Jet shapes in top quark pair events in the di-lepton channel

Transcription

1 Summer Student Programme DESY Hamburg 204 Jet shaes in to quark air events in the di-leton channel Name: Harrison Schreeck Suervisor: James Howarth

2 Contents Introduction 2 heory 2. o Pair Production ALAS detector & LHC Hadron Colliders and MC Generators Jets at ALAS Observables Analysis 8 3. Background Events and Systematic Uncertainties MC unes Phi distribution /MC agreement Summary & Conclusion 3 I

3 II

4 Figure : o quark air roduction at the LHC. Via Quark-Antiquark (to) or gluon fusion (bottom). [3] Introduction Since its discovery in 995 at the evatron by the CDF[] and D0[2] the o quark has been studied in great detail. he o quark is very secial comared to other quarks as it does not hadronize due toits high mass and hence very short lifetime. At hadron colliders o quarks are usually roduced in airs (details of the roduction and decay of o quark airs are given in Sec.(2.)). o quark air events are articularly interesting as they feature a high energy comonent, the hard-scattering arton interaction which leads to the creation of the to air, but also a soft energy art because of the interacting roton remnants, called underlying event (UE). he UE consists of artons which have not interacted in the main hard-scattering and any additional hardscattering rocesses in the same collision, which is known as multile arton interaction (MPI). here are also contributions from other eects like initial and nal state radiation (ISR/FSR) and the interaction of the to decay roducts with the rest of the event. his is discussed in more detail in Sec.(2.3). Because soft interactions cannot be calculated by erturbative quantum chromodynamics (QCD), they are modelled henomenologically in Monte Carlo generators. oair events can be used to check if the eects of UE are modelled roerly. In this analysis jet shaes in o air events are used to check tuning of the Monte Carlo models used to simulate o-air events. 2 heory In this section an overview is given of the used event observables, the concet of Monte Carlo generators, and the selection criteria for o-antito events. 2. o Pair Production o quarks are usually roduced in airs at hadron collider via QCD interaction, although a single to roduction via electroweak interaction is also ossible but with a signicantly lower cross section. he various roduction channels for to-antito airs, at leading order, can be

5 seen in Fig.(). Because the o quark has a much higher mass (73 ± 0.52 ± 0.72 GeV [4]) than any other quark, it decays before hadronization and nearly exclusively into a W boson and a b quark. he W boson then decays into either a quark/antiquark air (hadronically) or into a leton and the corresonding avour neutrino (letonically). o-quark events are therefore characterized by the decay of the two W bosons. If both W bosons decay hadronically, the event has 6 jets in total with two of them being b jets, which can exerimentally be searated from light jets. his decay channel has by far the largest branching ratio, but has the disadvantage of signicant backgrounds from multi-jet events. If one W boson decays hadronically and the other letonically, which is called the leton + jets channel, there are 4 jets with two b-jets and a high leton together with missing transverse energy ( E ) from the neutrino. he branching ratio o Pair Branching Fractions "alljets" 46% τ+jets 5% τ+τ % τ+µ 2% τ+e 2% µ+µ % µ+e 2% e+e % "diletons" e+jets 5% µ+jets 5% "leton+jets" Figure 2: Branching fraction of the dierent ossible decay channels for o Quark airs. [5] for this decays channel is roughly 5% er leton, which gives 30% in total (taus are usually not considered because they are much more dicult to identify). his decay channels suers less from background contributions and has a reasonably high branching ratio, which is why this channel is often called 'golden channel'. he last decay channel is the dileton channel in which both W bosons decay letonically. his gives just 2 b-jets, two isolated, high letons and missing transverse energy from the two neutrinos. his channel has by far the lowest branching ratio ( 5%), but features a very unique signature which makes it easy to identify and distinguish from background events. his channel is used in the following analysis because of its high urity. he main backgrounds in this channel are Drell-Yan events, single to and WW/WZ/ZZ+jets events. By requiring two b-tags (inclusive) and other selection criteria, such as exactly two letons with oosite charge, these backgrounds are suressed. he b-tagging is achieved using the MV algorithm [6]. his algorithm combines the results of multile variables to identify a bjet at an eciency of 70 %. o remove the Drell-Yan background, only the eµ channel is used, which decreases the statistics but leaves, in combination with the other criteria, only single-to events as a relevant background. A list of all selection criteria used can be seen in ab.(). 2.2 ALAS detector & LHC he ALAS detector [7] is a general-urose article detector at the Large Hadron Collider (LHC) at CERN in Geneva. he LHC [8] is the worlds largest article accelerator with a circumference of 27 km where rotons are collided with rotons. In its rst run the center of mass energy was 2

