Measurement of W/Z+ Jets Cross-Section at ATLAS

Measurement of W/Z+ Jets Cross-Section at he collaboration Abstract he production of a W or Z boson in conjunction with jets is an interesting process in its own right as well as a signal channel (and background) for many interesting standard model and beyond standard model physics signals. Final states with,, or more jets accompanying a W/Z boson will be observable at the LHC and will serve as a crucial part of the physics program. he variety of possible jet multiplicities allows for precision tests of jet reconstruction algorithms and techniques. In addition, the reconstruction of leptons and of missing transverse energy becomes more complex in the presence of a multi-jet final state. In this note, we will quantify the differences of lepton, missing transverse energy and jet reconstruction with respect to that observed in inclusive W and Z production. he wide kinematic range for production of W/Z + jets allows serves as a testing ground for perturbative QCD predictions, both fixed order alone and in conjunction with parton shower Monte Carlos.

Introduction In this note, we examine the triggering, reconstruction and analysis of events containing a W or Z boson plus jets in. We concentrate on channels with decays into electrons and muons, ignoring for the moment taus (except to account for backgrounds to the other decay channels). Much of the effort on the triggering and reconstruction of leptons and of missing transverse energy is in common with the inclusive W/Z note []; thus, we do not reproduce all of the details from that note, but rather comment on the impact of a multijet environment on these issues. Fully simulated signal and background event samples are treated as pseudo-data. Comparisons of the reconstructed/orrected quantities, when possible, are made to truth-level hadron information (and in some cases to parton-level information with parton-to-hadron corrections applied). Our primary end-result are hadron-level cross-sections, similar to what we will have with the real data. We present expectations/yields/systematics scaled to fb, an integrated luminosity that should be accumulated within the first two years of running. An important source of theoretical systematic uncertainties at the LHC is represented by the parton distribution dunctions (PDFs). hus, assessing the level of PDF uncertainties is crucial for studying both processes within and beyond the Standard Model. Experimental systematic uncertainties are the main limitations to the possibility of improving our knowledge on PDFs. Among these, errors due to a miscalibration of the jet energy scale (JES) are expected to be the dominant systematics for the determination of W/Z + jets cross-sections. A comparison of the impact of theoretical and experimental systematic uncertainties is therefore useful. he impact of JES uncertainties of, and % (%) are examined and compared to the level of PDF uncertainties. Reference Cross-Sections Reference cross-sections are collected in [], but we briefly discuss here the cross-sections relevant for this note. NLO is the first order at which the W/Z + jets cross-sections have a realistic normalization (and realistic shapes for some kinematic distributions) []. he current state of the art for NLO calculations is for W/Z + jets, although there is ongoing work for the calculation of jet final states. cross-sections for W/Z + 0, and () final states can be conveniently calculated at LO and NLO (LO only) using the MCFM [] program, and it is from this program that we determine our reference cross-sections ) he MCFM cross-sections were generated using the CEQ6. PDFs and a renormalization/factorization scale of m Z + p,z, with similar kinematic cuts on the leptons and jets as will be described in Section.. Corrections from Parton to Hadron Level Cross-section measurements in data and LO/NLO predictions are to be compared at the hadron level (particle level) ). Hence, the data have to be unfolded with respect to the detector response. For comparisons of data to NLO parton level predictions from MCFM, either the data need to be corrected to the parton level or the theory corrected to the hadron level. We discuss the latter correction below for the specific case of Z + jets (but which can also be applied without great error to the case of W + jets). he MCFM predictions have to be corrected with respect to the non-perturbative effects of fragmentation and underlying event (UE). he fragmentation and underlying event corrections are ) For this note, we compare the MCFM predictions only for Z + jets. ) his is also sometimes referred to in as truth level.

Z->mumu: UE correction vs E jets Z->mumu: UE correction vs E jets extracted using PYHIA [] Monte Carlo samples by comparing the hadron level results, with the current underlying event tune, to corresponding results in samples in which fragmentation and multiple-parton-interactions have been switched off. he corrections are determined by dividing the hadron-level distribution of the observables from standard PYHIA by the respective distributions from PYHIA with the non-perturbative effects switched off. o the extent to which the partons that can comprise a jet in MCFM mimic the effects of the parton shower in PYHIA, the corrections derived from the procedure above can be applied to the MCFM output []. We study the hadronization corrections for both cone (R=0. and 0.7; termed Cone0 and Cone07 hereafter) and k jet algorithms (D=0. and 0.6; termed Kt0 and Kt06). Figure shows the correction from parton to hadron level from fragmentation alone (a) and from both fragmentation and underlying event (b) for Cone0 jets. he impact of fragmentation is to reduce the amount of energy in the jet cone. hus, from fragmentation effects alone, jets at the hadron level tend to have lower p than jets at the parton level. he impact of the underlying event is to add energy to the hadron level jet. In general, the underlying event tends to add more energy to the jet than lost by fragmentation, but the exact ratio depends on the radius of the jet. Whereas the fragmentation corrections for Cone07 jets are smaller than for Cone0 jets, the underlying event corrections are larger due to the larger cone size. Kt0 shows the lowest combined corrections since fragmentation and underlying event effects basically cancel out. he performance of Kt06 jets is comparable to the one of Cone0 jets. Except for Cone07 jets, the non-perturbative effects are negligible for jets with p > 0 GeV in the current PYHIA tune. (a) # jets (standard) / # jets (no frag.).8.6.. 0.8 Pythia Z µµ Fragmentation correction vs P jets Cone0 jets 0 0 0 0 60 70 80 90 0 P jets (GeV) (b) # jets(standard)/ # jets (no UE, no frag).8.6.. 0.8 Pythia Z µµ UE+fragmentation correction vs P jets Cone0 jets 0 0 0 0 60 70 80 90 0 P jets (GeV) Figure : Ratio of Cone0 Jet p distributions (a) between standard PYHIA and PYHIA without fragmentation and (b) between standard PYHIA and PYHIA without non-perturbative corrections. Monte Carlo Datasets Most of the Monte Carlo data samples used in these studies are generated with ALPGEN [6] interfaced with HERWIG [7] using the leading order PDF set CEQ6LL [8]. he cross-sections are calculated using a renormalization/factorization scale of m Z + p,z, similar to that used for the MCFM predic-

