using the direct balance technique for each inut energy scale, EM (a) and EM+JES (b), as a function of the hoton transverse momentum. Statistical and systematic uncertainties (light band) are included with the total uncertainty shown as the dark band. R Data /R MC MPF EM all algorithms Uncertainty - L dt = 8 b Statistical Systematic otal s = 7 ev Data ALAS γ Fig. 6: Average resonse ratio of data to Monte Carlo simulation using the MPF method at the EM scale as a function of the hoton transverse momentum. Statistical and systematic uncertainties (light band) are included. he total uncertainty is shown as the dark band. in data and Monte Carlo simulation is found to be within statistical uncertainties for 45 γ < GeV. Both techniques observe a shift in the data to Monte Carlo simulation ratio for 5 γ < 45 GeV. he total systematic uncertainties of the γ- in situ technique is estimated to be less than.6% for 45 γ < 4 GeV.. Multi transverse momentum balance he reach in the γ- transverse momentum balance technique is limited by the available event statistics. he multi balance technique where a recoil system of low- s balances several s at lower can be used to assess the calibration at higher. Jet transverse momenta u to the ev region can be robed. he same method can also be used to obtain correction factors for ossible non-linearities at very high. Here, the method is only used to assess the JES uncertainty... he multi balance technique he method exloits the balance in events where the highest (leading ) is roduced back-to-back in φ to a multi system. he leading is required to have significantly larger transverse momentum than other s in the event. In this way the leading is at a higher scale comared to other reconstructed s, called non-leading s. he ensemble of the non-leading s assing the selection cuts is referred to as the recoil system. he event toology used in this analysis is sketched in Figure 7. he vectorial sum of the transverse momenta of all nonleading s defines the transverse momentum of the recoil system ( Recoil ), which is exected to aroximately balance the transverse momentum of the leading ( Leading ). hus a correlation between the momentum scale of the leading and the

45 44 ALAS collaboration: Jet measurement with the ALAS detector Variable Cut value Jet > GeV Jet raidity y <.8 Number of good s Recoil > 8 GeV α <. radian β > radian Jet /Recoil <.6 able : Selection criteria to define the event samle for the multi balance analysis... Selection of multi events Fig. 7: Sketch of the event toology used for the multi balance technique in the x y-lane. scale of the non-leading s can be established. If the absolute JES is well-known for all non-leading s, the JES of the leading can be verified by studying the multi balance (MJB) that is defined as the ratio: MJB= Leading Recoil. (9) Moreover, the Recoil is a good estimator of the true leading, and it is therefore interesting to study MJB as a function of Recoil. In the ideal case MJB should be equal to one; however, various effects such as the resence of close-by s, soft gluon emission, ile-u or the selection criteria themselves may introduce a bias. he comarison between the balance measured in the simulation ([MJB] MC ) and the data ([MJB] Data ) can be interreted as a source of systematic uncertainty and therefore the ratio r=[mjb] Data /[MJB] MC () can be used to assess the high JES uncertainty. he s belonging to the recoil system must be confined to a lower energy scale with resect to the leading in order to ensure that the multi balance is testing the absolute high scale and not only the intercalibration between s. here are various analysis methods to constrain the leading to a higher scale with resect to the s in the recoil system. In this analysis it is done by setting an uer limit on the ratio between the transverse momentum of the second highest ( Jet ) and the Recoil. his cut is very efficient in selecting multi events while minimising the bias on the transverse momentum of the leading. wo trigger selections have been used to cover a wide range with large enough statistics. he first trigger selection requires at least one with > 5 GeV at the EM scale in the level- calorimeter trigger. he data collected with this trigger are used to cover the region of Recoil < 6 GeV. he second trigger selection, which requires at least one with > 95 GeV for the level- trigger, is used to oulate the region of 6 GeV. he two trigger thresholds are fully efficient for s with Recoil > 8 GeV and > 5 GeV. o avoid a trigger bias, the multi balance is studied in events containing a recoil system with transverse momentum larger than 8 GeV. In order to select events with one being roduced against a well-defined recoil system, a selection is alied using two angular variables (α and β as deicted in Figure 7):. α = φ π, where φ is the azimuthal oening angle between the highest and the recoil system.. β is the azimuthal oening angle of the non-leading that is closest to the leading in φ, measured with resect to the leading. Events are selected by requiring:. α = φ π <. radian.. β > radian, i.e. no s within φ = radian around the leading. he cuts alied to α and β retain the bulk of the events. A further selection is alied to ensure that the leading is at a higher scale with resect to the s comosing the recoil system. his is done by requiring that the asymmetry ratio A of Jet to the transverse momentum of the recoil system satisfies the following inequality: A= Jet Recoil <.6. () his cut enables the efficient suression of events with toologies very close to those of di events. his can be seen from the distributions of the ratio of the Jet to the leading shown in Figure 8 before and after the cut is alied. Events are weighted according to the re-scale values alied at the trigger level. his selection therefore ensures that the leading is at a higher scale with resect to the s forming the recoil system.

46 ALAS collaboration: Jet measurement with the ALAS detector 45 Events ALAS s = 7 ev L dt - = 8 b Events 4 ALAS s = 7 ev L dt - = 8 b R=.6 anti-k t EM+JES 5 Data PYHIA MC ALPGEN HERWIG++ R=.6 anti-k t EM+JES Data PYHIA MC ALPGEN HERWIG++ Data/MC Jet Jet / (a) Before asymmetry cut Data/MC Jet Jet / (b) After asymmetry cut Fig. 8: Distribution of the ratio of the sub-leading to the leading for anti-k t s with R =.6 before (a) and after (b) the asymmetry cut, see Equation, has been alied for data (full circles) and for simulation (lines). All the distributions in the simulation are normalised to the number of data events. Events selected by re-scaled triggers have entered the histogram weighted by the re-scale value. Only statistical uncertainties are shown. At the same time this cut does not bias either the leading or the recoil system. his has been confirmed using Monte Carlo simulation by checking that the average resonse of the leading and recoil system is not significantly shifted from one after the asymmetry cut is alied. A summary of the selection criteria used in the analysis is given in able... Measurement of the multi balance Jet Recoil / true ALAS simulation anti-k t, R=.6 EM+JES s = 7 ev PYHIA MC ALPGEN HERWIG++ he multi balance is studied as a function of the transverse momentum of the recoil system, Recoil, which is a good estimator of the true leading as shown in Figure 9 for various Monte Carlo simulations. he ratio of reconstructed Recoil to the true leading as a function of the true leading is, on average, consistent with unity to better than %. he multi balance obtained from the selected events for the anti-k t algorithm with R=.6 is shown in Figure 4 for data and Monte Carlo simulation. he transverse momentum of the recoil system ranges from 8 GeV u to. ev for the anti-k t s with R=.6. he multi balance at low Recoil values shows a bias towards values lower than one. his is a due to effects which broaden the leading and the Recoil, and is a direct consequence of binning in Recoil. his effect is observed already for truth s and is, after reconstruction, correctly reroduced by the Monte Carlo simulation. he data to Monte Carlo simulation ratio obtained from the multi balance distributions are shown in the lower art of Figure 4. he average value of the data to Monte Carlo simulation ratio is within % for transverse momenta u to the ev-region. he data to Monte Carlo simulation ratio rovides an estimate of the uncertainty on the leading scale true Jet Fig. 9: Ratio of the reconstructed recoil system to the true leading for anti-k t s with R=.6 as a function of the true leading for three samles of Monte Carlo simulations. Only statistical uncertainties are shown...4 Estimate of the systematic uncertainty on the multi balance wo main categories of systematic uncertainty have been considered:. he reference of the recoil system.

47 46 ALAS collaboration: Jet measurement with the ALAS detector MJB MJB Data /MJB MC ALAS s = 7 ev L dt - = 8 b R=.6 EM+JES anti-k t Data PYHIA MC ALPGEN HERWIG Recoil Fig. 4: Multi balance MJB as a function of the recoil system for data and Monte Carlo simulation for anti-k t s with R =.6. Only statistical uncertainties are shown. MJB Relative uncertainty. Default.5 5 ALAS simulation s = 7 ev otal Standard Flavour Close-by PYHIA MC anti-k t R=.6 EM+JES Recoil Fig. 4: he multi balance MJB as a function of Recoil (full dots) with statistical uncertainties for anti-k t s with R=.6. he three bands are defined by the maximum shift of MJB when the s that comose the recoil system are shifted u and down by the standard JES uncertainty, close-by and flavour uncertainties. he black lines show the total uncertainty obtained by adding in quadrature the individual uncertainties. he lower art of the figure shows the relative uncertainty due to the scale uncertainty of the s that comose the recoil system, defined as the maximum relative shift with resect to the nominal value, as a function of Recoil. he systematic uncertainty on the recoil system has been calculated taking into account the following effects:. JES uncertainty: he JES uncertainty described in Section 9 is alied to each comosing the recoil system.. Close-by : Jets belonging to the recoil system are often roduced with another nearby in the multi environment, and the resonse is deendent on the angular distance to the closest. he close-by uncertainty has been estimated by studying the ratio between the calorimeter s and matched track s as a function of the transverse momentum for different isolation cuts. his uncertainty is discussed in more detail in Section 7.. Flavour comosition of the recoil system: he JES uncertainty is estimated for the average comosition of the inclusive samle. A discreancy in the secific flavour comosition between data and Monte Carlo simulation may result in an additional JES uncertainty. he rocedure described in Section 8 is used to estimate this uncertainty. It requires as inut the average resonse and the flavour comosition uncertainty as a function of the. In the samles used, the uncertainty on the due to flavour comosition is about %. he systematic uncertainty on MJB due to the uncertainty on Recoil is estimated by calculating the multi balance after shifting the of all s in the recoil system u and down by the systematic uncertainties. he total systematic uncertainty is obtained by summing in quadrature the contribution of each source and is shown in Figure 4 for anti-k t s with R=.6. he contributions of each single source are also shown searately. he standard JES uncertainty is the dominant source of uncertainty over the entire range. he second category of systematic uncertainties includes sources that affect MJB used to robe the energy scale at high. hese are discussed below. Variable Nominal Range Jet GeV 5-5 GeV α. radian.-.4 radian β. radian.5-.5 radian Jet /Recoil able : Nominal cut values and the range of variation used to evaluate the systematic uncertainty on the selection criteria for the multi balance technique. Events below the values are rejected.. he MJB used to robe the leading, due to selection criteria or an imerfect Monte Carlo simulation modelling of the event. he standard JES uncertainty has been obtained for isolated s. In the case of multi events the additional uncertainty due to close-by s (see Section 7) and the different flavour comosition (see Section 8) should be taken into account. In the following the various sources considered are discussed:. Selection criteria: he imerfect descrition given by the Monte Carlo simulation for the variables used to select the events might induce a systematic uncertainty on the multi balance. In order to evaluate this systematic uncertainty, all relevant selection criteria are varied in a range where the corresonding kinematic variables are not strongly biased and can be examined with small enough statistical fluctua-

48 ALAS collaboration: Jet measurement with the ALAS detector 47 Relative analysis+modelling systematic uncertainty ALAS Data otal Jet threshold α cut β cut asymmetry cut Underlying event Fragmentation Pile-u L dt - = 8 b s = 7 ev anti-kt R=.6 EM+JES Recoil (a) / MJB MC MJB Data.5 Data / MC otal statistical+systematic uncertainty PYHIA MC otal systematic uncertainty anti-k t R=.6 Analysis+modeling systematic uncertainty. EM+JES Recoil JES systematic uncertainty.5 5 ALAS Data s = 7 ev L dt - = 8 b (b) Recoil Fig. 4: a) Single contributions as a function of Recoil to the relative uncertainty on MJB due to the sources considered in the selection criteria and event modelling for anti-k t s with R=.6 (various lines) and the total uncertainty (full line) obtained as the squared sum of all uncertainties. b) Ratio of data to Monte Carlo simulation for the multi balance (MJB) as a function of the recoil system for anti-k t s with R =.6. he various shaded regions show the total uncertainty (dark band) obtained as the squared sum of all total systematic uncertainties (light band) and of the statistical uncertainty (error bars). Also dislayed are the contributions to the systematic uncertainty due to multi analysis cuts and event modelling (darkest band) and to the energy scale for s in the recoil system (hatched band). Source uncertainty Jet energy scale of the recoil system 4% Flavour comosition % Close-by s % Jet threshold < % α cut < % β cut < % Jet / Recoil cut % Underlying event modelling % Fragmentation modelling.5% Pile-u < % able : Maximum values of the systematic uncertainties in the whole Recoil range for anti-k t s with R=.4 or R=.6, for all effects considered in the multi balance analysis. tions. he nominal values and the range of variations of the selection criteria are listed in able. he systematic uncertainty on MJB originating from these sources is evaluated by calculating the multi balance after varying the cut for each variable in the range mentioned above. For each value of the selection criteria the ratio (r) between the MJB values calculated from data and Monte Carlo simulation is evaluated as a function of the recoil system. he maximum deviation of the r with varied cuts (r varied ) with resect to the nominal ratio (r nominal ), being exressed in the double ratio r varied /r nominal () is assumed to reresent the systematic uncertainty for the source. A quadratic sum of the systematic uncertainties for all sources is taken as the total systematic uncertainty.. Jet raidity accetance: he analysis uses only s with y <.8 to have a smaller energy scale uncertainty on the recoil system. his selection, however, could cause an additional systematic uncertainty, if the fraction of s roduced outside the raidity range differs in the data and Monte Carlo simulation. his effect is evaluated by studying MJB (calculated as usual from only s with y <.8) for events with Recoil > 8 GeV, as a function of the total transverse energy ( E ) summed over all s with y < 4.5, in the data and Monte Carlo simulation. he agreement between the data and Monte Carlo simulation is satisfactory, and MJB is stable over the entire E range with the largest deviations u to % with the largest deviations at relatively high E. Since the majority of events have a very small E, this effect is considered to be negligible.. Soft hysics modelling: Imerfect modelling of multile arton interactions, of fragmentation and of arton shower radiation may affect the multi balance in two ways. Firstly the selection criteria may act differently on samles with different modelling of the event toology. Secondly MJB itself can be directly affected, since the modelling variation acts differently on the leading and the recoil system. he systematic uncertainty for each of these sources is estimated by evaluating the ratio between the MJB measured using the nominal Monte Carlo simulation and an alternative Monte Carlo simulation samle where the articular

49 48 ALAS collaboration: Jet measurement with the ALAS detector source of uncertainty is varied. As alternative Monte Carlo simulation samles HERWIG++ and PYHIA with the PE- RUGIA tune are used. In addition, the arameter controlling the centre-of-mass energy deendence of the cut-off arameter determining whether an event is roduced via a matrix element or by the underlying event model (PARP(9)) is lowered from PYHIA PARP(9)=.5 to PYHIA PARP(9)=.6. his change increases the energy in the forward region. he systematic uncertainty introduced by these variations is at most %. 4. Pile-u: Imerfect descrition of the ile-u may introduce a systematic uncertainty. his effect is estimated by evaluating the ratio MJB ile u /MJB nominal, () where the nominal samle is simulated without ile-u collisions. he systematic uncertainty due to ile-u is smaller than % for the whole range considered. All systematic uncertainties due to the selection criteria, event modelling and ile-u, and the total uncertainty obtained by summing them in quadrature are shown as a function of Recoil in Figure 4 for anti-k t s with R=.6. he final systematic uncertainty resulting from the uncertainties of the recoil reference system and from the multi balance variable added in quadrature is resented in Figure 4b for anti-k t s with R =.6. he total systematic uncertainty amounts to about 4% for s of = ev. At high transverse momentum the main contribution to the systematic uncertainty is due to the standard JES uncertainty of the EM+JES scheme. he maximum values of the uncertainties in the range considered for each source are summarised in able. he comarison of data to Monte Carlo simulation for all in situ techniques for the seudoraidity range η <. is shown in Figure 4 together with the JES uncertainty region as estimated from the single hadron resonse measurements and systematic variations of the Monte Carlo simulations. he results of the in situ techniques suort the estimate of the JES uncertainty obtained using the indeendent method described in Section 9. Data / MC Multi- rack- γ - direct balance γ - MPF JES uncertainty ALAS Ldt=8 b - s=7 ev Data and Monte Carlo incl.s R=.6, EM+JES anti-k t Fig. 4: Ratio of over reference in data and Monte Carlo simulation for several in situ techniques for η <.. Only statistical uncertainties are shown. Suerimosed is the energy scale uncertainty obtained from single hadron resonse measurements and systematic Monte Carlo simulation variations as a function of (light band) for η <....5 Summary of the multi balance results he data samle collected in allows the validation of the high- energy scale to within 5% u to ev for anti-k t s with R=.6 and u to 8 GeV for s with R=.4 calibrated with the EM+JES scheme. In this range the statistical uncertainty is roughly equivalent to, or smaller than, the systematic uncertainty..5 JES uncertainty from combination of in situ techniques he JES uncertainty can also be obtained by combining the results of the in situ techniques described in the revious sections. In this combination the ability of the Monte Carlo simulation to describe the data, the individual uncertainties of the in situ techniques and their comatibility are considered..4 Summary of JES validation using in situ techniques he energy calibration can be tested in situ using a wellcalibrated object as reference and comaring data to the PYH- IA Monte Carlo simulation tuned to ALAS data [6]. he in situ techniques have been discussed in the revious sections, i.e. the comarison of calorimeter energy to the momentum carried by tracks associated to a (Section.), the direct transverse momentum balance between a and a hoton and the hoton balance using the missing transverse momentum rojection technique (Section.) as well as balance between a high- recoiling against a system of lower s (Section.).5. Combination technique he requirements for combining the uncertainties from the individual in situ techniques are:. Proagate all uncertainties of the individual in situ techniques to the final uncertainty.. Minimise biases on the shaes of the measured distributions, i.e. on the deendence of the data to Monte Carlo simulation ratio.. Otimise the uncertainties on the average while resecting the two revious requirements. his is equivalent to minimise the χ between the average and the individual measurements.