6 Event selection criteria n Jets 2 n Letons = 2 Oosite sign letons Cosmic muon removal n B-Jets 2 H > 30 GeV able : List of alied event selection criteria. 7 ev (200-20) and 8 ev (202). he LHC was built to search for the Higgs boson and other new articles. Because of the large center of mass energy it also serves as a o-quark factory. he cross section at the LHC is two orders of magnitude higher than at the evatron where the o-quark was discovered and studied for the rst time. he ALAS detector has a solid angle coverage of nearly 4π and features an inner detector resonsible for tracking that covers the seudoraidity range η < 2.5. he azimuthal angle φ is covered comletely. he inner detector is built of silicon ixel detectors, a semiconductor tracker (SC) and a straw-tube transition radiation tracker(r). he inner detector is surrounded by a 2 magentic eld created by a suerconducting solenoid. he calorimeters used in the detector are samling calorimeters. he electromagnetic calorimeter uses lead and liquid argon while the hadronic calorimeter uses scintillating tiles.muons are measured in the muon sectrometer (MS) which has a toroidal magnet system to measure the muon track momenta searately. At ALAS a trigger system with three levels is imlemented, where the rst one is a hardware trigger and the other two are software triggers. 2.3 Hadron Colliders and MC Generators At hadron colliders, the colliding articles are not elementary articles but comosite articles, which results in some exerimental challenges. When two rotons collide, the hard interaction occurs between the artons, which are the valence quarks, gluons and sea quarks. he collision is divided into three arts (see Fig.(3)), which is called factorization theorem. he rst art is the short-distance artonic cross section and the second art consists of long-range eects, described by Parton Density Functions (PDFs), fragmentation functions and form factors. Figure 3: Parton interaction at a hadron collider. [3] he colliding artons carry only a fraction x of the momentum from the arent article. he robability of a certain arton (valence quark, gluon, sea quark) to carry a secic fraction x is described by the PDFs. he PDFs are not calculated directly by erturbative QCD but are extracted from ts to data from dee inelastic scattering exeriments like HERA at DESY. he hard-scattering rocess between the two artons from the rotons can be calculated with erturbative QCD, as the energy is high and the strong couling constant α s is small. he 3