tions. he full datasets are obtained by merging samples of W(Z) + 0 up to partons, weighted according to the expected cross-sections, with an MLM [6] matching cut at p > 0 GeV, and normalized to an integrated luminosity of fb. All datasets correspond to exclusive samples, with the exception of the highest multiplicity sample (W(Z) + partons) which is inclusive. he samples correspond to the decays, W eν, W µν, Z e + e and Z µ + µ. A generator-level filter requires one truth Cone0 jet of p > 0 GeV and η <.0 and one (two for Z) electrons/muons with p > GeV and η <.7 in the event. PYHIA signal and background samples are also produced, using the standard underlying event tune. PYHIA Z e + e and W eν events are generated with a generator-level filter requiring one truth electron with p > GeV and η <.7. PYHIA Z ττ events are generated with a filter requiring two electrons/muons with p > GeV and η <.8; PYHIA W τν events are generated with a filter requiring electron/muon decays of the τ, with the decay leptons having p > GeV and η <.8. For Z ττ and Z e + e, the dilepton mass is required to be larger than 60 GeV. A large QCD dijet sample (.M events) is also produced, with a minimum hard-scattering transverse momentum of 7 GeV. Definitions and Cuts We adopt as much as possible definitions and cuts in common with the other notes, and in particular with the inclusive W/Z note [], with comparisons to alternate definitions/cuts where relevant. he reconstruction algorithms in this note are not necessarily optimal for the running conditions in the first two years, but provide a reasonable baseline. We expect further optimization as data become available.. Electrons Both the W and Z analyses impose common electron selection criteria. It is required that the transverse momentum of the electron candidate, p e > GeV, and that it lies in the range η <., excluding the barrel-to-endcap calorimeter crack region (.7< η <.). he electrons are required to fulfill the medium electron-id ) (hereafter, referred to as medium IsEM) [9], which consists of requirements on the calorimeter shower-shape and the matched track. In order to further suppress the contamination from fake electrons in the W selection an isolation requirement within a cone R = 0. of the candidate is imposed, requiring the number of tracks with p > GeV to be less than and the scalar sum of the track p to be less than GeV. he Z selection requires two electron candidates with an invariant mass of 8 < m ee < GeV and R > 0.. ). Muons As in the case of electrons, both the W and Z analyses impose common requirements on muon candidates. A muon candidate requires the combined reconstruction of an inner detector track and a track in the muon spectrometer []. he muon is required to have a transverse momentum of p µ > 0 GeV and η <.. In the Z analysis, the muons are required to have p µ > GeV and the range. < η <. is excluded. Isolation is applied by requiring the energy deposition in the calorimeter to be the less than GeV in a cone of R = 0. around the extrapolation of the muon ) General criteria corresponding to tight and loose electron ID are also available, with tight(loose) resulting in a lower (higher) efficiency, and a smaller (larger) background. ) No calorimeter isolation cuts are applied for these analyses, due to simulation problems, but will be in the actual data analyses. here is an implicit isolation cut, however, present in the trigger [].

track (hereafter referred to as cone0. isolation). he Z analysis selects two muon candidates with an invariant mass of 8 < m µµ < GeV (7 < m µµ < GeV for the Z + b jet analysis).. Missing ransverse Energy In the W analysis, a cut on the missing transverse transverse energy (/E ) is applied to suppress QCD backgrounds. he raw calorimeter-based /E is corrected for the presence of a muon or electron in the final state []. Studies are performed to establish the optimal value of the cut on /E that reduces QCD backgrounds to acceptable levels, while not introducing significant biases to the cross-section measurement. An optimal cut of /E > GeV is chosen.. Jets Jet clustering algorithms can be divided into two main classes: cones and iterative recombination (e.g., the k algorithm) []. Historically, cone algorithms have been used in hadron colliders, due to concerns about speed, especially at the trigger level, and of large systematic effects in busy multijet environments. Fast implementations of the k algorithm [], as well as detailed studies at the evatron performing precision measurements with the algorithm [] argue for the use of the k algorithm along with cone-based ones at the LHC. For the analyses in this note, we use jets clustered with the standard Seeded Cone algorithm with a radius of R = 0. (appropriate for the complex final states expected for the multi-jet environments explored in this note), built from calorimeter towers, and calibrated to the hadron level. In the Z µ + µ channel we also examine the impact of using clusters as a jet constituent for the same algorithm. A detailed comparison with other jet algorithms, including the k algorithm, is beyond the scope of this note. he jet kinematic selection is common for the Z and W analyses. A cone radius of 0. is selected. he lepton and jet candidates must be separated by R l j > 0.. It is required that the jet transverse momentum be p > 0 GeV in the range η <.0. ) he cross-section measurements themselves are prepared only for jets with E > 0 GeV. rigger Paths he trigger selection used here is the same as that used in the inclusive analyses []. In the electron channel, W eν + jets events are required to pass the isolated single-electron trigger; Z e + e + jets events are required to pass the isolated dielectron trigger or the isolated single-electron trigger. In the muon channel, W µν + jets events are required to pass the isolated single-muon trigger; Z µ + µ + jets events are required to pass the isolated dimuon trigger. he trigger efficiencies at the first, second and event filter levels are evaluated as a function of the jet multiplicity. he trigger efficiency is also studied as a function of the overall hadronic activity, the E of the leading jet and the Z,W transverse momentum. For this purpose, a Monte Carlo truth and data driven tag-and-probe method is implemented. Good agreement between the two methods is found. he overall trigger efficiency, with respect to that for the off-line cuts, for the inclusive analysis is compared to that obtained here. It is found that the trigger efficiency for the Z,W+jets analysis is, in general,. % lower than that of the inclusive sample. ) For technical reasons the W +jets analysis was perforned in the range η <.0.