50 ALAS collaboration: Jet measurement with the ALAS detector 49 he combination roceeds in the following stes:. oy Monte Carlo method: Monte Carlo seudo-exeriments are created that reresent the ensemble of measurements and contain the full data treatment chain including interolation and averaging (as described in the following stes). hese seudo-exeriments are used to consistently roagate all uncertainties into the evaluation of the average. he seudo-exeriments reresent the full list of available measurements and take into account all known correlations.. Interolation method: A linear interolation is used to obtain the nominal values 5. he final interolation function er measurement, within the range, is discretised into small ( GeV) bins for the urose of averaging.. Averaging: he data are averaged taking into account all known correlations to minimise the sread in the average measured from the Monte Carlo seudo-exeriments. he combination of the in situ calibration data is erformed using the software ackage HVPools [67]. he systematic uncertainties are introduced in HVPools for each comonent as an algebraic function of or as a numerical value for each data oint. he systematic uncertainties belonging to the same source are taken to be fully correlated throughout all measurements affected. he HVPools ackage transforms the in situ data and associated statistical and systematic covariance matrices into finegrained bins, taking into account the best knowledge of the correlations between the oints within each in situ measurement. Statistical and systematic correlations between the measurements could also be included, but as the different measurements use indeendent events, these correlations are neglected 6. he covariance matrices are obtained by assuming systematic uncertainties corresonding to the same source are fully correlated. Statistical uncertainties, taken as indeendent between the data oints, are added in quadrature to these matrices. he interolated measurements from different in situ methods contributing to a given momentum bin are averaged taking correlations between measurement oints into account. he measurements are erformed at different values and use different binning (oint densities) 7. o derive roer averaging weights for each in situ method, wider averaging regions 8 are defined. hese regions are constructed such that all in situ method covering the corresonding 5 A second order olynomial interolation rovides in rincile a better shae descrition. However, due to the smooth variations in the results of each in situ measurement, the differences between the results obtained with the two interolation rocedures are found to be negligible. 6 Care was taken to avoid an overla of the multi balance and γ- result. Allowing for an overla would have required taking into account the (strong) correlations, without a otential gain in recision. 7 he method avoids relacing missing information in case of a lower oint density (wider binning) by extraolating information from the olynomial interolation. 8 For examle, when averaging two measurements with unequal oint sacing, a useful averaging region would be defined by the measurement of the in situ method with the larger oint sacing, and the range have at least one measurement inside. he averaging regions are used to comute weights for the in situ methods, which are later alied in the bin-wise average in fine GeV bins. he averaging weights for each in situ method are comuted as follows:. he generation of seudo-exeriments fluctuates the data oints around the original measurements taking into account all known correlations. he olynomial interolation is redone for each seudo-exeriment for each in situ method.. For each in situ measurement and each Monte Carlo seudoexeriment the new bin content for each wider region is calculated from the integral of the interolating olynomials.. he contents of the wide bins are treated as new measurements and are again interolated with olynomials. he interolation function is used to obtain new measurements in small ( GeV) bins for each in situ method in the range covered by it. 4. In each small bin a covariance matrix (diagonal here) between the measurements of each in situ method is comuted. Using this matrix the averaging weights are obtained by χ minimisation. For the averaging weights the rocedure using the large averaging regions as an intermediate ste is imortant in order to erform a meaningful comarison of the recision of the different in situ methods. he average is comuted avoiding shae biases which would come from the use of large bins. herefore at this next ste the fine GeV bins are obtained directly from the interolation of the original bins. he bin-wise average between measurements is comuted as follows:. he generation of Monte Carlo seudo-exeriments fluctuates the data oints around the original measurements taking into account all known correlations. he olynomial interolation is redone for each generated Monte Carlo seudo-exeriment for each in situ method.. For each generated seudo-exeriment, small ( GeV) bins are filled for each measurement in the momentum intervals covered by that in situ method, using the olynomial interolation.. he average and its uncertainty are comuted in each small bin using the weights reviously obtained. his will be dislayed as a band with the central value given by the average while the total uncertainty on the average is reresent by the band width. 4. he covariance matrix among the measurements is comuted in each small bin. 5. χ rescaling corrections are comuted for each bin as follows: if the χ value of a bin-wise average exceeds the number of degrees of freedom (n dof ), the uncertainty on the average is rescaled by χ /n dof to account for inconsistencies 9. oints of the other measurement would be statistically merged before comuting the averaging weights. 9 Such (small) inconsistencies are seen in the comarison of the γ- and track results in one bin.

51 5 ALAS collaboration: Jet measurement with the ALAS detector he final systematic uncertainty for a given momentum is (conservatively) estimated by the maximum deviation between the average band and unity. he central value (measured bias) and the uncertainty on the average measurement are hence taken into account. If a correction for the measured bias were erformed, only the relative uncertainty on the average would affect the final JES calibration. A smoothing rocedure, using a variable-size sliding interval with a Gaussian kernel, is alied to the systematic uncertainty. It removes sikes due to statistical fluctuations in the measurements, as well as discontinuities at the first and/or last oint in a given measurement. /Resonse Resonse MC Data R=.6, EM+JES anti-k t Data γ- Multi- rack- η <. ALAS s = 7 ev L dt = 8 b Average - total uncertainty Average - statistical comonent - Fig. 44: Average resonse ratio of the data to the Monte Carlo simulation for s with η <. as a function of the transverse momentum for three in situ techniques. he error dislays the statistical and systematic uncertainties added in quadrature. Shown are the results for anti-k t s with R=.6 calibrated with the EM+JES scheme. he light band indicates the total uncertainty from the combination of the in situ techniques. he inner dark band indicates the statistical comonent..5. Combination results Following the method described in the revious section the JES uncertainty for s with η <. can be obtained. he multi balance analysis is reeated for s with η <.. and the uncertainty for low- s is taken from the γ- analysis. he resulting uncertainty is larger than the one in Section.. Figure 44 shows the ratio of the resonse in data and Monte Carlo simulation as a function of the transverse momentum for the three in situ techniques using as reference objects hotons (γ-), a system of low-energetic s (multi) or the transverse momentum of all tracks associated to s (track ). he errors shown for each in situ technique are the statistical and systematic uncertainties added in quadrature. he results from the track s cover the widest range from the lowest to the highest values. Comared to the γ- Relative weight in average R=.6, EM+JES anti-k t Data γ- rack- Multi- η <. ALAS s = 7 ev L dt = 8 b - Fig. 45: Weight carried by each in situ technique in the combination to derive the energy scale uncertainty as a function of the transverse momentum for anti-k t s with R =.6 calibrated with the EM+JES scheme. Relative systematic uncertainty anti-k t R=.6, EM+JES η <. ALAS Data s = 7 ev Default uncertainty L dt = 8 b In situ method combination With correction - Fig. 46: Jet energy scale uncertainty from the combination of in situ techniques (solid line) as a function of the transverse momentum for anti-k t s with R =.6 calibrated with the EM+JES scheme for η <.. he dashed line shows the JES uncertainty that could have been achieved, if in situ techniques had been used to recalibrate the s. For comarison, the shaded band indicates the JES uncertainties as derived from the single hadron resonse measurements and systematic Monte Carlo variations for η <.. results they have a relatively large systematic uncertainty. he γ- results cover a range u to about GeV. From this oint onwards the multi balance method hels to constrain the JES uncertainty. Figure 45 shows the contribution of each in situ technique to the total JES uncertainty in form of their weight. In the region GeV the γ- results make the highest contribution to the overall JES uncertainty determination. he contribution is about 8% at = GeV and decreases to

52 ALAS collaboration: Jet measurement with the ALAS detector 5 about 6% at = GeV. At the lowest the method based on tracks determines the JES uncertainty. At about = GeV the γ- results and the ones based on tracks have an about equal contribution. Above = GeV the results based on tracks have the highest contribution to the JES uncertainty. In this region the multi balance contributes to the JES uncertainty to about %. For the highest only the multi balance is used to determine the JES uncertainty. he final JES uncertainty obtained from the combination of the in situ techniques is shown in Figure 46. he JES uncertainty is about 9% at % for 5 = GeV and decreases to about < GeV. At the lowest the systematic uncertainty is determined by the in situ method based on tracks, for which the data have a higher central value than the Monte Carlo simulation. At 5 GeV, the uncertainty increases because the γ- results are 5% below unity and therefore ull the central value of the average down as shown in Figure 44. Moreover, the γ- and the track methods give different results. While for all other values the χ /n dof is within. χ /n dof <.8, it rises to χ /n dof = at 5 GeV. For > 5 GeV the multi balance contributes to the uncertainty and the resulting uncertainty is about 4 5% u to 7 GeV. At the highest reachable the JES uncertainty increases to %. Figure 46 also comares the JES uncertainty obtained from a combination of in situ techniques to the one derived from the single hadron resonse measurements and the systematic Monte Carlo simulation variations (see Section 9). he in situ JES uncertainty is larger than the standard JES uncertainty in most regions. It is similar in the region 5 GeV. Figure 46 also shows the JES uncertainty, that could have been achieved, if the in situ techniques had been used to correct the energy scale. In this case the JES uncertainty obtained from a combination of in situ techniques would be slightly smaller than the standard JES uncertainty over a wide range of 7 GeV. Jet energy calibration based on global roerties. Global sequential technique he global sequential calibration (GS) technique is a multivariate extension of the EM+JES calibration. Any variable x that is correlated with the detector resonse to the can be used. A multilicative correction to the energy measurement is derived by inverting the calibrated resonse R as a function of this variable: C(x)=R (x)/ R (x), (4) where R (x) denotes the average inverse resonse. After this correction, the remaining deendence of the resonse on the variable x is removed without changing the average energy, resulting in a reduction of the sread of the reconstructed energy and, thus, an imrovement in resolution. Several variables can be used sequentially to achieve the otimal resolution. his rocedure requires that the correction for a given variable x i (C i ) is calculated using s to which the correction for the revious variable x i (C i ) has already been alied. he transverse momentum after correction number i is given by : i = Ci (x i ) i = C i (x i ) C i (x i ) i =... (5). Proerties derived from the internal structure he roerties used in the GS calibration characterise the longitudinal and transverse toology of the energy deosited by the. A large energy deosit in the hadronic layers indicates, for examle, a larger hadronic comonent of the imlying an on average lower detector resonse in the non-comensating ALAS calorimeter. Close to a crack region, the transverse extent of the is correlated to how many articles of the hit the oorly instrumented transition region. Each of these roerties may be sensitive to several effects: energy deosited in the dead material, non-comensation of the calorimeter, or unmeasured energy due to the noise suression. In the GS calibration, no attemt is made to searate these effects. he roerties hel to significantly imrove the energy resolution, and imlicitly correct on average for these effects. he longitudinal structure of the is characterised by the fractional energy deosited in the different layers of the calorimeters before any calibration is alied ( layer fractions ) : f layer = Elayer EM E, (6) EM where E EM is the energy at the EM scale and Elayer EM the energy deosited in the layer of interest, also defined at the EM scale. he transverse structure can be characterised by the width defined as: width = i R i, i i, (7) i where the sums are over the constituents (i) and is the transverse constituent momentum. R i, is the distance in η φ-sace between the constituents and the axis. In the following study too-clusters are used as constituents.. Derivation of the global sequential correction he GS corrections are determined in η bins of width. from η = to η = 4.5. In each bin, the roerties that rovide the largest imrovement in energy resolution have been selected in an emirical way. he chosen roerties and the order in which they are alied are summarised in able. he imrovement in resolution obtained is found to be

53 5 ALAS collaboration: Jet measurement with the ALAS detector η region Corr Corr Corr Corr 4 η <. f ile f LAr f PS width. η <.4 f ile width.4 η <.7 f ile f HEC width.7 η <. f HEC width. η <. f LAr width. η <.4 f LAr.4 η <.5 f LAr width.5 η <.8 f FCal width.8 η <4.5 f FCal able : Sequence of corrections in the GS calibration scheme in each η region. indeendent of which roerty is used first to derive a correction. In the following section, GSL refers to the calibration alied u to the third correction (containing only the calorimeter layer fraction corrections) and GS to the calibration alied u to the last correction (including the width correction). Jet energy scale uncertainties for calibrations based on global roerties he JES uncertainties in the global sequential calibration scheme are evaluated using the transverse momentum balance in events with only two s at high transverse momentum. By construction the GS calibration scheme reserves the energy scale of the EM+JES calibration scheme for the event samle from which the corrections have been derived. Possible changes of the JES in event samles with different toologies or flavours are studied in Section 9.. Validation of the global sequential calibration using di events.. Di balance method he GS corrections can be derived from di events using the di balance method. his method is a tag-and-robe technique exloiting the imbalance between two back-to-back s. In contrast to the method resented in Section 9.6, a correction for a truth imbalance is alied. Di events are selected by requiring that the two highest s are back-to-back ( φ >.8 radian). he two s are required to be in the same seudoraidity region. he whose resonse deendence on the layer fractions or width is studied, is referred to as the robe, while the other is referred to as the reference. he average transverse momentum of the robe and the reference is defined as avg =(robe + ref )/. (8) Since the choice of the reference and the robe is arbitrary, events are always used twice, inverting the roles of reference and robe. Here, longitudinal refers to the direction along the axis. he GS corrections are measured through the asymmetry variable defined as: A(x)= robe (x) ref avg (x), (9) where x is any of the roerties used in the GS calibration (see able ). Both robe and ref deend on x, but the deendence is exlicitly written only for the robe, because the roerty used to build the correction belongs to the robe. he robe and the reference transverse momenta are defined with the same calibration. When comuting correction factor i, they are both corrected u to the (i ) th correction (see Section.). he mean resonse as a function of x is given by: R(x) = + A(x) / A(x) /. (4) he measurement of the resonse through the asymmetry defined in Equation 9 assumes that the asymmetry is zero. his is true on average, but not when comuted in bins of x. he measured asymmetry A(x) is therefore a mixture of detector effects and imbalance at the level of the generated articles. In order to remove the effect of imbalance at the level of generated articles, a new asymmetry is defined: A (x)=a(x) A true (x), (4) where A(x) is given by Equation 9 and A true (x) is: A true (x)= robe,true (x) ref,true avg,true (x), (4) where avg,true (x) = (robe,true (x)+ ref,true )/. he variable A true denotes the asymmetry for truth s (or true asymmetry) and is calculated by matching reconstructed s to truth s. he asymmetry A true is determined in the Monte Carlo simulation. When using A (x) instead of A(x) in Equation 4, the effects of imbalance at the level of generated articles are removed and the resulting resonse deends only on detector effects. Accounting for the truth imbalance is articularly imortant for the corrections that deend on the energy in the resamler and the width... Validation of the di balance method in the Monte Carlo simulation he di balance method can be checked in two different ways. he first uses the default PYHIA event samle with the MC tune and comares the resonse calculated using Equation 4 to the resonse calculated using the truth s. Figure 47 shows this comarison for s after the EM+JES calibration for 8 < GeV and η <.6. he results obtained using the asymmetry defined as in Equation 9 and when incororating the true asymmetry are shown. If the true asymmetry were ignored, the calculated resonse would be different from the the true resonse by u to 4% for high values of the width and the resamler fraction in this articular ference increases with decreasing bin. his dif- reaching 8% for s of

54 ALAS collaboration: Jet measurement with the ALAS detector 5 Resonse..5 ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 8 < < GeV PYHIA MC PYHIA Using A PYHIA Using A-A truth Resonse..5 ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 8 < < GeV PYHIA MC PYHIA Using A PYHIA Using A-A truth 5 5 Difference f PS Difference f LAr (a) f PS (b) f LAr Resonse..5 ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 8 < < GeV PYHIA MC PYHIA Using A PYHIA Using A-A truth Resonse ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 8 < < GeV PYHIA MC PYHIA Using A PYHIA Using A-A truth 5 Difference f ile (c) f ile Difference Width (d) width Fig. 47: Average resonse calculated using truth s (full circles), using the reconstructed asymmetry A (oen circles), and using A A true (triangles) as a function of the calorimeter layer energy fraction f PS (a), f LAr (b), f ile (c) and the lateral width (d) in the PYHIA MC samle. he lower art of each figure shows the differences between the resonse calculated using the truth and the one calculated with the di balance method without A true (full triangles) and with A true (oen circles). Anti-k t s with R=.6 calibrated with the EM+JES scheme are used and have 8 < GeV and η <.6. GeV. hese differences are reduced to less than % when a correction for A true is used. Similar results are found in the other and η bins. he second test comares the true asymmetry between different simulated samles. Figure 48 shows the true asymmetry as a function of f PS, f LAr, f ile and the width in the central region for 4 < 6 GeV for various event samles: the reference PYHIA samle with the MC tune, the PYH- IA samle with the PERUGIA tune and the HERWIG++ samle. he last two samles test the sensitivity to the descrition of soft hysics or the secifics of the hadronisation rocess that could cause differences in the truth imbalance. he true asymmetry differs by no more than 5% in this articular and η bin. For > 6 GeV and other η bins, the true asymmetries differ by less than %. At low (below 4 GeV in the barrel), the φ cut, in articular combined with the small PERUGIA and HERWIG++ samles yield statistical uncertainties of the order of 5%. In summary, the di balance method allows the determination of the resonse as a function of the layer fractions and the width over the entire transverse momentum and seudoraidity ranges. his method can therefore be alied to data to validate the corrections derived in the Monte Carlo simulation.

55 54 ALAS collaboration: Jet measurement with the ALAS detector rue as ymme t ry ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 avg 4 < < 6 GeV PYHIA MC PYHIA PERUGIA HERWIG++ rue as ymme t ry ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 avg 4 < < 6 GeV PYHIA MC PYHIA PERUGIA HERWIG Difference f PS Difference f LAr (a) f PS (b) f LAr rue as ymme t ry ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 4 < avg < 6 GeV PYHIA MC PYHIA PERUGIA HERWIG++ rue as ymme t ry ALAS Simulation s = 7eV anti-k t R=.6, EM+JES η <.6 4 < avg < 6 GeV PYHIA MC PYHIA PERUGIA HERWIG Difference f ile (c) f ile Difference Width (d) Jet width Fig. 48: Average asymmetry for truth s obtained from various Monte Carlo event generators and tunes (PYHIA with the MC and the PERUGIA tune and HERWIG++) as a function of the calorimeter layer fraction f PS (a), f LAr (b), f ile (c) and the lateral width (d) of the robe. Anti-k t s with R=.6 calibrated with the EM+JES scheme are used and have 4 avg < 6 GeV and η <.6. he distributions of the roerties are suerimosed on each figure. he lower art of each figure shows the differences between PYHIA MC and the other Monte Carlo generators... Differences between data based and Monte Carlo based corrections Figure 49 shows the difference between the reconstructed asymmetry and the true asymmetry for the PYHIA MC samle as a function of f PS, f LAr, f ile and width for s with 8 < GeV and η <.6. he reconstructed asymmetries in data and the PYHIA MC samle are comatible within statistical uncertainties. Similar agreement is found in the other η and regions. he asymmetries as shown in Figure 49 are used to derive data based corrections. he difference between data and Monte Carlo simulation rovides a quantitative measure of the additional energy scale uncertainty introduced by the GS calibration. After the first two corrections in able the resonse changes by less than % for data based and Monte Carlo based corrections. he resonse changes by an additional % to % after the third (Presamler) and the fourth (width) corrections are alied in the barrel. he agreement in the endca is within % (4%) for truth > 6 GeV (< 6 GeV). Data based corrections are also derived with true asymmetries coming from the PERUGIA and HERWIG++ samles. hese corrections are then alied to the reference PYHIA MC samle and the resonse yielded is comared to the re-