7 matrix elements of the rocess can be calculated using feynman rules in leading-order (LO), nextto-leading-order (NLO) or even higher orders, where more and more virtual corrections to the tree level rocess are considered. After the hard-scattering rocess the outgoing quarks and gluons start begin to shower and hadronize, where quarks radiate additional gluons and gluons slit into quark/antiquark airs. In this rocess the energy is lowered to a oint where erturbative QCD is no longer alicable, because α s is no longer small. Eventually quarks are conned into hadrons. o describe the hadronization dierent models are used. he most oular are String fragmentation (also called Lund model) and Cluster fragmentation shown in Fig.(4). he motivation behind the String model is that the QCD otential is between two coloured objects and the the force between them rises linearly for large distances, like a sring, which is usually visualised by cylindric shaed eld lines that look like strings, see Fig.(4(b)). he cluster model on the other hand is motivated by the observation that artons in a shower tend to be clustered in colorless grous. his is reresented by ellises shown in Fig.(4(a)). Both models are used today in Monte Carlo generators. Pythia6 [9], for examle uses the string model, while Herwig [0] uses the Cluster model. Both rograms use, as an inut, the erturbative calculations for a given rocess and then model the hadronization. he erturbative calculation is achieved in this analysis with POWHEG [] and MC@NLO [2] for Pythia and Herwig, resectively. Both of these generators use next-to-leading order calculations for the matrix elements. As mentioned in Sec.() the UE has to be considered as well. For the individual contributions secial Monte Carlo tunes are created, usually from data. he ALAS grou has develoed a secial MPI tune from dijet events at the LHC. It is now interesting to see if this tune is also sensible for o-antito events, which can be at higher scales than dijet-data. here are also other eects that have to be taken into account, such as color reconnection. Color reconnection describes the interaction of coloured artons during the showering and hadronization. Gluons are emitted and absorbed by the artons which modies, for examle, jet shaes. A summary of all the dierent eects that lay a role can be seen in Fig.(5). uning is needed in the rst lace because erturbative QCD calculations can only be made in the high energy regime. he MC tunes used in this analysis are the Perugia P20C tunes [3]. In one of them the Multi Parton Interaction is increased and in the other one the color reconnection is lowered, but not comletely turned o. 2.4 Jets at ALAS he reconstruction of jets in a given event is a rather dicult rocedure and there are multile algorithms to achieve this. he ALAS collaboration uses the so called anti-k t algorithm [5] to reconstruct jets. One arameter of this algorithm is the jet radius. he radius of a jet is dened as: R = ( η) 2 + ( φ) 2, (2.) where η = ln [ tan( θ 2 )] is the seudoraidity and φ the azimuth. At ALAS, R = 0.4 or R = 0.6 is used to identify jets. his value is chosen arbitrarily and other exeriments like CMS use R = 0.5 or R = 0.7 for examle. In this analysis, only jets of size R = 0.4 are used. In the coordinate system used at ALAS, the beam axis lies along the z-axis and θ is the angle between the article/jet and the z-axis. 4

8 (a) Cluster model (b) String model Figure 4: Dierent hadronization models. [4] Figure 5: Illustration of arton interaction in a collision. [3] 5

9 rack selection criteria 6 hits in the SC hit in the ixel detector η 0 able 2: List of alied track selection criteria. In this analysis, tracks in the inner detector are used to robe jet shaes. are required to be well measured, which means that there have to be at least 6 hits in the Semiconductor racker (SC) and at least one hit in the ixel detector. with a higher than 00 GeV are required to have a goodness of t robability > 0.0 to exclude tracks that have not been measured correctly. Additionally a cut on is used and tracks below this threshold are not considered. A list of all track selection criteria can be seen in ab.(2). In this analysis tracks are only considered if they are closer than R = 0.6 to one of the two b-jets. 2.5 Observables he main observable that is used in this analysis is the averaged sum of the transverse momenta of the tracks inside the jets:. (2.2) his observable is used to robe the energy of the jet in two dierent ways. he rst is to dene a cone inside the jet-cone and consider all tracks that are inside. he size of this cone is then increased until it matches the jet-cone and even a little further, since jets do not sto at the arbitrary cut of R = 0.4. his robes the jet energy as a function of jet radii. A schematic visualization of this rocedure can be seen in Fig.(6). he other way that the is used is not to increase the size of the cone but to look at the dierential jet shae with an annulus starting at the center and then going outwards. Using this aroach it is ossible to look at Figure 6: Visualization of the growing cone inside the jet. the energy distribution inside the jet in more detail. A schematic of this technique is shown in Fig.(7). In addition to these observables based on the individual tracks, the angular distribution 6

10 Figure 7: Visualization of the growing annulus inside the jet. in φ-sace of the jets is also investigated. his observable is of a articular interest for events with an additional third jet, originating from initial or nal state radiation, see Fig.(8). his observable should also be sensitive to the underlying color reconnection in the event as described in [6]. he concrete observables used are φ(b, b), the azimuthal dierence between the two b- Figure 8: Schematic view on o-antito events with and without an additional third jet. jets, φ(b/ b, t t), the azimuthal dierence between the leading/sub-leading b-jet and the transverse t t system and φ(3rd jet, t t), the azimuthal dierence between the 3rd jet and the transverse t t system. In Addition to this denition, a variation with modied jet axes is used as suggested in [6]. he modied jet axis φ Jet is given as: φ Jet = φ Jet + n φ i with φ i = φ i φ Jet, (2.3) n i= where n is the number of tracks inside the Jet. his weighting of the jet axis by the tracks might be aected by the color reconnection tune and this modication should aect the ull between 7