6 ag and Probe Studies he tag and probe method is used in Z e + e +jet events to determine the single object ei efficiency as well as the offline reconstruction and identification efficiencies from data. As described in detail in the tag and probe section of [7], a diagnostic sample of size N is defined by requiring at least one electron candidate to satisfy tag requirements. A control sample of size N is defined by additionally requiring that the second electron satisfies the probe requirements. N and N may be used to extract the single electron efficiency. Absolute reconstruction, identification and trigger efficiencies are calculated independently and may be multiplied together to give the overall efficiency for an electron. Results in this note are quoted at medium IsEM level and the cuts used are those taken as standard in this note. Results are quoted at fb of integrated luminosity. 6. Global Results in Comparison with the Inclusive PYHIA Generated Sample Comparisons are made with an inclusive PYHIA generated sample used in [], which doesn t have the generator level truth jet cuts that are present in this sample. he efficiencies measured from these events may be found in notes [9] and [7]. he difference in global efficiencies between the two samples are of the order of a few percent or less. 6. Differential Efficiencies he dependence of the efficiency on the electron parameters (η, φ, p ) in the PYHIA sample is well documented in [9] and [7] and the dependence observed is similar in the ALPGEN sample. he effects of jet parameters on efficiencies are shown in Fig.. Some points are noted: Firstly, a lower trigger efficiency is observed in regions of higher jet activity (higher jet multiplicity, hadronic activity and p of the most energetic jet. hese events are more likely to fail isolation cuts; secondly, the drop in efficiency at low hadronic p is due to the lower electron p in this region. 6. Background reatment he method of fake rates as explained in [7] is used to estimate the background magnitude. It is observed that the signal-background ratio is lower in the ALPGEN sample. he measured efficiencies after background subtraction (as opposed to earlier results which are from signal analysis only) are tabulated in able. he difference in efficiency is due to the imperfection in the fitting + subtraction procedure. We see that the main discrepancy is seen at the reconstruction level, which is to be expected as this is where the background level is highest. able : Efficiency (Signal only)-efficiency(after BG subtraction) (%) Level Efficiency Reconstruction.00 LVL -0.7 LVL 0.0 EF 0.0 Whole trigger -0.6 6

Reconstruction Efficiency 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0. 0. Measured efficiency MC truth 0 0 60 80 0 0 ΣE t (GeV) Reconstruction Efficiency 0.9 0.9 0.8 0.8 0.7 0.7 0.6 Measured efficiency 0.6 MC truth 0. 0. 0...... N jets rigger efficiency (L*L*EF) 0.9 0.9 0.9 0.88 0.86 0.8 Pseudo data MC ruth rigger efficiency (L*L*EF) 0.9 0.9 0.9 0.88 0.86 0.8 Pseudo data MC ruth 0.8 0.8 0 0 0 0 00 0 00 0 00 0 00 ΣE t (GeV) 0.8 0.8..... 6 N jets Figure : he tag and probe efficiencies (L L EF) are compared to truth information as a function of (left) hadronic activity, and (right) jet multiplicity. he reconstruction efficiencies are shown in the two top plots, and the trigger efficiencies in the bottom two. 7 Measurement of Z + Jet Cross-Sections 7. Introduction his Section discusses the measurement of the inclusive Z( e + e, µ + µ ) + jets cross-sections as a function of the jet transverse momentum and jet multiplicity. he measurement is compared with LO and NLO perturbative QCD predictions. hese measurements will be used, in addition, to validate the event generators which are used to predict the W/Z+jets backgrounds for searches in. In order to prepare the measurement, we use fully-simulated signal and background Monte Carlo events as pseudo-data, with which we perform all steps of the analysis. We also compare the predictions of fully simulated signal Monte Carlo sets from different event generators. he goal of the analysis simulation is to validate the lepton and jet reconstruction in high jet multiplicity events, develop the necessary analysis techniques (unfolding, background extraction) and evaluate the statistical and systematic limitations in terms of probing the QCD predictions and of discriminating between predictions of different event generators. wo separate studies are performed on the feasibility of the Z e + e and the Z µ + µ channels (Sections 7. and 7.). 7. Z e + e + Jets 7.. Signal and Background Distributions he presence of additional jets in the event has an impact on the kinematics of both the leptons and jets. he distributions of electron p, jet p, R between electrons and the minimum R between 7