56 ALAS collaboration: Jet measurement with the ALAS detector 55 A =A-A truth..5 ALAS s = 7eV, L dt = 8 b anti-k t R=.6, EM+JES η <.6 8 < < GeV Data PYHIA MC - A =A-A truth..5 ALAS s = 7eV, L dt = 8 b anti-k t R=.6, EM+JES η <.6 8 < < GeV Data PYHIA MC Difference f PS Difference f LAr (a) f PS (b) f LAr A =A-A truth.5..5 ALAS s = 7eV, L dt = 8 b anti-k t R=.6, EM+JES η <.6 8 < < GeV Data PYHIA MC - A =A-A truth ALAS s = 7eV, L dt = 8 b anti-k t R=.6, EM+JES η <.6 8 < < GeV Data PYHIA MC - Difference f ile (c) f ile Difference Width (d) Jet width Fig. 49: Difference between the average reconstructed asymmetry and the average true asymmetry in data (oen circles) and in the reference PYHIA MC samle (full circles) as a function of the calorimeter layer fractions f PS (a), f LAr (b), f ile (c) and the lateral width (d). he lower art of each figure shows the differences between data and Monte Carlo simulation. Anti-k t s with R=.6 calibrated with the EM+JES scheme are used and have 8 < GeV and η <.6. sonse obtained after alying the reference data based corrections using the true asymmetry from the reference PYHIA MC samle. he difference in resonse is found to be lower than.5% in all the and η bins where the statistical uncertainty is small enough. As a further cross-check the same GS corrections (here the Monte Carlo based ones) are alied to both data and Monte Carlo simulation samles. he difference between data and simulation reflects differences in the roerties used as inut to the GS calibration in the inclusive samles. Figure 5 shows the mean value of f PS, f LAr, f ile and width as a function of in the barrel for data and various Monte Carlo simulation samles: the nominal PYHIA MC, PYHIA PERUGIA and HERWIG++. he agreement for f ile and f PS between data and PYHIA with the MC tune is within 5% over the entire range. For f LAr, this agreement is also within 5% excet for < GeV where a disagreement of 7.5% is observed. A larger disagreement is found for the width. Jets are 5% (%) wider in data than in Monte Carlo simulation at GeV (6 GeV). he standard deviations of the f LAr and the f PS distributions show also agreement within 5% between data and PYH- IA MC simulation for f LAr and f PS over the entire range. For f ile and width, disagreements of % are observed in some bins. Similar results are found in the other

57 56 ALAS collaboration: Jet measurement with the ALAS detector <f PS >.5 ALAS s = 7eV..5. L dt = 8 b - anti-k t R=.6, EM+JES η <.6 Data PYHIA MC PYHIA PERUGIA HERWIG++ <f LAr > ALAS s = 7eV L dt = 8 b - anti-k t R=.6, EM+JES η <.6 Data PYHIA MC PYHIA PERUGIA HERWIG Data/MC Data/MC (a) f PS (b) f LAr <f ile >..5. ALAS s = 7eV L dt = 8 b - anti-k t R=.6, EM+JES η <.6 Data PYHIA MC PYHIA PERUGIA HERWIG++ <Width>.4 ALAS s = 7eV.5 L dt = 8 b..5 - anti-k t R=.6, EM+JES η <.6 Data PYHIA MC PYHIA PERUGIA HERWIG Data/MC Data/MC (c) f ile (d) Jet width Fig. 5: Mean value of the calorimeter layer fractions f PS (a), f LAr (b), f ile (c) and the width (d) as a function of for η <.6 for data and various Monte Carlo simulations. Anti-k t s with R =.6 calibrated with the EM+JES scheme are used. he ratio of data to Monte Carlo simulation is shown in the lower art of each figure. η bins for the calorimeter layer fractions and the width, excet for. η <.8, where the agreement for the width is slightly worse than in the other eta ranges. Figure 5 shows that PYHIA with the MC and the PYH- IA PERUGIA tunes agree to within a few er cent. he agreement of the HERWIG samle with data is as good as for the other samles for f LAr and f ile, excet for < GeV. For f PS and the width, disagreements of 5 % are observed between HERWIG++ and the other samles for < 6 GeV. For > 6 GeV, HERWIG++ is found to describe the width observed in data better than the other samles. he systematic uncertainty can be quantitatively estimated by comaring how the correction coefficients E GS /E EM+JES differ between data and Monte Carlo simulation. he correction coefficient as a function of in the barrel calorimeter in data and in the PYHIA MC samle after GSL and GS corrections are shown in Figure 5a and Figure 5b. he ratios of data to Monte Carlo simulation are shown in the lower art of each figure. Figure 5c and Figure 5d show the same quantity, but as a function of η for 8 < GeV. Deviations from unity in the ratios between data and Monte Carlo simulation as shown in Figure 5 reresent the systematic uncertainty associated to the GS corrections. his uncertainty is added in quadrature to the EM+JES uncertainty. he results for all the and η ranges are the following:

58 ALAS collaboration: Jet measurement with the ALAS detector 57 > /E EM+JES <E GSL Data/MC ALAS s = 7eV L dt = 8 b anti-k t R=.6 η <.6 - (a) GSL comarison PYHIA MC Data GSL > /E EM+JES <E GS Data/MC ALAS s = 7eV L dt = 8 b anti-k t R=.6 η <.6 - (b) GS comarison PYHIA MC Data GS > /E EM+JES <E GSL ALAS s = 7eV - L dt = 8 b anti-k t R=.6 8 < < GeV PYHIA MC Data > /E EM+JES <E GS ALAS s = 7eV - L dt = 8 b anti-k t R=.6 8 < < GeV PYHIA MC Data Data/MC η (c) GSL η comarison Data/MC η (d) GS η comarison Fig. 5: Average energy after GSL (a,c) and GS (b,d) corrections divided by the average energy after the EM+JES calibration as a function of (a,b) in the calorimeter barrel and as a function of η for 8 < GeV (c,d) in data and the Monte Carlo simulation. Anti-k t s with R=.6 are used. he double ratio[e GS(GSL) /E EM+JES ] Data /[E GS(GSL) /E EM+JES ] MC is shown in the lower art of each figure. For < GeV and η <., the data to Monte Carlo ratio varies from.5% to.7% deending on the η region. For > GeV and η <., the uncertainty is lower than.5%. For. η <.8, the the data to Monte Carlo ratio varies from.4% to % deending on the bin. For a given, the uncertainty is higher for. η <.8 than for η <., because of the oorer descrition of the width. For. η <.8 the GSL scheme shows slightly larger difference than the GS scheme. In general, the uncertainty on the data to Monte Carlo ratio is lower than % for < 8 GeV and η <.8. he uncertainty coming from the imerfect descrition of the roerties and the differences between data based and Monte Carlo simulation based corrections resented in Section. are not indeendent. he average resonse after the GS calibration in each and η bin, which deends on both the distribution of the roerties and the GS corrections, is close to the resonse after the EM+JES calibration. A change in the distribution of a roerty therefore translates into a change in the GS correction as a function of this roerty such that the average resonse stays the same in the samle used to derive the correction. he differences described in Section. are therefore artly caused by differences in the roerties.

59 58 ALAS collaboration: Jet measurement with the ALAS detector. Sensitivity of the global sequential calibration to ile-u An imortant feature of the GS calibration is its robustness when alied in the resence of ile-u interactions, which translates into small variations in the size of each of the corrections and the distributions of the roerties. he corrections derived in the samle without ile-u are directly alicable to the samle with ile-u with only a small additional effect on the energy scale. he difference between the resonse after each GS correction and the resonse after the EM+JES calibration in the Monte Carlo simulation samles, after the offset correction as described in Section 8. is alied, changed by less than % for truth > GeV after each of the GS corrections, and by % for lower truth, when samles with and without ile-u are comared. hese variations are smaller than the uncertainty on the energy in the absence of ile-u over the entire range, thus demonstrating the robustness of the additional corrections with resect to ile-u.. Summary on the JES uncertainty for the global sequential calibration he systematic uncertainty on the global sequential calibration in the inclusive samle has been evaluated. It is found to be lower than % for η <.8 and < 8 GeV. his uncertainty is added in quadrature to the JES based on the EM+JES calibration scheme. Jet calibration schemes based on cell energy weighting Besides the simle EM+JES calibration scheme, ALAS has develoed several calibration schemes [8] with different levels of comlexity and different sensitivity to systematic effects. he EM+JES calibration facilitates the evaluation of systematic uncertainties for the early analyses, but the energy resolution is rather oor and it exhibits a rather high sensitivity of the resonse to the flavour of the arton inducing the. hese asects can be imroved using more sohisticated calibrations. he ALAS calorimeters are non-comensating and give a lower resonse to hadrons than to electrons or hotons. Furthermore reconstruction inefficiencies and energy deosits outside the calorimeters lower the resonse to both electromagnetic and hadronic articles, but in different ways. he main motivation for calibration schemes based on cell energy density is to imrove the energy resolution by weighting differently energy deosits from electromagnetic and hadronic showers. he calorimeter cell energy density is a good indicator, since the radiation length X is much smaller than the hadronic interaction length λ I. wo calibration schemes imlementing this idea have been develoed:. For the global calorimeter cell energy density calibration (GCW) the weights deend on the cell energy density and are obtained from Monte Carlo simulation by otimising Calorimeter Layer Nb. E/V Poly. Degree bins on E/V PresamlerB PresamlerE EMB EME EMB and EMB with η < EMB and EMB with η EME and EME with η < EME and EME with η ilebar, ilebar and ilebar 6 4 ileext, ileext and ileext 6 4 HEC- with η < HEC- with η FCAL 6 FCAL and FCAL 6 Cryo term Ga Scint able 4: Number of energy density bins er calorimeter layer used in the GCW calibration scheme and the degree of the olynomial function used in the weight arametrisation. the reconstructed energy resolution with resect to the true energy. his calibration is called global because the is calibrated as a whole and, furthermore, the weights that deend on the calorimeter cell energy density are derived such that fluctuations in the measurement of the energy are minimised and this minimisation corrects for all effects at once.. For the local cluster calibration (LCW) multile variables at the calorimeter cell and the too-cluster levels are considered in a modular aroach treating the various effects of non-comensation, dead material deosits and out-ofcluster deosits indeendently. he corrections are obtained from simulations of charged and neutral articles. he tooclusters in the calorimeter are calibrated locally, without considering the context, and s are then reconstructed directly from calibrated too-clusters. Final energy scale corrections also need to be alied to the GCW and LCW calibrated s, but they are numerically smaller than the ones for the EM+JES calibration scheme. hese corrections are derived with the same rocedure as described in Section 8. he resulting s are referred to as calibrated with GCW+JES and LCW+JES schemes.. Global cell energy density weighting calibration his calibration scheme (GCW) attemts to assign a larger celllevel weight to hadronic energy deositions in order to comensate for the different calorimeter resonse to hadronic and electromagnetic energy deositions. he weights also comensate for energy losses in the dead material. In this scheme, s are first found from too-clusters or calorimeter towers at the EM scale. Secondly the energies of the calorimeter cells forming s are weighted according to their energy density. Finally, a JES correction is derived from

60 ALAS collaboration: Jet measurement with the ALAS detector 59 the sum of the weighted energy in the calorimeter cells associated to the as a function of the and seudoraidity. he weights are derived using Monte Carlo simulation information. A reconstructed is first matched to the nearest truth requiring R min <.. No second truth should be within a distance of R=. he nearest truth should have a transverse energy E > GeV. he transverse energy of the reconstructed should be E EM > 5 GeV, where E EM is the transverse energy of the reconstructed measured at the electromagnetic scale. For each, calorimeter cells are identified with an integer number i denoting a calorimeter layer or a grou of layers in the ALAS calorimeters. Afterwards, each cell is classified according to its energy density which is defined as the calorimeter cell energy measured at the electromagnetic scale divided by the geometrical cell volume (E/V). A weight w i j is introduced for each calorimeter cell within a layer i at a certain energy density bin j. he cells are classified in u to 6 E/V bins according to the following formula: j = ln E/ GeV V/mm + 6, (4) ln where j is an integer number between and 5. Calorimeter cells in the resamler, the first layer of the electromagnetic calorimeter, the ga and crack scintillators (Ga, Scint) are excluded from this classification. A constant weight is alied to these cells indeendent of their E/V. he cryostat (Cryo) term is comuted as the geometrical average of the energy deosited in the last layer of the electromagnetic barrel LAr calorimeter and the first layer of the ile calorimeter. his gives a good estimate of the energy loss in the material between thelar and theile calorimeters. In the case of the seven layers without energy density segmentation the weights are denoted by v i. able 4 shows the number of energy density bins for each calorimeter layer. he energy is then calculated as: E GCW = 6 i= j= w i j E i j + 7 i= v i E i, (44) where w i j (v i ) are the GCW calibration constants. In order to reduce the number of degrees of freedom, for a given layer i, the energy density deendence of each element w i j is arameterised by a common olynomial function of third and fourth degree deending on the layer (see able 4). In this way the number of free arameters used to calibrate any is reduced from 67 to 45. he weights are comuted by minimising the following function: χ = N N = ( E GCW E ), (45) truth where N is the total number of s in the Monte Carlo samle used. his rocedure rovides weights that minimise the energy resolution. he mathematical bias on the mean energy that is introduced in articular at low energies (see Ref. [68]) is corrected by an additional energy calibration following the method described in Section 8 and discussed in Section... Local cluster weighting calibration his calibration scheme [6, 69] corrects locally the too-clusters in the calorimeters indeendent of any context. he calibration starts by classifying too-clusters as mainly electromagnetic or hadronic deending on cluster shae variables [57]. he cluster shae variables characterise the toology of the energy deosits of electromagnetic or hadronic showers and are defined as observables derived from calorimeter cells with ositive energy in the cluster and the cluster energy. All weights deend on this classification and both hadronic and electromagnetic weights are alied to each cluster... Barycentre of the longitudinal cluster deth he barycentre of the longitudinal deth of the too-cluster (λ centre ) is defined as the distance along the shower axis from the front of the calorimeter to the shower centre. he shower centre has coordinates: i = k E k > E k i k k Ek > E k, (46) with i taking values of the satial coordinates x,y,z and E k denoting the energy in the calorimeter cell k. Only calorimeter cells with ositive energy are used. he shower axis is determined from the satial correlation matrix of all cells in the too-cluster with ositive energies: C i j = k E k > Ek (i k i )( j k j ) k Ek> Ek, (47) with i, j= x,y,z. he shower axis is the eigenvector of this matrix closest to the direction joining the interaction oint and the shower centre... Cluster isolation he cluster isolation is defined as the ratio of the number of unclustered calorimeter cells that are neighbours of a given too-cluster to the number of all neighbouring cells. he neighbourhood relation is defined in two dimensions, i.e. within the individual calorimeter layer. After calculating the cluster isolation for each individual calorimeter layer, the final cluster isolation variable is obtained by weighting the individual layer cell ratios by the energy fractions of the too-cluster in these layers. his assures that the isolation is evaluated where the too-cluster has most of its energy. he cluster isolation is zero for too-clusters where all neighbouring calorimeter cells in each layer are inside other tooclusters and one for too-clusters with no neighbouring cell inside any other too-cluster. Unclustered calorimeter cells that are not contained in any toocluster. In general, too-clusters are formed in a three dimensional sace defined by η, φ and the calorimeter deth.

61 6 ALAS collaboration: Jet measurement with the ALAS detector Jet resonse.. ALAS simulation Barrel Barrel-Endca ransition Endca Endca-Forward ransition Forward Jet resonse.. ALAS simulation Barrel Barrel-Endca ransition Endca Endca-Forward ransition Forward R =.6, GCW+JES Anti-k t E = GeV E = 6 GeV E = GeV E = 4 GeV E = GeV (a) GCW η det.7.6 R =.6, LCW+JES Anti-k t E = GeV E = 6 GeV E = GeV E = 4 GeV E = GeV (b) LCW η det Fig. 5: Average simulated energy resonse at the GCW (a) and the LCW (b) scale in bins of the GCW+JES and LCW+JES calibrated energy and as a function of the detector seudoraidity η det... Cluster energy correction All corrections are derived from the Monte Carlo simulations for single charged and neutral ions. he hadronic shower simulation model used is QGSP BER. he detector geometry and too-cluster reconstruction is the same as in the nominal Monte Carlo simulation samle. A flat distribution in the logarithm of ion energies from MeV to ev is used. he corrections are derived with resect to the true deosited energy in the active and inactive detector region ( calibration hits ). rue energy deositions are classified in three tyes by the ALAS software:. he visible energy, like the energy deosited by ionisation.. he invisible energy, like energy absorbed in nuclear reactions.. he escaed energy, like the energy carried away by neutrinos. he local cluster calibration roceeds in the following stes:. Cluster classification: he exected oulation in logarithmic bins of the too-cluster energy, the cluster deth in the calorimeter, and the average cell energy density are used to calculate classification weights. he weights are calculated for small η regions by mixing neutral and charged ions with a ratio of :. his assumes that / of the ions should be charged. Clusters are classified as mostly electromagnetic or mostly hadronic. he calculated weight denotes the robability for a cluster to stem from a hadronic interaction.. Hadronic weighting: oo-clusters receive calorimeter cell correction weights derived from detailed Monte Carlo simulations of charged ions. Calorimeter cells in too-clusters are weighted according to the too-cluster energy and he escaed energy is recorded at the lace where the article that escaes the detector volume ( world volume in GEAN4 terminology) is roduced. the calorimeter cell energy density. he hadronic energy correction weights are calculated from the true energy deosits as given by the Monte Carlo simulation (w HAD ) multilied by a weight to take into account the different nature of hadronic and electromagnetic showers. he alied weight is w HAD +w EM ( ), (48) where w EM = and is the robability of the too-cluster to be hadronic as determined by the classification ste. Dedicated correction weight tables for each calorimeter layer in.-wide η -bins are used. he correction weight tables are binned logarithmically in too-cluster energy and cell energy density (E/V).. Out-of-cluster (OOC) corrections: A correction for isolated energy deosits inside the calorimeter, but outside tooclusters is alied. hese are energy deositions not assing the noise thresholds alied during the clustering. hese corrections deend on η, the energy measured around the too-cluster and the cluster barycentre λ centre. here are two sets of constants for hadronic and electromagnetic showers and both are used for each cluster with the resective weights of and. he OOC correction is finally multilied with the cluster isolation value discussed in Section.. in order to avoid double counting. 4. Dead material (DM) corrections: Energy deosits in materials outside the calorimeters are corrected. For energy deosits in ustream material like the inner wall of the cryostat, the resamler signals are highly correlated to the lost energy. he corrections are derived from the sum of true energy deositions in the material in front and behind the calorimeter and from the resamler signal. he correction for energy deosited in the outer cryostat wall between the electromagnetic and the hadronic barrel calorimeters is based on the geometrical mean of the energies in the layers just before and just beyond the cryostat