11 Backgrounds WW + 0//2/3 jets ZZ + 0//2/3 jet ZW + 0//2/3 jets Single to able 3: Considered Backgrounds for the analysis two jets and therefore the distribution in φ-sace. 3 Analysis In this section the single stes of the analysis will be exlained in detail. he data used here is the 20 fb samle from the ALAS detector, collected at a center of mass energy of 8 ev. 3. Background Events and Systematic Uncertainties Although the amount of background is very small because of the chosen selection criteria, searate Monte Carlo samles were used to subtract any remaining background contributions from the data. he backgrounds considered are listed in ab.(3). hese samles were scaled and then subtracted from the data. For the POWHEG + Pythia MC samle systematic uncertainties were looked at. hese include jet energy scale (JES), b-jet energy scale (bjes) and trigger eciencies as well as misstagging. he lots shown in Sec.(3.3) are created with the background subtraction and include the systematic uncertainties. 3.2 MC unes In the rst ste the dierent MC tunes are comared with the data. he tunes however are generated using a simle beam-sot model and are not comared directly to data. o make the comarison ossible the dierence between the tunes and a nominal samle which uses the same simler beam-sot model is calculated. his dierence is then added to a nominal samle with a better beam-sot model (POWHEG+Pythia), which gives two new tunes. hese tunes are then used for the comarison. he result for the leading Jet can be seen in Fig.(). he rst thing to notice is that the MC tunes are in good agreement with the data. Looking at the shae of the distribution itself, one can see in the inclusive Plot (Fig.(9(a))) the sum of the momenta is rising, which is exected since more tracks are included in a bigger cone. From the dierential lot (Fig.(9(b))) one can see that most of the energy, is around the center of the jet and if one goes further outside the average energy of the tracks decreases. For the sub-leading b-jet and the extra gluon jet the shae is similar but shows small dierences. In case of the sub-leading jet one can see that the maximum in the dierential distribution is slightly shifted to the right, which means that the high tracks are not as centred as in the leading jet. Additionally one can see that for values R > 0.4 the dierential distribution is not at but starts to rise. he same behaviour can also be seen for the extra jet. Because this rise starts at R = 0.4, which is the ALAS jet radius, it is likely that the rise is caused by the analysis itself. One exlanation is that other jets are too close and tracks of these jets are accidentally counted. o check this hyothesis, an analysis was made with an additional jet removal. All events in which there was a jet closer than R = 0.6 to the sub-leading jet were ignored and only those considered where 8

12 MPI une MPI une (a) inclusive (b) dierential Figure 9: Comarison of Monte Carlo tunes with data for the leading B-Jet MPI une 0.5 MPI une (a) inclusive (b) dierential Figure 0: Comarison of Monte Carlo tunes with data for the sub-leading B-Jet MPI une 0.2 MPI une (a) inclusive (b) dierential Figure : Comarison of Monte Carlo tunes with data for extra jets from gluons (3rd or 4th jet). 9

13 (a) Without jet removal. (b) With jet removal. Figure 2: Comarison of dierential for the sub-leading b-jet with and without additional jet removal for the region R 0.6 (nominal MC samle). Events 0.6 Events Nominal 0. Nominal b b b b b b (a) 2-Jet events (b) 3-Jet events Figure 3: φ(b, b) distribution for events with exactly 2 or 3 jets. the jet was isolated. he result of this analysis can be seen in Fig.(2). he removal of the jets does indeed atten the shae of the histogram, which suorts the theory that tracks from these jets are resonsible for the rise seen before Phi distribution he second major variable used in this analysis, the φ dierence between the two b-jets, is also tested with the MC tunes. he dierences between the two b-jets in φ-sace should be aected esecially by the low color reconnection tune. herefore the nominal MC samle is comared with the low colour reconnection tune and the data. Fig.(3) shows the result when the normal jet axes are used and Fig.(4) shows the result with the weighted jet axes. he rather large uncertainties for the low colour reconnection tune make a comarison more dicult but neither of the lots show a signicant dierence between the two MC samles. From the lots one can also see that a third jet from a gluon does not change the shae of the distribution signicantly, most likely because gluons jets tend to be soft and do not carry enough momentum to change the φ-distribution of the two high- b-jets. 0