Z e + e + jet Z e + e + jets Z e + e + jets Process xsec fraction xsec fraction xsec fraction Z e + e 0± 9.9±0.8 89± 87.9±. 900± 80.0±. QCD jets ±89 6.0±0. 6± 6.0±0.8 78±0 6.9±.8 t t 96±8.9±0. ± 6.0±0. 6±.0±. Z ττ.±. 0.0±0.00 (0.67±0.) (0.0±0.00) (0.±0.0) (0.0±0.00) W eν (8±) (0.±0.0) (.9±.6) (0.±0.0) (.±0.) (0.±0.0) able : he accepted cross-sections (in fb) and the corresponding surviving fractions (in %) from signal and background in the Z e + e + jets analysis, after applying the cuts outlined in Section. A jet transverse momentum of > 0 GeV is applied. he numbers in brackets are extrapolated from results obtained for a lower jet multiplicity each electron and the jets (for different jet multiplicities) are studied using fully-simulated Z e + e samples. As expected, the electrons are more boosted (larger p and lower R between electrons) in events with jets, and the distance between electrons and jets becomes smaller in high-multiplicity events. he average jet p, p jet increases with the number of jets. Due to the OR of the single electron and dielectron trigger channels used in this analysis, any efficiency loss of the isolated electron triggers for large jet multiplicities has only a negligible impact. he total Z reconstruction efficiency (offline+trigger) is stable with respect to both the jet multiplicity and the transverse momentum of the leading jet. 7.. Background Estimation he most important backgrounds to the Z e + e + jets signal are processes with real electrons (t t, W eν, Z ττ) and QCD jet production. All backgrounds are estimated from Monte Carlo. Z ττ W eν and t t are simulated with PYHIA. he QCD background is derived from a filtered PYHIA dijet sample. Statistics for this sample are increased by applying a very loose electron selection and then re-weighting the events with the additional rejection factor for the final electron ID. he combined distribution of the invariant mass for signal and background events is shown in Fig. a-c for various jet multiplicities. able gives an overview of the accepted cross-section expected from Monte Carlo from signal and backgrounds. With increasing jet multiplicity, t t replaces QCD as the dominant background source. he errors displayed in the able are of statistical nature. Systematics stemming from the QCD reweighting, and from comparing the results of different generators, are not included in this able. Eventually the QCD background will be determined with data driven methods. he simulation of the t t background also has to be validated separately with data. Figures d-f show the distribution of signal and backgrounds for the observables (jet multiplicity and p jet ). 7.. Unfolding of Detector Effects he reconstructed data have to be unfolded from the detector level to the hadron level, correcting for efficiency, resolution and non-linearities in electron and jet reconstruction. In this note, the individual unfolding corrections are assumed to factorize in leading approximation, and the individual contributions are investigated separately. For the data analysis, an approach will be used consisting of unfolding the combined impact of jet reconstruction efficiency and jet resolution in a bin-by-bin 8

Invariant mass, jets P leading jet Invariant mass, jet Invariant mass, jets P second jet (a) (b) / GeV events / fb Z->ee+jet incl fb Z ee + bkg QCD op Z τ τ W eν / GeV events / fb Z->ee+jets incl fb Z ee + bkg QCD op Z τ τ W eν 0 60 70 80 90 0 0 0 0 0 M(e,e) (GeV) 0 60 70 80 90 0 0 0 0 0 M(e,e) (GeV) (c) / GeV events / fb Z->ee+jets incl fb Z ee + bkg QCD op Z τ τ W eν (d) Njets events / fb 6 fb Z ee + bkg QCD op Z τ τ W eν 0 60 70 80 90 0 0 0 0 0 M(e,e) (GeV) 0 Events with >= N jets (P (jet)>0 GeV) (e) / GeV events / fb Z->ee+jet incl fb Z ee + bkg QCD op Z τ τ W eν (f) / GeV events / fb Z->ee+jets incl fb Z ee + bkg QCD op Z τ τ W eν 0 0 0 00 0 00 P, leading jet (GeV) 0 60 80 0 0 0 60 80 00 P, second jet (GeV) Figure : he distribution of the dielectron mass for signal and background for (a) Z e + e + jet, (b) Z e + e + jets and (c) Z e + e + jets ; the number of events with N jets (E > 0 GeV) (d) and of the E of the leading (e) and the next-to-leading (f) jet for Ldt = fb. 9