62 ALAS collaboration: Jet measurement with the ALAS detector 6 wall. Corrections for other energy deosits without clear correlations to too-cluster observables are obtained from look-u tables binned in too-cluster energy, the seudoraidity η, and the shower deth. wo sets of DM weights for hadronic and electromagnetic showers are used. he weights are alied according to the classification robability defined above. All corrections are defined with resect to the electromagnetic scale energy of the too-cluster. Since only calorimetric information is used, the LCW calibration does not account for low-energy articles which do not create a too-cluster in the calorimeter. his is, for instance, the case when the energy is absorbed entirely in inactive detector material or articles are bent outside of the calorimeter accetance.. Jet energy calibration for s with calibrated constituents he simulated resonse to s at the GCW and LCW energy scales, i.e. after alying weights to the calorimeter cells in s or after the energy corrections to the too-clusters, are shown in Figure 5 as a function of η det for various energy bins. he inverse of the resonse shown in each bin is equal to the average energy scale correction. he final energy correction needed to restore the reconstructed energy to the true energy is much smaller than in the case of the EM+JES calibration shown in Figure. 4 Jet energy scale uncertainties for calibrations based on cell weighting he energy scale uncertainty for s based on cell weighting is obtained using the same in situ techniques as described in Section. he results for each in situ technique together with the combination of all in situ techniques are discussed in Section 4.. In order to build u confidence in the Monte Carlo simulation the descrition of the variables used as inuts to the cell weighting by the Monte Carlo simulation is discussed in Section 4. for the global cell weighting scheme and in Section 4. for the local cluster weighting scheme. Only calorimeter cells inside s with > GeV and y <.8 built of too-clusters and with a cell energy of at least two standard deviations above the noise thresholds are considered for this comarison. Similar results have been obtained using cells inside s built from calorimeter towers. he Monte Carlo simulation reroduces the generic features of the data over many orders of magnitude. However, the following aragrahs discusses those differences, all of which are on the order of a few ercent. Figure 5 shows the calorimeter cell energy density distributions in data and Monte Carlo simulation for cells in reresentative longitudinal segments of the barrel and forward calorimeters. Fewer cells with high energy density are observed in data than redicted by Monte Carlo simulation in the barrel resamler (a) and in the second layer of the barrel electromagnetic calorimeter (b). his behaviour is observed for other segments of the barrel electromagnetic calorimeter, but not for the second layer of the ile barrel calorimeter (c). Here, a good agreement between data and Monte Carlo simulation is found over the full energy density sectrum. Only for the lowest energy densities are slight differences found. Good agreement is also resent in the first layer of the ile extended barrel calorimeter, while the energy density is on average smaller for the second and third layer in the data than in the Monte Carlo simulation. Such a deficit of high energy density cells in data is also observed for the second and third layer of the scintillators laced in the ga between the ile barrel and extended barrel modules. Better agreement is found between data and Monte Carlo simulation for the first layer of the scintillators. he second layer of the endca electromagnetic calorimeter (d) shows a similar behaviour to that observed in the barrel: fewer cells are found at high energy density in the data than in the Monte Carlo simulation. his effect is resent in all three layers of the endca electromagnetic calorimeter, yet it becomes more ronounced with increasing calorimeter deth. A similar effect, but of even larger magnitude has been observed for cells belonging to the endca resamler. he first layer of the endca hadronic calorimeter (e) shows a better agreement between data and Monte Carlo simulation. his agreement is also resent for other layers of the HEC. In the first layer of the forward calorimeter more cells with energy densities in the middle art of the sectrum are found in data than in Monte Carlo simulation (f). his effect has been observed in other FCAL layers, and it becomes slightly more ronounced with increasing FCAL deth. 4. Energy density as inut to the global cell weighting calibration he global cell energy density weighting calibration scheme (see Section.) alies weights to the energy deosited in each calorimeter cell according to the calorimeter cell energy density (E/V, where V is the calorimeter cell volume defined before). his attemts to comensate for the different calorimeter resonse to hadronic and electromagnetic showers, but it also comensates for energy losses in the dead material. he descrition of the calorimeter cell energy density in the Monte Carlo simulation is therefore studied to validate this calibration scheme. 4. Cluster roerties inside s as inut to the local cluster weighting calibration he LCW weights are defined with resect to the electromagnetic scale energy of the too-clusters and can therefore be alied in any arbitrary order. his allows systematic checks of the order in which the corrections are alied. here are four cluster roerties used in the LCW calibration scheme:. he energy density in cells in too-clusters.. he cluster energy fraction deosited in different calorimeter layers.. he isolation variable characterising the energy around the cluster.

63 ] 6 ALAS collaboration: Jet measurement with the ALAS detector - N / ( E ) [MeV Data/MC 7 anti-k t R=.6 GCW+JES PreSamlerB ALAS Data PYHIA MC log [ E / MeV ] s = 7 ev log [ E / MeV ] (a) BarrelPresamler mm ] - N / ( E /V) [MeV Data/MC EMB ALAS anti-k t R=.6 GCW+JES Data PYHIA MC = 7 ev log [ E /V / (MeV / mm ) ] log [ E /V / (MeV / mm ) ] (b) Second layeremb s mm ] - N / ( E /V) [MeV Data/MC ilebar ALAS anti-k t R=.6 GCW+JES Data PYHIA MC = 7 ev log [ E /V / (MeV / mm ) ] log [ E /V / (MeV / mm ) ] (c) Second layer ile in barrel s mm ] - N / ( E /V) [MeV Data/MC EME ALAS anti-k t R=.6 GCW+JES Data PYHIA MC = 7 ev log [ E /V / (MeV / mm ) ] log [ E /V / (MeV / mm ) ] (d) Second layer ofemec s mm ] - N / ( E /V) [MeV Data/MC HEC ALAS anti-k t R=.6 GCW+JES Data PYHIA MC = 7 ev log [ E /V / (MeV / mm ) ] log [ E /V / (MeV / mm ) ] (e) First layer ofhec s mm ] - N / ( E /V) [MeV Data/MC FCAL ALAS anti-k t R=.6 GCW+JES Data PYHIA MC = 7 ev log [ E /V / (MeV / mm ) ] log [ E /V / (MeV / mm ) ] (f) First layer offcal s Fig. 5: Calorimeter cell energy density distributions used in the GCW calibration scheme in data (oints) and Monte Carlo simulation (shaded area) for calorimeter cells in the barrel resamler (a), the second layer of the barrel electromagnetic calorimeter (b), the second layer of the barrel hadronic ile calorimeter (c), the second layer of the endca electromagnetic calorimeter (d), the first layer of the endca hadronic calorimeter (e) and the first layer of the forward calorimeter (f). Anti-k t s with R=.6 requiring > GeVand y <.8 calibrated with the GCW+JES scheme are used. Monte Carlo simulation distributions are normalised to the number of cells in data distributions. he ratio of data to Monte Carlo simulation is shown in the lower art of each figure. Only statistical uncertainties are shown. 4. he deth of the cluster barycentre in the calorimeter. In addition, the cluster energy after each correction ste and the cluster location can be comared in data and Monte Carlo simulation. 4.. Cluster isolation Figure 54 shows the distributions of the cluster isolation variable for all too-clusters in calibrated s with > GeV and y <.8 for too-clusters classified as electromagnetic (a) and hadronic (b). he cluster isolation variable is bounded between and, with higher values corresonding to higher isolation (see Section..). Most of the too-clusters in lower energetic s have a high degree of isolation. he eaks at.5,.5 and.75 are due to the too-clusters in boundary regions which are geometrically difficult to model or regions with a small number of calorimeter cells. Such too-clusters contain redominantly ga scintillator cells or are located at the boundary of the HEC and the FCAL calorimeters.

64 ALAS collaboration: Jet measurement with the ALAS detector 6 Number of clusters / ALAS Electromagnetic clusters in s R=.6 LCW+JES anti-k t y <.8, LCW+JES Data PYHIA MC > GeV s = 7 ev (a) Electromagnetic too-clusters Cluster isolation Number of clusters / ALAS Hadronic clusters in s R=.6 LCW+JES anti-k t y <.8, LCW+JES Data PYHIA MC > GeV s = 7 ev (b) Hadronic too-clusters Cluster isolation Fig. 54: Distributions of the isolation variable for too-clusters classified as electromagnetic (a) and as hadronic (b) in data (oints) and Monte Carlo simulation (shaded area). oo-clusters associated to anti-k t s with R=.6 with > GeV and y <.8 calibrated with the LCW+JES scheme are used. Mean cluster isolation ALAS Electromagnetic clusters in s anti-k t R=.6 LCW+JES LCW+JES y <.8, > GeV Data s = 7 ev PYHIA MC Mean cluster isolation ALAS Hadronic clusters in s anti-k t R=.6 LCW+JES LCW+JES y <.8, > GeV Data s = 7 ev PYHIA MC Cluster energy at EM-scale [MeV] 4.6 Cluster energy at EM-scale [MeV] 4 (a) Electromagnetic too-clusters (b) Hadronic too-clusters Fig. 55: Mean value of the cluster isolation variable for too-clusters classified as electromagnetic (a) and as hadronic (b) as a function of the too-cluster energy measured at the EM scale, in data (closed circles) and Monte Carlo simulation (oen squares). oo-clusters associated to anti-k t s with R=.6 with > GeV and y <.8 calibrated with the LCW+JES scheme are used.

65 64 ALAS collaboration: Jet measurement with the ALAS detector Number of clusters / 6mm 4 ALAS Electromagnetic clusters in s anti-k R=.6 LCW+JES t LCW+JES y <.8, > GeV Data PYHIA MC Number of clusters / 6mm 5 4 ALAS Hadronic clusters in s anti-k R=.6 LCW+JES t LCW+JES y <.8, > GeV Data PYHIA MC Cluster λ centre [mm] (a) Electromagnetic too-clusters Cluster λ centre [mm] (b) Hadronic too-clusters Fig. 56: Distributions of the longitudinal cluster barycentre λ centre for too-clusters classified as electromagnetic (a) and as hadronic (b) in data (oints) and Monte Carlo simulation (shaded area). oo-clusters associated to anti-k t s with R=.6 with > GeV and y <.8 calibrated with the LCW+JES scheme are used. [mm] Mean cluster λ centre Electromagnetic clusters in s 8 anti-k t R=.6 cluster s LCW+JES y <.8, > GeV 6 4 ALAS Data s = 7 ev PYHIA MC [mm] Mean cluster λ centre ALAS Hadronic clusters in s anti-k t R=.6 cluster s LCW+JES y <.8, > GeV Data s = 7 ev PYHIA MC Cluster energy at EM-scale [MeV] (a) Electromagnetic too-clusters 4 Cluster energy at EM-scale [MeV] (b) Hadronic too-clusters 4 Fig. 57: Mean value of the longitudinal cluster barycentre λ centre as a function of the too-cluster energy measured at the EM scale for too-clusters classified as electromagnetic (a) and as hadronic in data (b) in data (closed circles) and Monte Carlo simulation (oen squares). oo-clusters associated to anti-k t s with R=.6 with > GeV and y <.8 calibrated with the LCW+JES scheme are used.

66 br_cluster_emscale_e br_cluster_emscale_e br_cluster_emscale_e ALAS collaboration: Jet measurement with the ALAS detector 65 W /E calib EM-scale E Data/MC LCW+JES ALAS Data PYHIA MC s=7 ev > GeV, y <..5 br_cluster_emscale_eta E too-cluster W /E calib EM-scale E DAA/MC LCW+JES ALAS Data PYHIA MC > GeV s=7 ev η too-cluster (a) Hadronic resonse weights /E EM-scale W+OOC calib E Data/MC ALAS LCW+JES Data PYHIA MC s=7 ev > GeV, y <..5 br_cluster_emscale_eta E too-cluster /E EM-scale W+OOC calib E Data/MC LCW+JES ALAS Data PYHIA MC > GeV s=7 ev η too-cluster (b) Hadronic resonse and out-of-cluster weights /E EM-scale W+OOC+DM calib E Data/MC LCW+JES ALAS Data PYHIA MC s=7 ev > GeV, y < E too cluster /E EM scale W+OOC+DM calib E Data/MC LCW+JES ALAS Data PYHIA MC > GeV s=7 ev η too cluster (c) Hadronic resonse, out-of-cluster and dead material weights Fig. 58: Mean calibrated too-cluster energy divided by the uncalibrated too-cluster energy in data (oints) and Monte Carlo simulation (shaded area) as a function of the uncalibrated too-cluster energy (left) and seudoraidity (right) after hadronic resonse weighting (a), adding out-of-cluster corrections (b), and adding dead material corrections (c) alied to too-clusters in s. he corrections are sequentially alied. Anti-k t s with R =.6 in the LCW+JES scheme are required to have > GeV. In addition, for the results as a function of the too-cluster energy (left) the s have been restricted to y <..

67 66 ALAS collaboration: Jet measurement with the ALAS detector he features observed are similar for too-clusters classified as mostly electromagnetic and those classified as mostly hadronic. A reasonable agreement between data and Monte Carlo simulation (see Fig. 54) is found. he agreement in the eaks corresonding to the transition region between calorimeters is not as good as in the rest of the distribution. Figure 55 shows the mean value of the too-cluster isolation variable as a function of the too-cluster energy for all too-clusters in s with > GeV and y <.8 for tooclusters classified as electromagnetic (a) or as hadronic (b). he Monte Carlo simulation consistently redicts more isolated too-clusters than observed in the data, articularly at too-cluster energies E < GeV and for both hadronic and electromagnetic cluster classifications. his feature is resent in all raidity regions, excet for very low energy too-clusters classified as mostly electromagnetic in very central s. 4.. Longitudinal cluster barycentre Figure 56 shows the cluster barycentre λ centre distributions for all too-clusters in LCW calibrated s with > GeV and y <.8 and for both cluster classifications. Most too-clusters classified as electromagnetic have their centre in the electromagnetic calorimeter, as exected. hose too-clusters classified as mostly hadronic are very often in the electromagnetic calorimeter, since these low s do not enetrate far into the hadronic calorimeter. However, a structure is observed, related to the osition of the different longitudinal layers in the hadronic calorimeter. his structure is more rominent when looking at individual raidity regions, being smeared where the geometry is not changing in this inclusive distribution. Good agreement is observed between data and Monte Carlo simulation. Figure 57 shows the mean value of distributions of λ centre as a function of the cluster energy for all too-clusters in s with > GeV and y <.8, again for both tyes of tooclusters. In this case, too-clusters classified as mostly electromagnetic have their barycentre deeer in the calorimeter on average as the cluster energy increases. A different behaviour is observed for clusters tagged as hadronic, for which the mean deth in the calorimeter increases until aroximately GeV, at which oint the mean deth decreases again. he shae of the mean deth as a function of energy is different for different raidities due to the changing calorimeter geometry. However, the qualitative features are similar, with a monotonic increase u to some too-cluster energy, and a decrease thereafter. his is likely due to an increased robability of a hadronic shower to be slit into two or more clusters with increased cluster energy. A good agreement is observed between data and Monte Carlo simulation. 4.. Cluster energy after LCW corrections In this section the size of each of the three corrections of the too-cluster calibration is studied in data and Monte Carlo simulation. his rovides a good measure of how the differences between data and Monte Carlo simulation observed in revious sections imact the size of the corrections alied. Figure 58 shows the mean value of the ratio of the calibrated too-cluster energy to the uncalibrated too-cluster energy after each calibration ste as a function the too-cluster energy and seudoraidity. Only too-clusters in LCW calibrated s with > GeV are considered. For the results shown as a function of too-cluster energy the seudoraidity of the s is, in addition, restricted to y <.. he agreement between data and Monte Carlo simulation is within 5% for the full seudoraidity range and is generally better for lower too-cluster energies where the correction for the out-of-cluster energy dominates. As the too-cluster energy increases the largest corrections become the hadronic resonse and the dead material corrections. An agreement to about % is observed in a wide region in most of the barrel region after each correction. he agreement between data and Monte Carlo simulation is within % for all too-cluster seudoraidities after the hadronic and the out-of-cluster corrections. Larger differences are observed between data and Monte Carlo simulation in the transition region between the barrel and the endca and in the forward region once the dead material correction is alied. 4. Jet energy scale uncertainty from in situ techniques for s based on cell weighting For the calibration schemes based on cell weighting the JES uncertainty is evaluated using in situ techniques. he same techniques as described in Section are emloyed. he final JES uncertainty is obtained from a combination of all in situ techniques following the rescrition in Section Comarison of transverse momentum balance from calorimeter and tracking he result of the JES validation using the total transverse momentum of the tracks associated to s (see Section.) is shown in Figure 59 for s calibrated with the GCW+JES scheme and in Figure 6 for s calibrated with the LCW+JES scheme in various seudoraidity regions within η <.. he bin η <. is obtained by combining the η <.,. η <.8 and.8 η <. bins. Similar results as for the EM+JES scheme are obtained. In both cases, the agreement between data and simulation is excellent and within the uncertainties of the in situ method. he calibration schemes agree to within a few er cent, excet for the bins with very low numbers of events. 4.. Photon- transverse momentum balance he resonse measured by the direct balance technique (see Section..) for the GCW+JES and LCW+JES calibrations is shown in Figure 6. he agreement of the Monte Carlo simulation with data is similar for both calibration schemes. he data to Monte Carlo agreement is to 5%. Figure 6 shows the comarison of the resonse determined by the MPF technique (see Section..), measured in data and Monte Carlo simulation at the GCW and LCW energy

68 ALAS collaboration: Jet measurement with the ALAS detector ALAS η <. Anti-k t R=.6 GCW+JES - L dt = 6 b s = 7 ev Data ALAS. η <.8 Anti-k t R=.6 GCW+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (a) η <. (b). η < ALAS.8 η <. Anti-k t R=.6 GCW+JES - L dt = 6 b s = 7 ev Data ALAS. η <.7 Anti-k t R=.6 GCW+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (c).8 η <. (d). η < ALAS.7 η <. Anti-k t R=.6 GCW+JES - L dt = 6 b s = 7 ev Data ALAS η <. Anti-k t R=.6 GCW+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (e).7 η <. (f) η <. Fig. 59: Double ratio of the track to calorimeter resonse comarison in data and Monte Carlo simulation, R rtrk = [< r trk > ] Data /[< r trk >] MC, for anti-k t s with R=.6 using the GCW+JES calibration scheme as a function of for various η bins. Systematic (total) uncertainties are shown as a light (dark) band.

69 68 ALAS collaboration: Jet measurement with the ALAS detector ALAS η <. Anti-k t R=.6 LCW+JES - L dt = 6 b s = 7 ev Data ALAS. η <.8 Anti-k t R=.6 LCW+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (a) η <. (b). η < ALAS.8 η <. Anti-k t R=.6 LCW+JES - L dt = 6 b s = 7 ev Data ALAS. η <.7 Anti-k t R=.6 LCW+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (c).8 η <. (d). η < ALAS.7 η <. Anti-k t R=.6 LCW+JES - L dt = 6 b s = 7 ev Data ALAS η <. Anti-k t R=.6 LCW+JES - L dt = 6 b s = 7 ev Data R rtrk R rtrk Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty.85.8 Minimum bias data Jet trigger data Systematic uncertainty otal uncertainty (e).7 η <. (f) η <. Fig. 6: Double ratio of the track to calorimeter resonse comarison in data and Monte Carlo simulation, R rtrk = [< r trk > ] Data /[< r trk >] MC, for anti-k t s with R=.6 using the LCW+JES calibration scheme as a function of for various η bins. Systematic (total) uncertainties are shown as a light (dark) band.

70 ALAS collaboration: Jet measurement with the ALAS detector 69 / γ. ALAS s = 7 ev L dt = 8 b R=.6, GCW+JES anti k t Data PYHIA MC / γ. ALAS s = 7 ev L dt = 8 b R=.6, LCW+JES anti k t Data PYHIA MC.. Data / MC (a) GCW+JES γ γ Data / MC (b) LCW+JES γ γ Fig. 6: Average resonse as determined by the direct balance technique for anti-k t s with R =.6 calibrated with the GCW+JES (a) and LCW+JES (b) scheme as a function of hoton transverse momentum for both data and Monte Carlo simulation. he lower art of each figure shows the data to Monte Carlo simulation ratio. Only statistical uncertainties are shown. R MPF MPF GCW scale, all algorithms Data PYHIA MC R MPF MPF LCW scale, all algorithms Data PYHIA MC Data / MC ALAS L dt = 8 b s = 7 ev Data / MC ALAS L dt = 8 b s = 7 ev 5 5 γ γ (a) GCW (b) LCW Fig. 6: Average calorimeter resonse as determined by the MPF technique for the GCW (a) and LCW (b) calibration scheme as a function of hoton transverse momentum for both data and Monte Carlo simulation. he lower art of each figure shows the data to Monte Carlo simulation ratio. Only statistical uncertainties are shown.