14 Events 0.6 Events Nominal 0. Nominal b b b b (a) 2-Jet events (b) 3-Jet events Figure 4: φ(b, b) distribution for events with exactly 2 or 3 jets. Events Events Nominal Nominal b tt b tt b tt b tt (a) 2-Jet events (b) 3-Jet events Figure 5: φ(b, t t) distribution for events with exactly 2 or 3 jets. Aside from the azimuthal dierence between the 2 b-jets, also the dierence between the leading jet and the transverse t t system φ(b, t t) has been investigated. he result is shown in Fig.(5) and Fig.(6). he rst thing to notice here is that the leading b-jet refers to go into the direction of the transverse t t-system. Again there are no signicant changes to see for the low colour reconnection tune. he 2/3 jet distinction also has no visible eect. 3.3 /MC agreement he nal art of this analyis focuses on the /Monte Carlo agreement of the reviously used observables. In addition to the POWHEG+Pythia samle used in the revious stes, a second Monte Carlo samle MC@NLO+Herwig is used here. he motivation behind that being that Herwig seems to have roblems modelling the fragmentation in certain event tyes. he question is if the descrition of o-antito events is correct. Looking at the results in Fig.(7), Fig.(8) and Fig.(9) one can see that the agreement between the Monte Carlo samles and the data is good, considering the uncertainties. here seem to be some dierences in the shaes, but the uncertainties do not allow to say whether this eect is a statistical uctuation or a roblem with the modelling. On the other hand it is very clear that there is no signicant dierence between POWHEG+Pythia and MC@NLO+Herwig. Neither of them describes the data better than the

15 Events 0.4 Events Nominal Nominal b tt b tt (a) 2-Jet events (b) 3-Jet events Figure 6: φ(b, t t) distribution for events with exactly 2 or 3 jets (stat. only) POWHEG + Pythia (stat. syst.) MC@NLO + Herwig (stat. only) 5 (stat. only) POWHEG + Pythia (stat. syst.) MC@NLO + Herwig (stat. only) (a) inclusive (b) dierential Figure 7: Comarison of Pythia and Herwig samles with ALAS data for leading b-jet (stat. only) POWHEG + Pythia (stat. syst.) MC@NLO + Herwig (stat. only) 0 8 (stat. only) POWHEG + Pythia (stat. syst.) MC@NLO + Herwig (stat. only) (a) inclusive (b) dierential Figure 8: Comarison of Pythia and Herwig samles with ALAS data for sub-leading b-jet. other. For all three jets they show a very similar behaviour. 2

16 (stat. only) POWHEG + Pythia (stat. syst.) 5 (stat. only) POWHEG + Pythia (stat. syst.) MC@NLO + Herwig (stat. only) MC@NLO + Herwig (stat. only) (a) inclusive (b) dierential Figure 9: Comarison of Pythia and Herwig samles with ALAS data for extra jet. 4 Summary & Conclusion his analysis has shown that, although hadronization is very comlex rocess with many dierent variables which are not easy to model correctly, the descrition of it by current Monte Carlo generators is indeed sucient to describe jet shaes, at least in t t events. Further it was shown that the Perugia P20C tunes are in fact sensible for to air events, which might not be that surrising but is still a good cross-check. he φ-distribution between the two b-jets, esecially with the weighted jet-axes, is exected to have shown some dierences in the shaes, but these dierences were not visible within the statistic. his was not the main art of this roject and was not looked at in more detail. Future analyses could investigate this to see if more statistics reveal a shae dierence. It is also interesting that a third jet does not change the distributions signicantly. he comarison of POWHEG+Pythia and MC@NLO+Herwig showed that although there might be cases in which Herwig has roblems to model jet arameters correctly, t t events are modelled quite well. A very similar analysis has already been erformed with the 7 ev ALAS data [7]. Fig.(20) shows the result from this analysis. hey also comared Pythia and Herwig samles and received similar results. ogether with the results from the analysis erformed here there seems to be no reason to refer one generator. 3

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