unfolding procedure. he corrections are derived with fully-simulated Monte Carlo. he simulation of the jet calibration and resolution will have to be validated with real data. he event weight is corrected for the electron reconstruction efficiency. Since this is the dominant correction and since it varies strongly with both pseudorapidity and with the transverse momentum of the electron, the correction is derived as a function of the generated η in four bins of generated p. he event weight is also corrected for the global efficiency for the electron trigger with respect to the offline selection, determined as: eff trig = (99.6+ 0.)%. he errors on deriving this efficiency, stemming from the limited Monte Carlo statistics, are taken into account as systematic errors for the unfolding procedure. he jet observables are corrected for shifts in the measured jet energy scale (mainly non-linearities at low p ), the jet energy scale resolution and the jet reconstruction efficiency. All corrections are derived for ten bins in p with a comparable number of events in each bin in order to avoid large statistical fluctuations. Figure shows the jet reconstruction efficiency and the shift in the population of the p bins due to the p resolution, extracted from ALPGEN Z e + e + jets Monte Carlo. he jet p scale and resolution are determined using a matching window of R(truth reco jet) < 0. and 0. < p (reco)/p (truth)<.. he jet reconstruction efficiency is determined as the fraction of truth jets which are matched to reconstructed jets applying the same requirements. As expected, the largest bias is observed for low values of p jet. he impact of the resolution, shown in Fig. b, is derived by comparing the p distribution of truth jets before and after a gaussian smearing with the resolution as determined above. Due to the large statistical uncertainties, a global average correction of 0.98 ± 0.00 is determined for jets with p > 0 GeV. he reconstructed jet p is corrected with the jet energy scale corrections, and the event is weighted for each required jet with the correction for efficiency-loss in reconstruction, and the overpopulation due to the jet p resolution. he unfolding corrections are validated by comparing the distributions of truth jet variables with the corresponding ones for corrected reconstructed jets. Figure compares the distribution of the p of the leading and the next-to-leading jet, in different unfolding stages, with the p distribution of truth jets. Within the statistical and systematic errors, the p distributions of truth jets and corrected reconstructed jets are in agreement. (a) Jet reco efficiency.0 0.98 0.96 0.9 Cone0 tower jets Jet reconstruction efficiency (b) N(smeared)/N(unsmeared).0 0.98 0.96 0.9 Shape distorsion due to resolution effects Cone0 tower jets 0.9 0.9 0 0 0 00 0 00 Jet (GeV) P 0 0 0 00 0 00 P Jet (GeV) Figure : Jet reconstruction efficiency (a), and the impact of resolution on the jet p spectrum (b).

P st truth jet P nd truth jet (a) Cross section (fb) /GeV ruth jet P Reco jet P, all corrections Reco jet P, EM corrections Reco jet P, uncorrected (b) Cross section (fb) /GeV ruth jet P Reco jet P, all corrections Reco jet P, EM corrections Reco jet P, uncorrected 0 0 0 00 0 P leading jet (GeV) 0 60 80 0 0 0 60 80 00 P next-to-leading jet (GeV) Figure : Comparison of the distribution of the p of the leading jet (a) and the next-to-leading jet (b) in truth and corrected reconstructed Monte Carlo. 7.. Background Subtraction he Z ττ, t t and W eν backgrounds are subtracted using the Monte Carlo estimates, as will also be done for the collision data. he QCD background is subtracted by weighting all events with a global factor, calculated as - QCD-fraction (as in able ). In collision data, the factor can be derived by a combined fit for signal and background of the invariant mass peak (using sidebands). his method assumes a comparable distribution of the jets in QCD events with two electron fakes and in Z e + e events. Alternatively, the background sample can be derived by inverting selected electron-id cuts. he latter method is preferable but cannot be tested here for the lack of statistics of fully simulated QCD Monte Carlo events. For the final simulation of the measurement, signal and background samples are combined and unfolded to the hadron level as described above. 7.. Comparison of Event Generators and MCFM at the Hadron Level We consider the comparison of theory and measurement for theoretically well-defined quantities: the inclusive cross-section for Z ll+ jet, Z ll+ jets and Z ll+ jets and the differential cross-sections with respect to the p of the leading and the next-to-leading jets. he MCFM predictions are corrected for the residual energy loss due to non-perturbative effects for jets with p > 0 GeV, determined from the current PYHIA tune of underlying event and fragmentation as 0.98±0.0 for Z e + e + jet, 0.98±0.0 for Z e + e + jets and 0.9±0.06 for Z e + e + jets. PDF uncertainties on the MCFM predictions are calculated using the complete set of error PDFs. he inclusive PYHIA and ALPGEN Z e + e samples are normalized to the NLO inclusive MCFM Z e + e cross-section at the generator level. Figures 6(a-c) show the comparison of the distribution of the observables (jet multiplicities and the p of the leading and next-to leading jets) at the hadron level for ALPGEN and PYHIA Monte Carlo with LO and NLO MCFM calculations. he fully simulated ALPGEN and PYHIA samples are unfolded to the hadron level as described in Section 7... he error bars are calculated only from intrinsic Monte Carlo quantities as the quadratic sum of statistical errors from the Monte Carlo sample size and the systematic errors from the unfolding corrections derived for Monte Carlo. he shape of the jet p distribution predicted by ALPGEN agrees well with the shape predicted by MCFM. Due to the tuning of the leading soft radiation in the parton shower, PYHIA predicts a larger inclusive cross-section for Z e + e + jet but a clearly softer p spectrum.