71 7 ALAS collaboration: Jet measurement with the ALAS detector / ) MC / ( / ) Data.5 γ γ..5 s = 7 ev L dt = 8 b Data R=.6, GCW+JES anti k t Uncertainty Statistical Systematic otal / ) MC / ( ( / ) Data.5 γ γ..5 s = 7 ev L dt = 8 b Data R=.6, LCW+JES anti k t Uncertainty Statistical Systematic otal ( ALAS ALAS (a) GCW+JES γ (b) LCW+JES γ Fig. 6: Average resonse in data to the resonse in Monte Carlo simulation using the direct balance technique of anti-k t s with R =.6 calibrated with the GCW+JES (a) and LCW+JES (b) scheme as a function of hoton transverse momentum. Statistical and systematic uncertainties (light band) are included with the total uncertainty shown as the dark band. R Data /R MC.5..5 ALAS L dt = 8 b s = 7 ev Data R Data /R MC.5..5 MPF LCW, all algorithms Uncertainty Statistical Systematic otal 5 MPF GCW, all algorithms Uncertainty Statistical Systematic otal (a) GCW γ 5 L dt = 8 b s = 7 ev Data ALAS (b) LCW γ Fig. 64: he ratios of the MPF calorimeter resonse in data to the resonse in Monte Carlo simulation using the MPF method for each inut energy scale GCW (a), and LCW (b) as a function of the hoton transverse momentum. Statistical and systematic uncertainties (light band) are included. he total uncertainty is shown as the dark band.

72 ALAS collaboration: Jet measurement with the ALAS detector 7 Fractional uncertainty form di balance ALAS Data (a) GCW+JES R =.6, GCW+JES Anti k t.6 η < η <.. η <.8. η <. Fractional uncertainty form di balance ALAS Data (b) LCW+JES R =.6, LCW+JES Anti k t.6 η < η <.. η <.8. η <. Fig. 65: Uncertainty in the resonse obtained from the di η-intercalibration technique for anti-k t s with R =.6 as a function of the for various η -regions of the calorimeter. he s are calibrated with the GCW+JES (a) and the LCW+JES (b) calibration schemes. Only statistical uncertainties are shown. scales. o calculate the resonse using the MPF technique at these energy scales the E miss is calculated using GCW or LCW calibrated too-clusters as an inut 4. All the JES calibrations are found to be consistent between data and Monte Carlo simulation to within to 4%. he ratios of resonse in data to the resonse in Monte Carlo simulation using the direct balance technique for the GCW+JES and LCW+JES calibration schemes as a function of the hoton transverse momentum are shown in Figure 6. he agreement of data and Monte Carlo simulation is within 5% and is comatible with unity within the statistical and systematic uncertainties. A similar result for the MPF technique is shown in Figure 64. Good agreement between data and Monte Carlo simulation is found. (see Section 4..) and using the sum of track momenta (Section 4..). Figure 65 shows the resulting uncertainties as a function of for various η-bins. he uncertainty is taken as the RMS sread of the relative resonse from the Monte Carlo redictions around the relative resonse measured in data (see Section 9.6.6). he JES uncertainty introduced by the di balance is largest at lower and smallest at higher. For > GeV the JES uncertainty for the GCW+JES scheme is less than % for. η <. and about.5% for.8 η <.. For = GeV the JES uncertainty is about % for. η <. and about 9.5% for.6 η <4.5. he JES uncertainties for the LCW+JES calibration scheme are slightly larger than those for GCW+JES scheme. 4.. Intercalibration of forward s using events with di toologies he transverse momentum balance in events with only two s at high transverse energy can be used to determine the JES uncertainty for s in the forward detector region. he matrix method, described in Section 9.6, is used in order to test the erformance of the GCW+JES and LCW+JES calibrations for s with η >. and to determine the JES uncertainty in the forward region based on the well calibrated in the central reference region. he same selection and method as for the test of the EM+JES calibration is alied, with two excetions: the reference region is defined by η det <. instead of η det <.8, and a fit is alied to smooth out statistical fluctuations. he JES uncertainty in the reference regions is obtained from the γ- results 4 For the GCW calibration scheme the cell energies in the tooclusters are multilied by the cell energy weights described in Section Multi transverse momentum balance he multi balance (MJB) technique, described in Section., is used to evaluate the JES uncertainty in the high transverse momentum region for the GCW+JES and LCW+JES calibration schemes. he method and selection cuts used are the same as those for the EM+JES calibrated s. Figure 66 shows the MJB for anti-k t s with R=.6 obtained using the GCW+JES and LCW+JES calibrations in the data and Monte Carlo simulation as a function of the recoil. he agreement between the data and MC simulations, evaluated as the data to Monte Carlo simulation ratio, are very similar to those for the EM+JES calibration. he systematic uncertainties on the MJB for these cell energy weighting calibration schemes are evaluated in the same way as the EM+JES calibration, described in Section..4, excet for the comonent of the standard JES uncertainty on the recoil system. he JES uncertainty for s in the recoil system is obtained from the in situ γ- balance discussed in Section 4... In this case, the systematic uncertainty on the

73 7 ALAS collaboration: Jet measurement with the ALAS detector MJB... ALAS s = 7 ev L dt = 8 b anti kt R=.6 GCW+JES Data PYHIA MC ALPGEN HERWIG++ MJB... ALAS s = 7 ev L dt = 8 b anti kt R=.6 LCW+JES Data PYHIA MC ALPGEN HERWIG++ MJB Data /MJB MC (a) GCW+JES Recoil MJB Data /MJB MC (b) LCW+JES Recoil Fig. 66: Multi balance MJB as a function of the recoil system for data and Monte Carlo simulation for the anti-k t algorithm with R=.6 using the GCW+JES (a) and LCW+JES (b) calibration scheme. Only statistical uncertainties are shown. MJB.. ALAS simulation s = 7 ev Default otal In situ γ+ Flavour Close by MJB.. ALAS simulation s = 7 ev Default otal In situ γ+ Flavour Close by Relative uncertainty.8.. PYHIA MC anti k R=.6 GCW+JES t (a) GCW+JES Recoil Relative uncertainty.8.. PYHIA MC anti k R=.6 LCW+JES t (b) LCW+JES Recoil Fig. 67: he multi balance MJB MC as a function of the recoil system (full dots) for anti-k t s with R =.6 using the GCW+JES (a) and LCW+JES (b) calibration schemes. he three bands are defined by the maximum shift of MJB when the s that comose the recoil system are shifted u and down by the JES uncertainty determined from the γ- balance, close-by and flavour uncertainties. he black lines show the total uncertainty obtained by adding in quadrature the individual uncertainties. he lower art of the figure shows the relative uncertainty due to the scale uncertainty of the s that comose the recoil system, defined as the maximum relative shift with resect to the nominal value, as a function of Recoil.

74 ALAS collaboration: Jet measurement with the ALAS detector 7 / MJB MC MJB Data Data / MC otal statistical+systematic uncertainty otal systematic uncertainty Analysis+modelling systematic uncertainty Recoil JES systematic uncertainty (with in situ γ+) / MJB MC MJB Data Data / MC otal statistical+systematic uncertainty otal systematic uncertainty Analysis+modelling systematic uncertainty Recoil JES systematic uncertainty (with in situ γ+) 5.85 ALAS Data L dt = 8 b PYHIA MC s = 7 ev anti kt R=.6 GCW+JES (a) GCW+JES Recoil 5.85 ALAS Data L dt = 8 b PYHIA MC s = 7 ev anti kt R=.6 LCW+JES (b) LCW+JES Recoil Fig. 68: Ratio of the data to MC for the multi balance as a function of the recoil system for anti-k t s with R=.6 using the GCW+JES (a) and LCW+JES (b) calibration schemes. he various shaded regions show the total uncertainty (dark band) obtained as the squared sum of the total systematic uncertainty (light band) and of the statistical uncertainty (error bars). Also dislayed are the contributions to the systematic uncertainty due to analysis cuts and event modelling (darkest band) and to the energy scale for s in the recoil system (hatched band). /Resonse MC..5. R=.6, GCW+JES anti-k t Data η <. ALAS s = 7 ev L dt = 8 b - /Resonse MC..5. R=.6, LCW+JES anti-k t Data η <. ALAS s = 7 ev L dt = 8 b - Resonse Data.5 5 Resonse Data γ- Multi- rack- Average - total uncertainty Average - statistical comonent (a) GCW+JES.85.8 γ- Multi- rack- Average - total uncertainty Average - statistical comonent (b) LCW+JES Fig. 69: Jet resonse ratio of the data to the Monte Carlo simulation as a function of for three in situ techniques using as reference objects: hotons (γ-), a system of low energetic s (multi) or the transverse momentum of all tracks associated to s (tracks in s). he error bar dislays the statistical and systematic uncertainties added in quadrature. Shown are the results for anti-k t s with R=.6 calibrated with the GCW+JES (a) and LCW+JES (b) calibration schemes. he light band indicates the combination of the in situ techniques. he inner dark band shows the fraction due to the statistical uncertainty.

75 74 ALAS collaboration: Jet measurement with the ALAS detector Relative systematic uncertainty anti-k t R=.6, GCW+JES η <. ALAS Data s = 7 ev In situ method combination L dt = 8 b With correction (a) GCW+JES - Relative systematic uncertainty anti-k t R=.6, LCW+JES η <. ALAS Data s = 7 ev In situ method combination L dt = 8 b With correction (b) LCW+JES - Fig. 7: Jet energy scale uncertainty (solid line) as a function of for anti-k t s with R =.6 for η <. calibrated with the GCW+JES (a) and the LCW+JES (b) calibration scheme. he dashed line shows the JES uncertainty that could have been achieved, if in situ techniques had been used to recalibrate the s. MJB due to the recoil system JES uncertainty is then calculated by shifting the of recoil s u and down by the γ- JES uncertainty. In order to aly the γ- JES uncertainty to the recoil system, the MJB analysis is erformed with s selected within the range η <., where the JES uncertainty based on γ- events has been derived. he close-by and flavour comosition systematic uncertainties are also re-evaluated for the GCW+JES and LCW+JES s using the same method (see Section 7). Figure 67 shows the total and individual JES systematic uncertainties on the recoil system for anti-k t s with R=.6 calibrated by the GCW+JES and LCW+JES schemes. he increase of the JES uncertainty at high above 8 GeV is caused by a large JES systematic uncertainty due to limited γ- event statistics at high. he systematic uncertainties associated with the analysis method and event modelling are re-evaluated in the same way as for the EM+JES calibration scheme and then added to the recoil system JES systematic uncertainties. he summary of all systematic uncertainties and the total uncertainty obtained by adding the statistical and systematic uncertainties in quadrature is shown in Figure 68 for anti-k t s with R= Cell weighting JES uncertainty from combination of in situ techniques Figure 69 shows the resonse ratio of data to Monte Carlo simulation for the various in situ techniques as a function of the transverse momentum for the GCW+JES (a) and the LCW+JES (b) calibration schemes. Statistical and systematic uncertainties are dislayed. he average from the combination of all in situ techniques is overlaid. he weight of each in situ technique contributing to the average is similar to the one for the EM+JES calibration scheme shown in Figure 45. he contributions are also similar for the LCW+JES and the GCW+JES calibration schemes. Figure 7 shows the final JES uncertainty for the GCW+JES (a) and the LCW+JES (b) calibration schemes for η <.. At the lowest the JES uncertainty is about 9% to % and decreases for increasing at. For > 5 GeV it is about % and = 5 GeV it is about to 4%. For s in the ev-regime the JES uncertainty is to %. Figure 7 also shows the JES uncertainty attainable, if the in situ techniques had been used to correct the energy. Using the in situ techniques for calibration would have resulted in an imroved JES uncertainty for both calibration schemes based on cell energy weighting. he JES uncertainty obtained in the central reference region ( η <.) is used to derive the JES uncertainty in the forward region using the di balance technique. he central region JES uncertainty is combined with the uncertainties from the di balance shown in Figure Summary of energy scale uncertainties of various calibration schemes he EM+JES uncertainties are derived from single hadron resonse measurements and from systematic variations of the Monte Carlo simulation (see Section 9). he JES uncertainty for the GS calibration scheme is given by the sum in quadrature of the EM+JES uncertainty and the uncertainty associated to the GS corrections. he latter, derived in Section, is conservatively taken to be.5% for < < 8 GeV and η <. and % for < GeV and. < η <.8. hese uncertainties are also suorted by in situ techniques.

76 ALAS collaboration: Jet measurement with the ALAS detector 75 Fractional JES systematic uncertainty s=7 ev Ldt=8 b R=.6, η <. Anti k t LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty (a) η <. Data + Jet Monte Carlo ALAS Fractional JES systematic uncertainty R=.6,. η <.8 Anti k t s=7 ev Ldt=8 b LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty Data + Jet Monte Carlo (b). η <.8 ALAS Fractional JES systematic uncertainty R=.6,.8 η <. Anti k t s=7 ev Ldt=8 b LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty EM+JES intercalibration uncertainty Data + Jet Monte Carlo (c).8 η <. ALAS Fractional JES systematic uncertainty R=.6,. η <. Anti k t s=7 ev Ldt=8 b LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty EM+JES intercalibration uncertainty LCW+JES intercalibration uncertainty GCW+JES intercalibration uncertainty Data + Jet Monte Carlo (d). η <. ALAS Fractional JES systematic uncertainty R=.6,. η <.8 Anti k t s=7 ev Ldt=8 b LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty EM+JES intercalibration uncertainty LCW+JES intercalibration uncertainty GCW+JES intercalibration uncertainty Data + Jet Monte Carlo (e). η <.8 ALAS Fractional JES systematic uncertainty R=.6,.8 η <. Anti k t s=7 ev Ldt=8 b Data + Jet Monte Carlo (f).8 η <. LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty EM+JES intercalibration uncertainty LCW+JES intercalibration uncertainty GCW+JES intercalibration uncertainty ALAS Fractional JES systematic uncertainty R=.6,. η <.6 Anti k t s=7 ev Ldt=8 b Data + Jet Monte Carlo LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty EM+JES intercalibration uncertainty LCW+JES intercalibration uncertainty GCW+JES intercalibration uncertainty (g). η <.6 ALAS Fractional JES systematic uncertainty R=.6,.6 η < 4.5 Anti k t s=7 ev Ldt=8 b Data + Jet Monte Carlo (h).6 η <4.5 LCW+JES total uncertainty GCW+JES total uncertainty EM+JES total uncertainty EM+JES intercalibration uncertainty LCW+JES intercalibration uncertainty GCW+JES intercalibration uncertainty Fig. 7: Fractional JES uncertainties as a function of for anti-k t s with R=.6 for the various η regions for the LCW+JES (full line) and the GCW+JES (dashed line) schemes. hese are derived from a combination of the in situ techniques which are limited in the number of available events at large. he fractional JES uncertainty for EM+JES derived from single hadron resonse measurements and systematic Monte Carlo simulation variations is overlaid as shaded area for comarison. he η- intercalibration uncertainty is shown as oen symbols for η >.8 for the EM+JES and for η >. for the LCW+JES and GCW+JES schemes. ALAS

77 76 ALAS collaboration: Jet measurement with the ALAS detector he JES uncertainties in the LCW+JES and GCW+JES calibration schemes are derived from a combination of several in situ techniques. Figure 7 shows a comarison of the JES uncertainties for the EM+JES, the LCW+JES and the GCW+JES calibration schemes for various η-regions. he uncertainties in the LCW+JES and GCW+JES schemes derived in Section 4 are similar, but the uncertainty for the GCW+JES calibration scheme is a bit smaller for very low and very large. Over a wide kinematic range, 4 6 GeV, all calibration schemes show a similar JES uncertainty. At 5 GeV the uncertainties based on the in situ techniques are about % larger comared to the uncertainty results from the EM+JES calibration scheme. For < 4 GeV and > 6 GeV the EM+JES calibration scheme has a considerably smaller uncertainty. For the high regions the JES calibration based on in situ suffers from the limited number of events in the data samles. At low the systematic uncertainty on the in situ methods leads to a larger JES uncertainty. 6 Jet reconstruction efficiency A tag-and-robe method is imlemented to measure in situ the reconstruction efficiency relative to track s. Because track s (see Section 6.) and calorimeter s (see Section 6.) are reconstructed by indeendent ALAS sub-detectors, a good agreement between data and Monte Carlo simulation for this matching efficiency means that the absolute reconstruction efficiency can be determined from the simulation. 6. Efficiency in the Monte Carlo simulation he reconstruction efficiency is determined in the Monte Carlo simulation by counting in how many cases a calorimeter can be matched to a truth. Reconstructed s are matched to truth s, if their axes are within R<.4. Figure 7a shows the reconstruction efficiency for antik t s with R=.6 calibrated with the EM+JES, GCW+JES, and LCW+JES calibration schemes as a function of the transverse momentum of the truth. he efficiency reaches its maximum value for a truth transverse momentum of GeV. he lower art of the figure shows the ratio of the efficiency in the GCW+JES and LCW+JES calibration schemes to that obtained from the EM+JES scheme. Similar erformance is found for all calibration schemes. he small differences at low might be caused by the slightly better energy resolution obtained with the GCW+JES and the LCW+JES calibration schemes. Moreover, s based on the LCW+JES scheme are built from calibrated too-clusters while the s calibrated with the EM+JES and the GCW+JES calibration schemes use too-clusters at the electromagnetic scale. 6. Efficiency in situ validation he ability of the Monte Carlo simulation to correctly reroduce the reconstruction in the data is tested using track s that rovide an indeendent reference. A tag-and-robe technique is used as described in the following stes:. Only track s with > 5 GeV and η <.9 are considered.. he track with the highest in the event is defined as the reference object.. he reference object is required to have > 5 GeV he reference track is matched to a calorimeter with > 7 GeV, if R(tag,calo)< he robe track must be back-to-back to the reference in φ with φ.8 radian. 6. Events with additional track s within φ.8 radian are rejected. 7. he calorimeter reconstruction efficiency with resect to track s is then defined as the fraction of robe s matched to a calorimeter using R(robe,calo)<R (with R=.4 or R=.6) with resect to all robe s. he reconstruction efficiency is measured in a samle of minimum bias events and is comared to a minimum bias Monte Carlo simulation. Due to the restriction of η <.9 on track s, the measurement is only valid for calorimeter s with η <.9+R, where R=.4 or R=.6. Figures 7b-d show the measured calorimeter reconstruction efficiency with resect to track s as a function of the calorimeter transverse momentum for anti-k t s with R=.6 calibrated with the EM+JES, GCW+JES, and LCW+JES calibration schemes 7. he reconstruction efficiency reaches a lateau close to % at a transverse calorimeter momentum of about 5 GeV. he matching efficiency in data (ε Data ) and in Monte Carlo simulation (ε MC ) shows a good overall agreement excet at low where the efficiency in data is slightly lower than in the Monte Carlo simulation. Similar erformance is found for all calibration schemes. he systematic uncertainties on the reconstruction efficiency measured in situ are obtained by varying the following event selection requirements for both data and Monte Carlo simulation: the oening angle φ between the reference and 5 Reference track s with < 5 GeV are not used, since they would result in a samle of biased robe track s. In this case, mostly events where the robe track has fluctuated u in energy (such that it asses the 5 GeV threshold) would be ket. he 5 GeV cut has been determined by measuring the reconstruction efficiency relative to track s as a function of the reference track. he measured efficiency for low robe track was found to be deendent on the reference track when the latter is smaller than 5 GeV. he reconstruction efficiency is stable for a reference track greater than 5 GeV. 6 he less restrictive matching criterion with resect to revious sections is motivated by the lower. 7 echnically, the efficiency is first measured as a function of the track. Using the known relation between the average track and the average calorimeter, the track is then converted to the calorimeter.