P nd jet P leading jet As a further step towards real data, the systematic errors are adjusted to the values expected from the collision data and propagated to the measured cross-section. Figure 6(d) shows the relative systematic uncertainty on the cross-section (normalized to ) expected for different uncertainties on the jet energy scale for the production of a Z with - jets (p > 0 GeV). Since the difference between the LO and NLO cross-section predictions are on the order of 0%, with a % uncertainty on the jet energy scale, we are still able to differentiate between LO and NLO predictions, whereas with an error of % on the jet energy scale this is not possible. he uncertainty on the jet energy resolution and its impact on the unfolding procedure is an additional source of systematic errors on the cross-section measurement. hey are investigated for jet resolutions up to two times the ones currently expected. An uncertainty of 0% on the jet resolution propagates to an error of -% on the Z e + e + jet cross-section measurement. A wrong assumption of the jet p distribution in calculating the unfolding corrections from the jet energy resolution can also lead to a systematic shift in the cross-section measurement. A comparison between the unfolding corrections derived from PYHIA and from ALPGEN yields a systematic uncertainty of up to. %. (a) (b) Njets cross section (fb) 6 mcfm NLO mcfm LO Pythia Alpgen cross section (fb) / GeV mcfm NLO mcfm LO Pythia Alpgen 0 Events with >= N jets (P (jet)>0 GeV/c) 0 0 0 00 0 00 P, leading jet (GeV) (c) (d) cross section (fb) / GeV mcfm NLO mcfm LO Pythia Alpgen 0 60 80 0 0 0 60 80 00 P, next-to-leading jet (GeV) Cross section bias.. 0.8 0.6 0. Z->ee+jets % JES uncertainty % JES uncertainty % JES uncertainty Inclusive Jet Multiplicity Figure 6: he inclusive jet cross-section as a function of jet multiplicity is shown in (a); the p of the leading jet (b) and of the next-to-leading jet (c) are shown for the unfolded PYHIA and ALPGEN Monte Carlo predictions and for MCFM for an Ldt = fb. In (d), the relative systematic uncertainties on the cross-section (normalized to ) are shown for different uncertainties on the jet energy scale. All jets are required to have a transverse momentum greater than 0 GeV.

7. Z µ + µ + Jets he impact of a high jet multiplicity environment on the lepton reconstruction efficiency is also investigated for the case of the muon channel. he results are comparable to the ones described for the electrons in Section 7... Muon reconstruction efficiencies for different isolation requirements are also investigated. 7.. Background Estimation he important backgrounds for the Z µ + µ + jets analysis are processes with similar topologies (t t, W µν, Z τ + τ ) with real muons, and QCD multi-jet production. For t t, W µν, and Z τ + τ, PYHIA and ALPGEN Monte Carlo samples are used. It can be assumed that the dominating QCD dijet contribution of highly energetic muons are from decays of b b mesons. Monte Carlo samples generated with PYHIA b b(µ + µ ) are thus used to increase the muon background statistics. Figure 7 shows the distribution of the invariant mass for signal and for background, with the backgrounds derived using PYHIA (a) and ALPGEN (b). 7.. Signal and Background Distributions (a) / GeV events / fb Z µ µ + bkg QCD op Z τ τ W µ ν (b) / GeV events / fb Z µ µ + bkg QCD op Z τ τ W µ ν 0 60 70 80 90 0 0 0 0 0 m(µ,µ) (GeV) 0 60 70 80 90 0 0 0 0 0 m(µ,µ) (GeV) Figure 7: Background estimation, as a function of dimuon mass, for PYHIA (a) and ALPGEN (b) requiring isolated muons (cone0.0, E isolation < GeV) and at least one jet (p > 0 GeV, η <.0). Muons from Z µ + µ are highly energetic and isolated. herefore, muons coming from background can be rejected by imposing isolation requirements. In this analysis, several different isolation cuts are investigated. able shows results for signal and background considering different isolation criteria, using PYHIA samples. As the size of the muon isolation cone is increased, the background is reduced, and in particular the background from b b. For our analysis, the cone0.0 isolation cut is used; after the imposition of this isolation cut, the b b background is reduced, and no bias is observed for the muon reconstruction efficiency for high jet multiplicities. he invariant mass window considered is 8 GeV in order to increase the signal to background ratio (in particular to discriminate against the t t background). able shows the accepted cross-sections and the surviving fraction of signal and background for different jet multiplicities using PYHIA and ALPGEN for

(a) events / fb 6 Z µ µ + bkg QCD op Z τ τ W µ ν (b) events / fb 6 Z µ µ + bkg QCD op Z τ τ W µ ν # events with Njets # events with Njets (c) events / fb / 8GeV Z µ µ + bkg QCD op Z τ τ W µ ν (d) events / fb / 8GeV Z µ µ + bkg QCD op Z τ τ W µ ν 0 0 0 00 0 00 Pt, leading jet (GeV) 0 0 0 00 0 00 Pt, leading jet (GeV) (e) events / fb / 8GeV Z µ µ + bkg QCD op Z τ τ W µ ν (f) events / fb / 8GeV Z µ µ + bkg QCD op Z τ τ W µ ν 0 60 80 0 0 0 60 80 00 Pt, nd leading jet (GeV) 0 60 80 0 0 0 60 80 00 Pt, nd leading jet (GeV) Figure 8: Distributions of signal and background jet multiplicities, with backgrounds determined by PYHIA (a) and ALPGEN (b). he jets in this plot are required to have a transverse momentum greater than 0 GeV. he leading jet p and nd leading jet p distributions for signal and background using PYHIA (c),(e) and ALPGEN (d),(f) data samples to determine the backgrounds. In order to provide higher statistics for the background determination, the background events in an invariant mass window of GeV, are scaled down for an invariant mass window of 8 GeV.