78 ALAS collaboration: Jet measurement with the ALAS detector 77 Jet reconstruction efficiency Ratio ALAS Simulation Anti k t R=.6 EM+JES GCW+JES LCW+JES GCW+JES / LCW+JES / EM+JES. EM+JES true (a) Efficiency from truth s Jet reconstruction efficiency Data/MC ALAS s = 7 ev Anti k t R=.6, EM+JES Data MC (b) Efficiency from track s for EM+JES Jet r econstruction efficiency ALAS s = 7 ev Anti k t R=.6, GCW+JES Data MC Jet r econstruction efficiency ALAS s = 7 ev Anti k t R=.6, LCW+JES Data MC Data/MC (c) Efficiency from track s for GCW+JES Data/MC (d) Efficiency from track s for LCW+JES Fig. 7: Calorimeter reconstruction efficiency with resect to truth s (a) and track s (b,c,d) as a function of the truth (a) or the calorimeter (b,c,d) for the three calibration schemes: EM+JES (b), GCW+JES (c) and LCW+JES (d). he lower art of the figure (a) shows ratio of the efficiency of the LCW+JES and the GCW+JES calibration schemes to that of the EM+JES calibration scheme. he ratio of data to Monte Carlo simulation is also shown in the lower art of the figure for (b), (c) and (d). he hatched area corresond to the systematic uncertainty obtained by variations in the in situ method. the robe track s, the R requirement between the tag track and the calorimeter and the robe track and the calorimeter. he sensitivity in both data and Monte Carlo simulation to the azimuthal oening angle as well as to the R(tag,calo) variation is small. However, the efficiency shows a sensitivity with resect to the R(robe,calo ). he variation of ε Data /ε MC for these different arameters is shown in Figure 7. At high the statistical uncertainties after the cut variations lead to an enlarged uncertainty band. 6. Summary of reconstruction efficiency he reconstruction efficiency is derived using the nominal inclusive Monte Carlo simulation samle. he systematic uncertainty is evaluated using a tag-and-robe technique using track s in both data and Monte Carlo simulation. he reconstruction efficiency is well described by the Monte Carlo simulation and is within the systematic uncertainty of the in situ method. A systematic uncertainty of % for s with. < GeV is assigned and negligible for higher he systematic uncertainty of the in situ determination is larger than the observed shift between data and Monte Carlo simulation. For < GeV a systematic uncertainty of % for s is assigned. 7 Resonse uncertainty of non-isolated s he standard ALAS calibration and associated JES uncertainty is obtained using only isolated s (see Section 8.).

79 78 ALAS collaboration: Jet measurement with the ALAS detector R. ALAS simulation s = 7 ev anti k t R=.6 EM+JES.6 < R min <.7.7 < R min <.8.8 < R min < < R min <..4 < R min <.5 track R.7.6 ALAS simulation s = 7 ev anti k t R=.6 EM+JES.6 < R min <.7.7 < R min <.8.8 < R min < < R min <..4 < R min <.5 PYHIA MC.5 PYHIA MC / R iso. Resonse w.r.t..4 < R <.5 min / R iso. Resonse w.r.t..4 < R <.5 min R non iso (a) Calorimeter truth R non iso (GeV) (b) rack truth Fig. 7: Average ratio of calorimeter (a) and the track (b) to the matched truth as a function of truth for anti-k t s with R=.6, for different R min values. he bottom art of the figure shows the relative resonse of non-isolated s with resect to that of isolated s, obtained as the calorimeter or track resonse for R min <. divided by the resonse for.4 R min <.5. Jets are, however, often roduced with nearby s in a busy environment such as found in multi toologies or in events where to-quark airs are roduced. herefore a searate study is needed to determine the additional JES uncertainty for s with nearby activity. Jets with > GeV and y <.8 calibrated with the EM+JES scheme are used. he close-by JES uncertainty is evaluated within y <.. 7. Evaluation of close-by effects he effect due to close-by s is evaluated in the Monte Carlo simulation by using truth s as a reference. Similarly, track s are used as a reference in both data and Monte Carlo simulation (see Sections 6. and 6. for comarison). he calorimeter resonse relative to these reference s is examined for different values of R min, the distance from the calorimeter to the closest in η-φ sace. he relative calorimeter resonse to the truth s rovides an absolute scale for the calorimeter s, while the relative resonse to the track s allows in situ validation of the calorimeter resonse and the evaluation of the systematic uncertainty. For this urose, the track resonse in data needs to be established for the non-isolated case and the associated systematic uncertainty has to be understood. In the relative resonse measurement in the Monte Carlo simulation, the truth is matched to the calorimeter or track in η-φ sace by requiring R <.. Similarly, the track is matched to the calorimeter within R<. when the relative resonse to the track is examined. If two or more s are matched within the R range, the closest matched is taken. he calorimeter resonse to the matched track is defined as the ratio of the calorimeter to the track transverse track momentum ( ) r calo/track = /track. (49) his resonse is examined as a function of the transverse momentum and for different R min values measured relative to the closest calorimeter with > 7 GeV at the EM energy scale 8. he ratio of the calorimeter resonse for nonisolated (i.e. small R min ) to the resonse of isolated (large R min ) s, is given by calo/track rnon iso/iso = rcalo/track non iso calo/track /riso. (5) his ratio is comared between data and Monte Carlo simulations. [ [ ] calo/track A close by = rnon iso/iso ]Data / calo/track rnon iso/iso. (5) MC he deviation of A close by is assumed to reresent the comonent of calorimeter JES uncertainty due to close-by s. his uncertainty, convolved with the systematic uncertainty in the track resonse due to a nearby, rovides the total JES systematic uncertainty due to the close-by effect. 7. Non-isolated resonse Events that contain at least two s with > GeV and absolute raidity y <.8 are selected. he resonse of nonisolated s is studied in the Monte Carlo simulation using the calorimeter resonser = /truth. 8 Unless otherwise stated, calorimeter s (selected as listed below) and nearby s (selected with > 7 GeV at the EM scale) are both used in the resonse measurement, if a matched track is found.

80 ALAS collaboration: Jet measurement with the ALAS detector 79 track iso / non iso < R min <.7.7 < R min <.8.8 < R min < < R min <..4 < R min <.5 ALAS Data L dt = 8 b s = 7 ev anti k t R=.6 EM+JES Resonse w.r.t..4 < R <.5 min (a) Data track iso / non iso < R min <.7.7 < R min <.8.8 < R min < < R min <..4 < R min <.5 ALAS simulation PYHIA MC s = 7 ev anti k t R=.6 EM+JES Resonse w.r.t..4 < R <.5 min (b) MC Fig. 74: Average track as a function of calorimeter for anti-k t s with R =.6 in data (a) and MC simulations (b) for different R min values. he lower art shows the relative resonse of non-isolated s with resect to that of isolated s, obtained as the track for R min <. divided by that for.4 R min <.5. track A close by..5 5 ALAS Data L dt = 8 b s = 7 ev anti k t R=.6 EM+JES.6 < R min <.7.7 < R min <.8.8 < R min < < R min < Fig. 75: Ratio of data to Monte Carlo simulation of the track track track for non-isolated s divided by the track for isolated s as a function of the. Only statistical uncertainties are shown. Figure 7a shows the calorimeter resonse as a function of truth for anti-k t s with R=.6. he resonse was measured for nearby s in bins of R min values. he lower art of the figure shows the ratio of the non-isolated resonse for R min <. to the isolated resonse.4 R min <.5, R non iso /R iso. (5) he observed behaviour at small R min values indicates that the non-isolated resonse is lower by u to 5% relative to the isolated resonse for > GeV, if the two s are within R min < R+.. he magnitude of this effect deends on and is largest at low. R=.6 R=.4 > >.4 R min < %.8%.5 R min < %.%.6 R min <.7.9%.9%.5%.7%.7 R min <.8 5.%.6% -.8 R min <.5%.9% - able 5: Summary of energy scale systematic uncertainty assigned for non-isolated s accomanied by a close-by within the denoted R min ranges. he second row in the table indicates the range of the non-isolated s. Anti-k t s with R=.6 and R=.4 are used. he track resonse relative to the matched truth is defined as R track track = / truth. (5) Figure 7b showsr track as a function of truth for anti-k t s with R =.6. he track resonse is more stable against the resence of close-by s and has a much weaker R min deendence than the calorimeter resonse. his results from the smaller ambiguity in the matching between the truth and track s that are both measured from the rimary interaction oint. Moreover, track s are less influenced by magnetic field effects than calorimeter s. 7. Non-isolated energy scale uncertainty Figure 74 shows the average track transverse momentum as a function of for anti-k t s with R=.6 in both data and Monte Carlo simulations for various R min values. he lower art of the figure shows the ratio of non-isolated to isolated

81 8 ALAS collaboration: Jet measurement with the ALAS detector calo / track r.5 ALAS s = 7 ev L dt = 8 b.6 < R min <.7.7 < R min <.8.8 < R min < < R min <..4 < R min <.5 calo / track r.5 ALAS simulation s = 7 ev.6 < R min <.7.7 < R min <.8.8 < R min < < R min <..4 < R min <.5 R=.6 EM+JES anti k t Data R=.6 EM+JES anti k t PYHIA MC / r iso r non iso..8 Resonse w.r.t..4 < R <.5 min / r iso r non iso..8 Resonse w.r.t..4 < R <.5 min (a) Data (b) Monte Carlo simulation Fig. 76: Ratio of calorimeter to the matched track as a function of calorimeter for anti-k t s with R=.6 in data (a) and Monte Carlo simulations (b) for different R min values. he lower art shows the relative resonse of non-isolated s with resect to that of isolated s, obtained as the resonse for R min <. divided by the resonse for.4 R min <.5. A close by..5 5 ALAS Data L dt = 8 b s = 7 ev anti k t R=.6 EM+JES.6 < R min <.7.7 < R min <.8.8 < R min < < R min < Fig. 77: Data to Monte Carlo simulation ratio of the relative resonse of non-isolated s with resect to that of isolated s for anti-k t s with R =.6 calibrated with the EM+JES scheme. Only statistical uncertainties are shown. track s defined as track r = track non iso/iso,non iso /track,iso. (54) he data to MC ratio defined as [ [ track Aclose by = track r ]Data / r non iso/iso ] track non iso/iso MC (55) is comared between data and Monte Carlo simulations in Figure 75. his ratio can be used to assess the otential of track s to test close-by effects in the small R min range. he agreement between data and Monte Carlo simulation is quite satisfactory: within to % for > GeV and slightly worse for < GeV. herefore, the track resonse systematic uncertainty is assigned searately for the two regions: Atrack close by is used as the uncertainty for < GeV, while for > track GeV a standard deviation of the Aclose by is calculated and assigned as the uncertainty. hese uncertainties are tyically.5% (.%) for anti-k t s with R=.6 (.4). he calorimeter relative to the matched track track (r calo/track ) is shown in Figure 76 as a function of for anti-k t s with R=.6 in data and Monte Carlo simulations. he non-isolated resonse relative to the isolated calo/track resonse, rnon iso/iso, shown in the bottom art of Figure 76 reroduces within a few er cent the behaviour in the ratio R non iso /R iso for the Monte Carlo simulation resonse of calorimeter to truth in Figure 7. calo/track he rnon iso/iso data to Monte Carlo ratio A close by (see Equation 5) is shown in Figure 77. he R min deendence of the non-isolated resonse in the data is well described by the Monte Carlo simulation. Within the statistical uncertainty, A close by differs from unity by at most % deending on the R min value in the range of R R min < R+.. No significant deendence is found over the measured range of < 4 GeV. he overall JES uncertainty due to nearby s is taken as the track resonse systematic uncertainty added in quadrature with the deviation from one of the weighted average of A close by over the entire range, but added searately for each R min range. he final uncertainties are summarised in able 5 for the two distance arameters. he A close by ratio has been examined for each of the two close-by s either with the lower or the higher, and no aarent difference is observed with resect to the inclusive case shown in Figure 77. herefore, both calorimeter s which are close to each other are subject to this uncertainty.

82 ALAS collaboration: Jet measurement with the ALAS detector Summary of close-by uncertainty he uncertainty is estimated by comaring in data and Monte Carlo simulation the track resonse. hey are both examined as function of the distance R min between the and the closest in the calorimeter. he close-by systematic uncertainty on the energy scale is.5 5.% (.7.7%) and.6.9% (..8%) for R=.6 (R=.4) s with < GeV and > GeV, resectively, in the range of R R min < R+. and raidity y <.. When the two s are searated in distance by R+. or more, the resonse becomes similar to that for the isolated s and hence no additional systematic uncertainty is required. No significant deendence is observed at > GeV for the close-by systematic uncertainty. 8 Light quark and gluon resonse and samle characterisation In the revious sections the JES uncertainty for inclusive s was determined. However, details of the fragmentation and showering roerties can influence the resonse measurement. In this section the JES uncertainties due to fragmentation which is correlated to the flavour of the arton initiating that (e.g. see Ref. [7]) are investigated. An additional term in the JES uncertainty is derived for event samles that have a different flavour content than the nominal Monte Carlo simulation samle. he energy scale systematic uncertainty due to the difference in resonse between gluon and light quark initiated s (henceforth gluon s and light quark s) can be reduced by measuring the flavour comosition of a samle of s using temlate fits to certain roerties that are sensitive to changes in fragmentation. Although these roerties may not have sufficient discrimination ower to determine the artonic origin of a secific, it is ossible to determine the average flavour comosition of a sufficiently large samle of s. he average flavour comositions can be determined using roerty temlates built in the Monte Carlo simulation for ure samles. emlates are constructed in di events, which are exected to comrise mostly gluon s at low transverse momentum and central raidities. hey are then alied to events with a high- hoton balancing a high- (γ- events), which are exected to comrise mostly light quark s balancing the hoton. he alication of this technique is further demonstrated with a samle of multi events, wherein the s are initiated mostly by gluons from radiation. 8. Data samles for flavour deendence studies wo data samles in addition to the inclusive samle discussed before are used for the studies of the flavour deendence of the resonse.. γ- samle Photons with > 45 GeV are selected in the barrel calorimeter (with seudoraidity η <.7) and a back-to-back ( φ > π. radians) to the hoton is required. he second-leading in the event is required to have a below % of the of the leading. Antik t s with R =.6 are used.anti-k t s with R=.6 are used.. Multi samle Jets with > 6 GeV and η <.8 are selected and the number of selected s defines the samle of at least two, three or four s. 8. Flavour deendence of the calorimeter resonse Jets identified in the Monte Carlo simulation as light quark s have significantly different resonse from those identified as gluon s (see Section 6.). he flavour-deendence of the resonse is in art a result of the differences in article level roerties of the two tyes of s. For a given s identified as gluon s tend to have more articles, and those articles tend to be softer than in the case of light quark s. Additionally, the gluon s tend to be wider (i.e. with lower energy density in the core of the ) before interacting with the detector. he magnetic field in the inner detector amlifies the broadness of gluon s, since their low- charged articles tend to bend more than the higher articles in light quark s. he harder articles in light quark s additionally tend to enetrate further into the calorimeter. he difference in calorimeter resonse between gluon s and light quark s in the Monte Carlo simulation is shown in Figure 78. Jets in the barrel ( η <.8) and in the endca (. η <.8) calorimeters are shown searately. For s calibrated with the EM+JES scheme light quark s have a 5 6% higher resonse than gluon s at low. his difference decreases to about % at high. Since resonse differences are correlated with differences in the roerties, more comlex calibration schemes that are able to account for shower roerties variations can artially comensate for the flavour deendence. At low the difference in resonse between light quark s and gluon s is reduced to 4 5% for the LCW+JES and GCW+JES schemes and about % for the GS scheme. For > GeV the flavour deendence of the resonse is below % for the LCW+JES and GCW+JES and the GS schemes. he closer two s are to one another, the more ambiguous the flavour assignment becomes. he flavour assignment can become articularly roblematic when one truth is matched to two reconstructed calorimeter s ( slitting ) or two truth s are matched to one reconstructed calorimeter ( merging ). Several different classes of close-by s are examined for changes in the flavour deendence of the resonse. No significant deviation from the one of isolated s is found. herefore, the cases can be treated searately. he energy scale uncertainty secific to close-by s is examined further in Section Systematic uncertainties due to flavour deendence Each energy calibration schemes restore the average energy to better than % with small uncertainties in a samle of

83 8 ALAS collaboration: Jet measurement with the ALAS detector Light quark gluon resonse ALAS Simulation PYHIA MC EM+JES GCW+JES LCW+JES GS η <.8 anti k t R=.6 Light quark gluon resonse ALAS Simulation PYHIA MC EM+JES GCW+JES LCW+JES GS. η <.8 anti k t R=.6 truth 4 truth (a) η <.8 (b). η <.8 Fig. 78: Difference in average resonse of gluon and light quark s as a function of the truth for anti-k t s with R=.6 in the barrel (a) and the endca (b) calorimeters as determined in Monte Carlo simulation. Various calibration schemes are shown. he data samle used contains at least two s with > 6 GeV and η <.8. Only statistical uncertainties are shown. Arbitrary units ALAS Simulation PYHIA MC Light quark s Gluon s 8 < GeV η <.8 anti k R=.6 EM+JES t n trk Arbitrary units ALAS Simulation PYHIA MC Light quark s Gluon s 8 < GeV Width η <.8 (a) Number of tracks n trk (b) Jet width Fig. 79: Distribution of the number of tracks associated to the n trk (a) and the width (b) for isolated anti-k t s with R=.6 classified as light quark s (solid circles) and gluon s (oen squares) in the Monte Carlo simulation. Jets with η <.8 and 8 < GeV are shown. he distributions are normalised to unit area. Uncertainties are statistical only.

84 ALAS collaboration: Jet measurement with the ALAS detector 8 Arbitrary units ALAS Data L dt=.4 b Data s=7 ev PYHIA MC PYHIA PERUGIA HERWIG++ η <.8 8 < GeV anti k t R=.6 EM+JES n trk Arbitrary units ALAS Data L dt=.4 b Width Data s=7 ev PYHIA MC PYHIA PERUGIA HERWIG++ η <.8 8 < GeV anti k t R=.6 EM+JES (a) Number of tracks n trk (b) Jet width Fig. 8: Distribution of the number of tracks associated to the, n trk (a) and the width (b) for isolated anti-k t s with R =.6 in data (solid circles) and Monte Carlo simulation. he PYHIA MC tune (oen circles) and PERUGIA tune (oen triangles), and HERWIG++ (oen squares) distributions are shown for s with η <.8 and 8 < GeV. he distributions are all normalised to unity. Uncertainties are statistical only. Arbitrary units.4 ALAS Data L dt=.4 b Data s=7 ev Gluon s Light quark s η <.8 8 < GeV Reweighted distributions anti kt R=.6 EM+JES Arbitrary units ALAS Data L dt=.4 b Data s=7 ev Gluon s Light quark s η <.8 8 < GeV Reweighted Distributions anti k t R=.6 EM+JES n trk Width (a) Number of tracks n trk (b) Jet width Fig. 8: Distribution of the number of tracks associated to the, n trk (a) and the width (b) for isolated anti-k t s with R=.6 in data (closed circles) and Monte Carlo simulation (bands). Light quark s are shown as a dark band, gluon s are shown as a light band. he width of the band reresents the maximum variation among the PYHIA MC and PERUGIA tunes and the HERWIG++ Monte Carlo simulation samles. Jets with η <.8 and 8 < GeV are included. he inclusive distributions are all normalised to unity. he inclusive Monte Carlo distributions, including the heavy quark contributions (not shown), are reweighted to match the inclusive distribution of the data. Uncertainties are statistical only.

85 84 ALAS collaboration: Jet measurement with the ALAS detector Number of s ALAS Data L dt=7. b Width Data s=7 ev Gluon s Light quark s b /c quark s 6 <8 GeV η <.8 anti k t R=.6 EM+JES Fig. 8: he width temlate fit in a γ- data samle using temlates derived from the inclusive Monte Carlo simulation samle created using the PYHIA MC tune. Jets with η <.8 and 6 < 8 GeV are shown. he fraction of heavy quark s is taken directly from the MC simulation. inclusive s. However, subsamles of s are not erfectly calibrated, as in the case of light quark s and gluon s. he divergence from unity is flavour deendent and may be different in Monte Carlo simulation and data, articularly if the flavour content in the data samle is not well-described by the Monte Carlo simulation. his results in an additional term in the systematic uncertainty for any study using an event or selection different from that of the samle in which the energy scale was derived. 8.. Systematic uncertainty from MC variations In order to test the resonse uncertainties of exclusive samles of either gluon or light quark s, a large number of systematic variations in the Monte Carlo simulation are investigated (see Ref. [] for details on the variations). he resonse difference of quark and gluon s to that of the inclusive s is found to be very similar for each of the systematic Monte Carlo variations. herefore the additional uncertainty on the resonse of gluon s is neglected. hese conclusions are in good agreement with the studies which derive the calorimeter resonse using the single hadron resonse in Refs. [49, 58], where the uncertainties of the quark and gluon resonse are similar within.5%. he results are found to be stable under variations of the Monte Carlo simulation samles including soft hysics effects like colour reconnections. With more data, a variety of final states may be tested to investigate more details of the light quark and gluon resonse. 8.. Systematic uncertainty from average flavour content he flavour deendent uncertainty term deends on both the average flavour content of the samle and on how well the flavour content is known, e.g. the uncertainty for a generic new hysics search with an unknown flavour comosition is different from the uncertainty on a new hysics model in which only light quark s are roduced. he resonse for any samle of s, R s, can be written as 9 : R s = f g R g + f q R q + f b R b + f c R c = + f g (R g )+ f q (R q ) + f b (R b )+ f c (R c ), (56) where R x is the detector resonse to s and f x is the fraction of s for x= g (gluon s), q (light quark s), b (b-quark s), and c (c-quark s) and f g + f q + f b + f c =. For simlicity, the fraction of heavy quark s is taken to be known. his aroximation will be dealt with in the systematic uncertainty analysis for heavy quarks in Section 8.4. Since variations in the flavour fractions and the flavour resonse translate into variations of the resonse for a given samle, the uncertainty on the resonse can be aroximately exressed as: R s = f g (R g )+ f q (R q )+ f g R g + f q R q + f b R b + f c R c, (57) where denotes the uncertainty on the individual variables. Since f b and f c are fixed here (i.e. without uncertainty), f g = f q. Also, the uncertainties on the resonse for the exclusive flavour samles (light quark, gluon, b, and c quarks) are aroximately the same as the inclusive resonse uncertainty ( R j ). he exression can therefore be simlified: R s f q (R g )+ f q (R q )+ f g R j + f q R j + f b R j + f c R j = f q (R q R g )+( f g + f q + f b + f c ) R j f q (R q R g )+ R j. (58) he second term is the inclusive energy scale systematic uncertainty, and the first term is the additional flavour deendent contribution. Droing the inclusive energy scale systematic uncertainty and rewriting Equation 58 as a fractional uncertainty, the flavour deendent contribution becomes: R s R s = f q ( Rq R g R s ). (59) he uncertainty on the flavour content ( f q ) and the inclusive resonse of the samle (R s ) deends on the secific analysis. he difference in resonse between light quark and gluon s deends only on the calibration used, as discussed in Section he following equations are strictly seaking only valid for a given bin in and η or in other variables that influence the flavour comosition.

86 ALAS collaboration: Jet measurement with the ALAS detector 85 Fraction of s Gluon s Light quark s b/c quark s Solid oints Data η <.8,.8 R <. min N s ALAS Data L dt=.4 b Heavy flavour syst. JES syst. Shae syst. Model syst. ALP/PY syst. Combined Fraction of Jets Gluon s Light quark s b/c quark s Solid oints Data η <.8,.8 R <. min N s ALAS Data L dt=.4 b Heavy flavour syst. JES syst. Shae syst. Model syst. ALP/PY syst. Combined.... Uncertainty. temlate fits. n trk Uncertainty. Width temlate fits (a) Number of tracks n trk temlate fits (b) Jet width temlate fits Fig. 8: Fitted values of the average light quark and gluon fraction in events with three or more s as a function of calculated using the number of tracks n trk temlates (a) and the width temlates (b). Non-isolated anti-k t s (.8 R min <.) with R=.6 and with η <.8 calibrated with the EM+JES scheme are shown. he fraction of heavy quark s is fixed to that of the Monte Carlo simulation. he flavour fractions obtained in data are shown with closed markers, while the values obtained from the Monte Carlo simulation are shown with oen markers. he error bars indicate the statistical uncertainty of the fit. Below each figure the imact of the different systematic effects is shown with markers and the combined systematic uncertainty is indicated by a shaded band. 8.4 Average flavour determination One way of investigating the flavour comosition of a samle is to use different MC generators that cover a reasonable range of flavour comositions. However, these different samles may suffer from under- or overcoverage of the uncertainty or from changes in other samle characteristics, e.g. sectra, which may result in a oor estimate of the true uncertainty. Another aroach, ursued in this section, is to estimate the flavour comosition of the samles by using exerimental observables that are sensitive to different flavours. As described in Section 8., gluon s tend to have a wider transverse rofile and have more articles than light quark s with the same. he width, as defined in Equation 7, and the number of tracks associated to the (n trk ) are thus exected to be sensitive to the difference between light quark s and gluon s. he width may have contributions from ileu interactions. In the following discussion only events with exactly one reconstructed rimary vertex enter the width distributions 4. he number of tracks associated to a is defined by counting the tracks with > GeV coming from the rimary hard scattering vertex with an oening angle between the and the track momentum direction R <.6. Figure 79 shows the width and n trk distributions for isolated light quark and gluon s with η <.8 and 8 < GeV in the inclusive Monte Carlo simulation samle. he gluon s are broader and have more tracks than light quark s. For this study anti-k t s with R=.6 calibrated with the EM+JES scheme are used. emlates are built from the inclusive Monte Carlo samle for the width and n trk of light quark and gluon s searately 4, using the flavour tagging algorithm of Section 6.. he temlates are constructed in bins of, η, and isolation 4 echniques to correct for these additional interactions are being develoed and are discussed in Section he n trk and width temlates are dealt with indeendently, and the results of their estimates of flavour fraction are not combined.

87 86 ALAS collaboration: Jet measurement with the ALAS detector Fraction of s Gluon s Light quark s b/c quark s Solid oints Data Combined systematic η <.8,. R <.5 min N s 4 ALAS Data L dt=.4 b Fraction of s Gluon s Light quark s b/c quark s Solid oints Data Combined systematic η <.8,. R <.5 min N s 4 ALAS Data L dt=.4 b.... Uncertainty. temlate fits. n trk Uncertainty. Width temlate fits (a) Number of tracks n trk temlate fits (b) Jet width temlate fits Fig. 84: Fitted values of the average light quark and gluon fraction in events with four or more s as a function of for isolated anti-k t s with R=.6 and with η <.8 calibrated with the EM+JES scheme. he fraction of heavy quark s is fixed from the Monte Carlo simulation. he number of tracks n trk (a) and the width (b) temlate distributions are used in the fits. he flavour fractions obtained in data are shown with closed markers, while the values obtained from the Monte Carlo simulation are shown with oen markers. he error bars indicate the statistical uncertainty of the fit. Below each figure the systematic uncertainty is shown as a shaded band. ( R to the nearest, R min ). Fits to the data are erformed with these temlates to extract the flavour comosition. Comarisons of the inclusive width and n trk distributions in Monte Carlo simulation and data are shown in Figure 8 for isolated s with R =.6. he width in Monte Carlo simulation is narrower than in the data for the PYHIA samles, in agreement with other ALAS analyses []. he inclusive n trk and width Monte Carlo simulation distributions are reweighted bin-by-bin according to the data distribution. his accounts for the differences observed between the data and Monte Carlo simulation. he same reweighting is alied to the light quark and gluon distributions. he reweighted n trk and width distributions for the various Monte Carlo simulation samles are shown in Figure 8. Since the reweighting is alied to all flavours equally the average flavour content of the samle does not change. After reweighting, the flavour comosition of the di samle extracted from the data is consistent with that of the Monte Carlo simulation. he extracted values for two reresentative bins are shown in able 6. his result is an imortant closure test and rovides some validation of the temlates. 8.5 Systematic uncertainties of average flavour comosition Uncertainties on the MC-based temlates used in fits to the data result in a systematic uncertainty on the extracted flavour comosition. Systematic effects from the Monte Carlo modelling of the fragmentation, the energy scale and resolution as well as the flavour comosition of the samle used to extract the temlates are discussed in the following. Since there is no single dominant uncertainty, each is individually considered for the extraction of the flavour comosition of a samle of s Monte Carlo modelling of width and n trk distributions Monte Carlo simulation samles generated with PYHIA with the MC and the PERUGIA tunes and HERWIG++ all show reasonable agreement with data (see Figure 8). herefore, two searate fits with temlates obtained from the latter two alternative Monte Carlo simulation samles are erformed. Reweighting of these alternate samles is erformed

88 ALAS collaboration: Jet measurement with the ALAS detector 87 Fraction of s ALAS Data L dt=.4 b Gluon s Light quark s b/c quark s Solid oints Data Heavy flavour syst. JES syst. Shae syst. Model syst. ALP/PY syst. Combined Fraction of s ALAS Data L dt=.4 b Gluon s Light quark s b/c quark s Solid oints Data Heavy flavour syst. JES syst. Shae syst. Model syst. ALP/PY syst. Combined.... Uncertainty. temlate fits. n trk 4 Inclusive multilicity Uncertainty. Width temlate fits. 4 Inclusive multilicity (a) Number of track n trk temlate fits (b) Jet width temlate fits Fig. 85: Fitted values of the average light quark and gluon fraction as a function of inclusive multilicity with total uncertainties on the fit as obtained using the number of tracks n trk (a) and the width (b) distributions. he fraction of heavy quark s is fixed from the Monte Carlo simulation. he flavour fractions obtained in data are shown with closed markers, while the values obtained from the Monte Carlo simulation are shown with oen markers. Anti-k t s with R =.6 calibrated with the EM+JES scheme are used. he error bars indicate the statistical uncertainty of the fit. Below each figure the imact of the different systematic effects is indicated by markers. and the combined systematic uncertainty is shown at the bottom of the figure as a shaded band. in the same manner as for the nominal PYHIA MC samle. he largest of the differences in the flavour fractions with resect to the nominal fits is taken as the uncertainty due to Monte Carlo modelling. his estimate should cover hysics effects that may imact light quark and gluon s differently he energy scale uncertainty and finite detector resolution he uncertainties in the measurement combined with the raidly falling sectrum, lead to bin migrations that affect the temlates. herefore, the temlates are rebuilt with all momenta scaled u and down according to the inclusive energy scale systematic uncertainty. he difference in the flavour content estimated with the modified temlates is taken as a systematic uncertainty Flavour comosition of the MC simulation he fraction of heavy quark s in the data is assumed to be the same as that redicted by the PYHIA MC Monte Carlo simulation in the temlate fits. he uncertainty associated with this assumtion is estimated by increasing and decreasing this Monte Carlo simulation based fraction of heavy quark s in the temlate fits by a factor of two and reeating the fits with the light quark and gluon temlates. he factor of two is taken in order to be conservative in the γ- and multi samles, due to the lack of knowledge of gluon slitting fraction to b b. he PYHIA Monte Carlo simulation was roduced using the modified LO arton distribution functions, which may not accurately reroduce the true flavour comosition. Particularly in the more forward seudoraidity bins, this could roduce some inherent biases in the fits. In order to estimate this uncertainty, the light quark and gluon temlates from the standard MC samle are combined according to the flavour content of a samle generated using ALPGEN. his Monte Carlo generator also uses a leading order PDF, but roduces more

89 88 ALAS collaboration: Jet measurement with the ALAS detector hard artons via multiarton matrix elements. his new combination is then reweighted to match the inclusive distribution in data, and the reweighted temlates are used to extract the flavour comosition of the samles. he difference between the flavour comosition derived in this manner and the flavour comosition derived using the nominal PYHIA Monte Carlo simulation is taken as a systematic uncertainty. 8.6 Flavour comosition in a hoton- samle he validity of the MC-based temlates and fitting method is tested by alying the method to the γ- data samle and comaring the extracted flavour comositions with the γ- Monte Carlo simulation redictions. his samle should contain a considerably higher fraction of light quark s than the inclusive di samle. Figure 8 shows the fit to the width in the γ- data for s with η <.8 and 6 < 8 GeV. he heavy quark fractions are fixed to those obtained from the γ- Monte Carlo simulation. he extracted light quark and gluon fractions are consistent with the true fractions in Monte Carlo simulation, though with large uncertainties, as shown in able Flavour comosition in a multi samle he temlate fit method is also useful for fits to multi events for various multilicities. hese events contain additional s that mainly result from gluon radiation and hence include a larger fraction of gluon s than does the γ- samle. For this articular analysis, the temlates built from the inclusive samle are used to determine the flavour content of the n- bin. However, the sectrum of the sub-leading s is more steely falling than the leading. An additional systematic uncertainty is estimated to account for the difference in sectra. his uncertainty is determined by rederiving temlates built with a flat distribution and a significantly steeer distribution than that of the di samle. he sloe of the steely falling distribution is taken from the of the sixth leading in Monte Carlo events with six s, generated using ALPGEN. he fits are reeated with these modified temlates, and the largest difference is assigned as a sectrum shae systematic uncertainty. Figure 8 comares the fractions of light quark and gluon s obtained with a fit of the width and n trk distributions in events with three or more s in data and Monte Carlo simulation as a function of for non-isolated (.8 R min <.) s with η <.8. he higher gluon fractions redicted by the Monte Carlo simulation are reroduced by the fit, and the data and the Monte Carlo simulation are consistent. he total systematic uncertainty on the measurement is below % over the measured range. he average flavour fractions obtained from fitting the width and n trk distributions in events with four or more s are shown in Figure 84. In both cases, the extracted fractions are consistent with the Monte Carlo redictions within the systematic uncertainties, and the total systematic uncertainty is similar to the one for the three- bin. he extracted light quark and gluon fractions, with the total systematic uncertainty from the width and n trk fits, are summarised in Figure 85 as a function of inclusive multilicity. he fractions differ by % between the data and the Monte Carlo simulation, but are consistent within uncertainties. he total systematic uncertainty is around % for each multilicity bin. hus, for the four- bin, the flavour deendent energy scale systematic uncertainty can be reduced by a factor of, from about 6% obtained assuming a % flavour comosition uncertainty to less than % after having determined the flavour comosition with a % accuracy. A summary of the flavour fit results using the width temlates for the different samles is rovided in able Summary of resonse flavour deendence he flavour deendence of the resonse has been studied, and an additional term to the energy scale systematic uncertainty has been derived. A generic temlate fit method has been develoed to reduce this uncertainty significantly for any given samle of events. emlates derived in di events were alied to both γ- and multi events, demonstrating the otential of the method to reduce the systematic uncertainty. he flavour deendent energy scale systematic uncertainty can be reduced from 6% to below %. 9 Global sequential calibrated resonse for a quark samle In this section, the erformance of the GS calibration (see Section ) is tested for a γ- samle. he energy scale after each GS correction can be verified using the in situ techniques such as the direct balance technique in γ- events (see Section.), where mainly quark induced s are tested. he flavour deendence of the GS calibration is tested for s with η <.. he measurement is first made with s calibrated with the EM+JES calibration and is reeated after the alication of each of the corrections that form the GS calibration. o maximise the available statistics one seudoraidity bin is used η <.. he Monte Carlo based GS corrections are alied to both data and Monte Carlo simulation. he systematic uncertainty associated with the GS calibration is evaluated by comuting the data to Monte Carlo simulation ratio of the resonse after the GS calibration relative to that for the EM+JES calibration. For 5 < 45 GeV, the agreement between the resonse in data and Monte Carlo simulation is.% after EM+JES and 4.% after GS calibration. For < 6 GeV, the agreement is 5% after EM+JES and.5% after GS calibration. herefore systematic uncertainties derived from the agreement of data and Monte Carlo simulation vary from % at = 5 GeV to.5% for = 6 GeV. hese results are comatible within the statistical uncertainty with the uncertainty evaluated using inclusive events (see Section..).