the background determinations. As the jet multiplicity increases, the t t background increases. For Z µ + µ + jets events, the t t background fraction increases to -0%. Figure 8 shows the inclusive jet multiplicity for the signal and backgrounds simulated with the PYHIA (a) and ALPGEN (b) Monte Carlo data samples. Figure 8(c-f) shows the distributions for signal and background for the leading and next-to-leading jets simulated with PYHIA (c,e) and ALPGEN (d,f). no isolation cone0.0 isol. cone0.0 isol. Process xsec fraction xsec fraction xsec fraction pythia Z µ + µ 766±788 90.6±0.9 789±78 96.9±.0 78±77 98.7±. W µν 8±8 0.±0. 0±8 0.0±0. 0.0±8 0.0±0. QCD(b b) 90±0 6.6±.7 ±.6±0.7 0.0±898 0.0±. t t 09±9.6±0. ±.±0. 99±0.±0. Z ττ 0.0±0.0 0.0±0.0 0.0±0.0 0.0±0.0 0.0±0.0 0.0±0.0 able : he accepted cross-sections (in fb) and the corresponding surviving fractions (in %) from signal and background for Z µ + µ + jets. Z µ + µ + jet Z µ + µ + jets Z µ + µ + jets Process xsec fraction xsec fraction xsec fraction pythia Z µ + µ 789±78 96.9±.0 660± 89.±. 97±9 87.7±. W µν 0±8 0.0±0. 0± 0.0±0. 0± 0.0±0. QCD(b b) ±.6±0.7 99±0.6±. 0± 0.0±.0 t t ±.±0. 789±9 6.0±0.7 77±.±. total background 66±8.±0.7 88±9.6±. 77±.±. alpgen Z µ + µ 908±6 96.±.0 68±76 88.7±.9 6±0 79.6±. W µν ±0 0.0±0.0 0±7 0.0±0. 0.0±0. 0.0±0. QCD(b b) ±.6±0.7 99±0.6±. 0± 0.0±.0 t t 6±9.9±0. 08±0 7.±.0 66±9 0.±.9 total background ±6.9±0.9 607±9.±. 66±6 0.±. able : he accepted cross-sections (in fb) and the corresponding surviving fractions (in %) from signal and background in the Z µ + µ +jets selection for different jet multiplicities, after applying the cuts outlined in Section. A jet transverse momentum of > 0 GeV is applied. 7.. Correction from Parton to Particle Level he MCFM predictions are corrected with respect to non-perturbative effects (fragmentation and underlying event) using similar corrections as those determined for the electron case. 7.. Comparison of Event Generators and MCFM at the Hadron Level Figure 9 (a) shows a comparison of the inclusive Z µ + µ + Njets, cross-section (shown as the number of events expected for fb ) as predicted by the event-generator ALPGEN, by PYHIA, and by MCFM. ALPGEN, as well as PYHIA, predicts fewer events than MCFM in all jet multiplicity bins. Since it is not the purpose of this analysis to determine the inclusive Z µ + µ cross-section,

the event generator output can be normalized globally to the inclusive Z µ + µ cross-section observed in data. For now, the cross-sections of all ALPGEN Z µ + µ samples and of the PYHIA Z µ + µ sample are normalized to the NLO inclusive cross-sections. he derived normalization factors are: ALPGEN,.8±0.069; PYHIA,.09±0.06. Figure 9 (b) shows the comparison of the inclusive Z µ + µ + Njets cross-sections after the normalization. Figure 9 also shows the distribution of the p of the leading jet (c) and next-to-leading jet (d), predicted by ALPGEN, by PYHIA (at the truth level of fully-simulated samples, normalized to the inclusive cross-section) and by MCFM, for an integrated luminosity of fb. As in the case for the electron channel, PYHIA predicts a noticeably softer p distribution than either ALPGEN or MCFM. his is connected to a higher jet multiplicity predicted in the low-p region, while ALPGEN predicts more high-p jets. 7.. Unfolding Detector Effects he reconstructed data are unfolded to the hadron level, correcting for efficiency losses, resolution and non-linearities in both muon and jet reconstruction, in a similar manner as for the electron channel. he unfolding procedure is derived (and validated) with fully-simulated Monte Carlo. Figure (a) shows the p distribution of the unfolded reconstructed leading jet (ALPGEN and PYHIA Monte Carlo) compared to NLO and LO MCFM predictions at hadron level. For p > 0 GeV, the PYHIA and ALPGEN distributions can be clearly distinguished. Figure (b) shows the unfolded p distribution for the reconstructed next-to-leading jet (ALPGEN and PYHIA Monte Carlo) compared to NLO and LO MCFM predictions at hadron level. 7..6 Systematic Errors Figure shows the relative systematic error expected for the N jet total cross-section for different uncertainties on the jet energy scale (%, corresponding to the ultimate, but challenging goal, %, a level expected within the first two years and %, a possibility for the earliest running). If a % error on the JES is achieved, the result is a systematic error of up to % for events jets. For the % scenario, the systematic errors are up to 0% for jet and % for jet events. 7. Z µ + µ + b Jets he measurement of the Z + b jet production cross-section at the LHC will provide an important test of perturbative QCD. he cross-section is sensitive to the b quark density of the proton and its precise measurement will help in reducing the current uncertainty on the partonic heavy flavor content of the proton s PDF. Such uncertainties are currently affecting the potential for the discovery of a number of new physics channels at the LHC. able shows the next-to-leading order cross-sections for Z + jets at the evatron and LHC [8]. As we can see from this able, at the LHC, the process gb Zb clearly dominates w.r.t. q q Zbb. he selection of Z + b jet events should be easier at the LHC than at the evatron for two reasons: we will have a cross-section for Z+b jet a factor 0 larger than at the evatron, and the relative production of Z + c jet will be less important at the LHC, thus reducing the probability of jet mis-tagging. With the present analysis, we provide a preliminary estimate of the selection efficiency for Z µ + µ + b jets events and for the main background channels. We also show the rejection power for Z µ + µ + c and light jets, as a function of the b-tagging efficiency. 6