90 ALAS collaboration: Jet measurement with the ALAS detector 89 Gluon / light / heavy quark fraction Samle Selection Data MC Di 8 < GeV, η <.8, 7 / / 5% 7 / / 5%. R min <.5 ±(stat.)±9(syst.)% Di 8 < GeV,. η <.8, 45 / 5 / % 9 / 58 / %. R min <.5 ±(stat.)±(syst.)% γ- 6 < 8 GeV, η <.8, 6 / 65 / 9% 6 / 74 / 9% Isolated ±(stat.) ± 9(syst.)% Multi -, 8 < GeV, η <.8, 8 / / 4% 84 / / 4%.8 R min <. ±(stat.)±7(syst.)% Multi 4-, 8 < GeV, η <.8, 89 / / 8% 8 / / 8%. R min <.5 ±6(stat.)±8(syst.)% able 6: he results of flavour fits using width temlates in three data samles: di events, γ- events, and multi events. he Monte Carlo simulation flavour redictions are taken from ALPGEN for the di and multi samles and PYHIA for the γ- samle. he first uncertainty listed is statistical and the second uncertainty is systematic, and both aly to the measured gluon and light quark fractions. he heavy quark fractions in the data are constrained to be the same as those in the MC simulation. he obtained results indicate that the uncertainty in a samle with a high fraction of light quark s is about the same as in the inclusive samle. JES uncertainties for s with identified heavy quark comonents Heavy flavour s such as s induced by bottom (b) quarks (b-s) lay an imortant role in many hysics analyses. he calorimeter resonse uncertainties for b-s is evaluated using single hadron resonse measurements in samles of inclusive di and b b di events. he JES uncertainty arising from the modelling of the b-quark roduction mechanism and the b-quark fragmentation can be determined from systematics variations of the Monte Carlo simulation. Finally, the calorimeter measurement can be comared to the one from tracks associated to the s for inclusive s and identified b-s. From the comarison of data to Monte Carlo simulation the b- energy scale uncertainty relative to the inclusive samle is estimated.. Selection of identified heavy quark s Jets are reconstructed using the anti-k t algorithm with R =.4 and calibrated with the EM+JES scheme. Jets with > GeV and η <.5 are selected. A reresentative samle of identified b-s is selected by a track-based b-tagging algorithm, called the SV tagger [8, 7]. his algorithm iteratively reconstructs a secondary vertex in s and calculates the decay length with resect to the rimary vertex. he decay length significance is assigned to each as a tagging weight. A is identified as a b- if this weight exceeds a threshold of 5.85 as exlained in Ref. [7]. o adjust the Monte Carlo simulation to the b-tagging erformance in data, a dedicated b-tagging calibration consisting of scale factors [7] is alied to the simulation and systematic uncertainties for the calibration are evaluated. For Monte Carlo studies, a samle of b-s is selected using a geometrical matching of the ( R<.4) to a true B-hadron.. Calorimeter resonse uncertainty he uncertainty of the calorimeter resonse to identified b-s has been evaluated using single hadron resonse measurements in situ and in test-beams [49]. he same method as described in Section 9. is used to estimate the b- resonse uncertainty in events with to-quark airs with resect to the one of inclusive s. For s within η <.8 and < 5 GeV the exected difference in the calorimeter resonse uncertainty of identified b-s with resect to the one of inclusive s is less than.5%. It is assumed that this uncertainty extends u to η <.5. Parameter Nominal Professor Bowler-Lund MSJ() MSJ() PARJ(4) PARJ(4).58.. PARJ(46) PARJ(54).7 PARJ(55).6 able 7: PYHIA steering arameters for the considered variations of the b-quark fragmentation functions.. Uncertainties due to Monte Carlo modelling he following uncertainties for b-s are studied using systematic variations of the Monte Carlo simulation:

91 9 ALAS collaboration: Jet measurement with the ALAS detector > truth / b <.8 ALAS simulation.6 s= 7 ev Anti k t R =.4 truth b s η < PYHIA MC PYHIA PERUGIA HERWIG++ Additional dead material > truth / b <.8 ALAS simulation.6 s= 7 ev Anti k t R =.4 truth b s η < PYHIA MC PYHIA PROFESSOR PYHIA BOWLER MODIFIED (a) MC generator and detector geometry (b) b-quark fragmentation Fig. 86: Average resonse for b-s as a function of obtained with the Monte Carlo event generators PYHIA with the MC and PERUGIA tunes and HERWIG++ (a) and PYHIA simulations with additional dead detector material. Average resonse for b-s using the PYHIA Professor tune and the PYHIA modified Bowler-Lund fragmentation function evaluated with resect to the nominal PYHIA inclusive samle (b). Only statistical uncertainties are shown.. Fragmentation and hadronisation modelling uncertainty obtained by comaring the Monte Carlo generators HERWIG vs PYHIA.. Soft hysics modelling uncertainty obtained by comaring the PYHIA MC to the PYHIA PERUGIA tune.. Modelling uncertainty of the detector material in front and in between the calorimeters. 4. Modelling uncertainty of the fragmentation of b-quarks. he event generators PYHIA and HERWIG++ are used to evaluate the influence of different hadronisation models, different arton showers, as well as differences in the underlying event model (see Section 4). Variations in roton arton density functions are also included. he influence of the soft hysics modelling is estimated by relacing the standard PYHIA MC tune by the PYH- IA PERUGIA tune. he imact of additional dead material is tested following the rescrition detailed in Section 9. he fragmentation function is used to estimate the momentum carried by the B-hadron with resect to that of the b-quark after quark fragmentation. he contribution of the b-quark fragmentation to the JES uncertainty is estimated using Monte Carlo samles generated with different sets of tuning arameters of two fragmentation functions (see able 7). he fragmentation function included as default in PYH- IA originates from a detailed study of the b-quark fragmentation function in comarison with OPAL [7] and SLD [7] data. he data are better described using the symmetric Bowler fragmentation function with r Q =.75 (PYHIA PARJ(46)), assuming the same modification for b- and c-quarks. he a (PYHIA PARJ(4)) and b (PYHIA PARJ(4)) arameters of the symmetric Lund function were left with the values shown in able 7. A more detailed discussion of uncertainties in the b-quark fragmentation function can be found in Refs. [74]. he choice of the fragmentation function for this study is based on comarisons to LEP exerimental data, mostly from ALEPH [75] and OPAL [7], as well as from the SLD exeriment [7] included in a henomenological study of the b-quark fragmentation in to-quark decay [76]. o assess the imact of the b-quark fragmentation, the nominal arameters of the PYHIA fragmentation function are relaced by the values from a recent tune using the Professor framework [77]. In addition, the nominal fragmentation function is relaced by the modified Bowler-Lund fragmentation function [78]. For each effect listed above the b- resonse uncertainty is evaluated from the ratio between the resonse of b-s in the Monte Carlo samles with systematic variations to the nominal PYHIA MC b- samle. he deviation from unity of this ratio is taken as uncertainty: ( ) b- R variation Uncertainty= R b-. (6) nominal he b- resonse obtained with PYHIA for the MC and the PERUGIA tunes, the HERWIG++ Monte Carlo event generator and using a simulation with additional dead material is shown in Figure 86a. Figure 86b shows the variation with various fragmentation functions, i.e. the standard one in the nominal PYHIA samle versus the ones in the PYHIA Professor tune samle and the PYHIA modified Bowler-Lund fragmentation function samle. he resonse variations are well within about %.

92 ALAS collaboration: Jet measurement with the ALAS detector 9 Additional fractional b JES uncertainty R=.4 b s, EM+JES, η <.5 Anti k t B fragmentation Additional dead material Additional fractional b JES uncertainty HERWIG++ Calorimeter resonse ALAS simulation truth Fig. 87: Additional fractional b- JES uncertainty as a function of the truth transverse momentum for anti-k t s with R =.4 calibrated with the EM+JES scheme for η <.5. Shown are systematic Monte Carlo variations using different modelling of the b-quark fragmentation and hysics effects as well as variations in the detector geometry and the uncertainty in the calorimeter resonse to b-s as evaluated from single hadron resonse measurements. Uncertainties on the individual oints are statistical only..4 Final bottom quark JES uncertainty he b- JES uncertainty is obtained adding the calorimeter resonse uncertainty (see Section. for generator details) and the uncertainties from the systematic Monte Carlo variations (see Section.) in quadrature. o avoid double counting when combining the b- uncertainty with the JES uncertainty of inclusive s the following effects need to be considered:. he uncertainty comonent due to the PERUGIA tune is not added, since the effect on b-s is similar to the one on inclusive s where it is already accounted for.. he average uncertainty for inclusive s due to additional dead detector material is subtracted from the corresonding b- uncertainty comonent. he JES uncertainty due to dead material is smaller for inclusive s, since in situ measurements are used. he resulting additional JES uncertainty for b-s is shown in Figure 87. It is about % u to GeV and below % for higher. o obtain the overall b- uncertainty this uncertainty needs to be added in quadrature to the JES uncertainty for inclusive s described in Section 9..5 Validation of the heavy quark energy scale using tracks he validation of the identified b- JES uncertainty uses the tracks associated to the b- as reference object and closely follows the method described in Section.. he transverse momentum of a is comared to the total transverse momentum measured in tracks associated to the (see Equation )..5. Method he double ratio of charged-to-total momentum observed in data to that obtained in Monte Carlo simulation defined in Equation will be referred to as R rtrk,inclusive. In analogy this ratio is studied for b-tagged s: R rtrk,b- [ r trk b- ] Data [ r trk b- ] MC. (6) he r trk distributions for all bins are calculated and the mean values of r trk for data and Monte Carlo simulation are derived. he relative resonse to b-s relative to inclusive s, R, is defined as.5. Systematic uncertainties R R r trk,b-. (6) R rtrk,inclusive he systematic uncertainties arise from the modelling of the b-fragmentation, b-tagging calibration, resolution and tracking efficiency. hey are assumed to be uncorrelated. he resulting fractional systematic uncertainties are shown on the right art of Figure 88 and are determined as follows:. MC generator: he r trk distribution is also calculated from HERWIG++ samles. he shift in the distribution is fitted by a constant function. he variations in the data to Monte Carlo simulation ratio are taken as a systematic uncertainty.. b-tagging calibration: he scale factors are varied correlated within their systematic uncertainty in the Monte Carlo simulation and the ratio is re-evaluated. he resulting shifts are added in quadrature to the systematic uncertainty.. Material descrition: he knowledge of the tracking efficiency modelling in Monte Carlo simulation was evaluated in detail in Ref. [64]. he systematic uncertainty on the tracking efficiency for isolated tracks increases from % ( η track <.) to 7% (. η track <.5) for tracks with > 5 MeV. he resulting effect on r trk is % for y <.,.% for. y <. and 5.5% for. y < racking in core: High track densities in the core influence the tracking efficiency due to shared hits between tracks, fake tracks and lost tracks. he number of shared hits is well-described in Monte Carlo simulation. he carried by fake tracks is negligible. A relative systematic uncertainty of 5% on the loss of efficiency is assigned. he shift of r trk due to this uncertainty on the loss of efficiency is evaluated in Monte Carlo simulation on generated charged articles. Monte Carlo seudoexeriments are generated according to the varied inefficiency. For each the ratio of the sum of the associated generated articles (truth tracks) with track > GeV to the sum of those associated truth tracks with > GeV which also have a matched reconstructed track with track > GeV, is calculated. In this latter samle a truth track without or with a reconstructed track with track > GeV is added or resectively discarded according to the inefficiency uncertainty. he relative shift in the ratio r trk is added in quadrature to the systematic uncertainty.

93 9 ALAS collaboration: Jet measurement with the ALAS detector trk > MC > Data / <r trk = <r R r rtrk,b trk.4... ALAS b s, y <. Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data Jet trigger data Minimum bias data Sys. Uncertainty ±.% Fractional systematic uncertainty ALAS b s, y <. Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data otal sys. uncertainty b tag. calibration MC generator Jet resolution Material descrition racking in core (a) y <. trk > MC > Data / <r trk = <r R rtrk,b.4... ALAS b s,. y <. Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data Jet trigger data Minimum bias data Sys. Uncertainty ± 4.% Fractional systematic uncertainty ALAS b s,. y <. Anti k t R=.4 EM+JES s=7ev, Ldt = 4 b Data otal sys. uncertainty b tag. calibration MC generator Jet resolution Material descrition racking in core (b). y <. trk > MC > Data / <r trk = <r R rtrk,b ALAS b s,. y <.5 Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data 4 Jet trigger data Minimum bias data Sys. Uncertainty ± 6.% Fractional systematic uncertainty ALAS b s,. y <.5 Anti k t R=.4 EM+JES s=7ev, Ldt = 4 b Data 4 otal sys. uncertainty b tag. calibration MC generator Jet resolution Material descrition racking in core (c). y <.5 Fig. 88: he ratio of the mean value of r trk in data and Monte Carlo (left) and the fractional systematic uncertainty (right) as a function of for y <. (a),. y <. (b) and. y <.5 (c). Anti-k t s with R=.4 calibrated with the EM+JES scheme are used. he dashed lines indicate the estimated uncertainty from the data and Monte Carlo simulation agreement. Note the changed axis ranges in (c). Only statistical uncertainties are shown on the data oints.

94 ALAS collaboration: Jet measurement with the ALAS detector 9 R = R rtrk,b /R r trk,inclusive.4... ALAS b s, y <. Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data Jet trigger data Minimum bias data Syst. uncertainty ±.% Fractional systematic uncertainty ALAS b s, y <. Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data otal sys. uncertainty MC generator b tag calibration (a) y <. R = R rtrk,b /R r trk,inclusive.4... ALAS b s,. y <. Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data Jet trigger data Minimum bias data Syst. uncertainty ±.5% Fractional systematic uncertainty ALAS b s,. y <. Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data otal sys. uncertainty MC generator b tag calibration (b). y <. R = R rtrk,b /R r trk,inclusive ALAS b s,. y <.5 Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data 4 ± 6.% Jet trigger data Minimum bias data Syst. uncertainty Fractional systematic uncertainty ALAS b s,. y <.5 Anti k t R=.4 EM+JES s=7ev, Ldt=4 b Data 4 otal sys. uncertainty MC generator b tag calibration (c). y <.5 Fig. 89: he ratio R (see Equation 6) of R rtrk,b- for identifed b-s and R rtrk,inclusive for inclusive s (left) and the fractional systematic uncertainty (right) as a function of for y <. (a),. y <. (b) and. y <.5 (c). Anti-k t s with R =.4 calibrated with the EM+JES scheme are used. he dashed lines indicate the estimated uncertainty from the data and Monte Carlo simulation agreement. Only statistical uncertainties are shown on the data oints. Note the changed axis ranges in (c).

95 94 ALAS collaboration: Jet measurement with the ALAS detector 5. Jet resolution: he energy resolution in Monte Carlo simulation is degraded. A random energy that corresonds to a resolution smearing of % is added to each. he resulting shift of the ratio r trk is evaluated and added in quadrature to the overall systematic uncertainty. he two biggest contributions to the systematic uncertainty are due to the material descrition and the difference between the r trk distribution for HERWIG++ and PYHIA.. Event selection for unch-through analysis Anti-k t s with R=.4 calibrated with the EM+JES scheme are used in this study. Jets in the barrel of the ile calorimeter with η <. are used. Events with at least two s are retained, if the highest satisfies j > GeV and the second highest satisfies j > 8 GeV. he two leading s are required to be back-to-back requiring φ > Results Figure 88 (left) shows the ratio of data to Monte Carlo simulation. An agreement of the calorimeter to track measurements is found within % in the bin y <., within 4% for. y <. and within 6% for. y <.5. he relative resonse R between identified b-s and inclusive s is shown in Figure 89 for all y-bins indicating the resulting relative b- energy scale uncertainty with resect to the inclusive s samle. he uncertainty for b-s is estimated to be %,.5% and 6% in the range y <.,. y <. and. y <.5, resectively. For the calculation of the systematic uncertainty in R it is assumed that at first order the uncertainty in the denominator and numerator of R from the tracking, namely tracking efficiency, material descrition, are fully correlated and cancel. he resolution for inclusive and identified b-s is considered to be similar. Both assumtions are exactly valid for high s; for low s the second order deviations are estimated to be about.%. he most significant systematic uncertainties on R are due to the choice of the Monte Carlo generator and the b-tagging calibration. hose indeendent uncertainties are added in quadrature. he Monte Carlo generator uncertainties from the inclusive samle and from the b-tagged samle are also added in quadrature.. Energy deositions in the hadronic calorimeter he energy deosits in the outermost layer of the barrel of the ile calorimeter are a good indicator of the energy deositions beyond the calorimeter. hese are shown in Figure 9 for the leading and the sub-leading. Most s deosit only about to 7 GeV energy in the outermost calorimeter layer. he Monte Carlo simulation gives a good descrition of the data for < 8 GeV. For higher the data distribution is below the Monte Carlo simulation, but the statistical uncertainties are large. Figure 9 shows the deendence of the energy deosition in the outermost layer of theile calorimeter measured at the EM scale for the leading and sub-leading. he energy in the third layer of theile calorimeter increases with rising. he data are well described by the Monte Carlo simulation in the low region. Starting from about 4 GeV the data tend to be 5 % above the Monte Carlo simulation. For high the statistical uncertainties are large..5.4 Summary he energy scale for identified b-s relative to that of inclusive s is evaluated for anti-k t s with R =.4 for the EM+JES calibration scheme. he resulting relative b- energy scale with resect to the inclusive s samle is derived within %,.5% and 6% in the range y <.,. y <. and. y <.5, resectively. Muon LAr ile Study of unch-through For s at very high transverse momentum it is ossible that art of the energy is not deosited in the calorimeter, but leaks out to the detector comonents beyond the calorimeter. his leads to a systematic reduction in the measured energy. Jets that deosit energy beyond the hadronic ile calorimeter and in the muon system are called unch-through s. A grahical reresentation of a candidate for a unch-through in data is shown in Figure 9. In this section the Monte Carlo simulation of energy deosits in the outermost calorimeter layer is tested. Quantitative estimates of the energy lost beyond the calorimeter are obtained using a tag-and-robe technique. Fig. 9: Grahical reresentation in a zoomed x-y view of an event candidate with one large transverse momentum ( = 76 GeV) having a large activity in the last ile calorimeter layer (8 GeV at the EM scale) and in the muon detectors. he tracks in the inner detector are shown as lines in the to right, the energy deosits in the LAr and ile calorimeters are shown as light boxes. he hits in the muon system are shown as oints. here are 8 hits measured in the muon system.

96 ALAS collaboration: Jet measurement with the ALAS detector 95 Number of events/gev Data EM+JES Number of events /GeV Data EM+JES ilebar energy for leading ilebar energy for subleading (a) Leading (b) Subleading Fig. 9: Distribution of the deosited energy in the outermost layer of theile barrel calorimeter measured at the EM-scale for the leading (a) and the subleading (b). Anti-k t s with R =.4 within η <. and calibrated with the EM+JES scheme are used. he leading is required to be above > GeV the subleading is required to be above > 8 GeV. Only statistical uncertainties are shown. <ilebar energy> Data EM+JES <ilebar energy> Data EM+JES (a) Leading Leading Subleading (b) Subleading Fig. 9: Average energy deosited in the outermost layer of the ile barrel calorimeter at the EM-scale for the leading (a) and the subleading (b) as a function of the transverse momentum. Anti-k t s with R=.4 within η <. and calibrated with the EM+JES scheme are used. he leading is required to be above > GeV the subleading is required to be above > 8 GeV. Only statistical uncertainties are shown.. Di balance as an indication of unch-through he relative calorimeter resonse between the two s in a di event can be measured using the di balance method. In Section 9.6 the reference is chosen as a well-measured object in the central detector region that is used to assess the JES uncertainty of the robe in the forward region. However, in the context of unch-through such a distinction cannot be made. Jet unch-through can occur in any detector seudoraidity region. Fluctuations in the article comosition or in the hadronic shower occur with equal robability for both s and it is not ossible to know a riori which of the s will be affected. A different aroach is therefore emloyed. he energy lost beyond the calorimeter will create a comonent of the missing transverse energy E miss in the direction of the unch-through