(a) events / fb 6 mcfm LO mcfm NLO Alpgen Pythia (b) events / fb 6 mcfm LO mcfm NLO Alpgen Pythia (c) events / fb / GeV 0 num events Njets (Et>0GeV) Alpgen Pythia mcfm LO mcfm NLO (d) events / fb / GeV 0 num events Njets (Et>0GeV) Alpgen Pythia mcfm LO mcfm NLO 0 0 0 0 00 0 00 Pt, leading jet (GeV) 0 0 0 60 80 0 0 0 60 80 00 Pt, nd leading jet (GeV) Figure 9: (a) he number of events expected for fb at the hadron level for ALPGEN, PYHIA and MCFM, with absolute normalizations. (b) All predictions are normalized to the inclusive Z µ + µ NLO MCFM cross-section. he p of the leading jet (c) and p of the next-to-leading jet (d) are plotted at the hadron level for ALPGEN, PYHIA (MC truth normalized to the Z µ + µ inclusive cross-section) and for the LO and NLO MCFM predictions. 7.. Event Selection We require two muons of opposite charge, with p > GeV, η <. and R > 0. from any jet axis. he Z selection is done by requiring m µµ in the range m Z ± 0 GeV. We select Cone0 jets with η <. and require the number of jets to be greater or equal to one. he analysis has been performed for two jet energy cuts: E jet > 0 GeV and E jet > 0 GeV. he b-tagging is performed cutting on the weight parameter, namely the combination of the secondary vertex (SV) and impact parameter (IPD) algorithms. In this analysis we cut at weight. Figure (a) shows the transverse momentum spectrum for all the muons found in the various data samples, before any cut is applied, while Fig. (b) shows the invariant mass of the two muons, after all the muon identification cuts. he plots are normalized to the number of entries. Figure (a) shows the b-tagging efficiency as a function of the weight parameter; cutting at weight, as we do in this analysis, ensures 60% efficiency for b jets. Figure (b) shows the rejection factor for c and light quarks as a function of the b-tagging efficiency; 60% efficiency gives a rejection factor of 7 for 7

(a) events / fb / 0GeV Alpgen reco corr. Pythia reco corr. mcfm LO mcfm NLO (b) events / fb / 0GeV Alpgen reco corr. Pythia reco corr. mcfm LO mcfm NLO 0 0 0 0 00 0 00 Pt, leading jet (GeV) 0 0 0 60 80 0 0 0 60 80 00 Pt, nd leading jet (GeV) Figure : he transverse energy of the leading jet in unfolded PYHIA and ALPGEN signal Monte Carlo shown along with predictions from MCFM for an Ldt = fb. c jets and for light jets, in fairly good agreement with what is found for other physics channels. Figure (a) shows the jet transverse energy spectrum for b, c and light jets in the Z µ + µ inclusive data sample, after all muon cuts, including the cut on m µµ, and for η jet <. and E jet > 0 GeV. Figure (b) shows the same events of (a) when the cut on the b-tagging weight is also added. A summary of the efficiency for the various muons cuts, for all the samples is shown in able 6. he final efficiency after additional cuts on jets is shown in able 7 for the Z inclusive, Z+b jet, Z+c jet and light jets samples. hose efficiencies are calculated requiring the transverse energy of the jet, E jet > 0 GeV or E jet > 0 GeV. Given the final efficiencies quoted in this able, for an integrated luminosity of f b and a signal cross-section of. pb, we should be able to select 60±0 events when cutting at E jet > 0 GeV GeV and 890 ± 70 events when cutting at E jet > 0 GeV. he contamination from Z+c and light jets should be of the order of 0% while the background from t t and W µν is negligible. 8 Measurement of W + Jet Cross-Sections he following analysis focuses on W + jets events, especially in regards to an evaluation of the JES and PDF uncertainties. Observable distributions are shown for signal and backgrounds at detector level, after a standard cut-based selection. A data driven method to remove backgrounds is discussed and the impact of the jet energy scale on jet multiplicity distributions is examined. he PDF reweighting technique is then applied to predict PDF uncertainties on electron and jet distributions. he PDF uncertainties on the measurement of the cross-section are compared to the experimental systematic uncertainties, as a function of the cumulative jet multiplicity. he ultimate goal will be to provide a similar comparison to MCFM predictions as is currently done for Z + jets. he results shown in Sections 8.-8. were obtained for the W eν decay. 8

Error on the cross section.. 0.8 0.6 % JES uncert. % JES uncert. 0. % JES uncert. Number of Jets Figure : Relative systematic errors expected on the measured cross-section from different uncertainties on the Jet Energy Scale. 8. Signal-Background Analysis 8.. W eν + Jets he number of signal events and the fraction of background events after the selection cuts of Section are applied are given in able 8, using the datasets mentioned in Section and assuming an integrated luminosity of fb. he able indicates that the largest contribution to the W eν background comes from QCD dijet production. It has to be noted that this QCD background is, among all background processes, the least understood both theoretically and experimentally. Due to the large dijet cross-section and to the high rejection power of the selection criteria, the available Monte Carlo statistics are not sufficient to evaluate the number of QCD background events by simply counting the events after all cuts to the Monte Carlo QCD background sample. o overcome this difficulty the QCD background contamination is obtained by using the product of the offline selection efficiency only, times the trigger selection efficiency. o properly take into account the correlation between these two quantities, the trigger selection efficiency is calculated as the ratio of the efficiency of the trigger and electron identification cuts and the electron identification efficiency. In Fig., we see the E spectrum for all jets in the events for the signal, W eν, and the backgrounds, after the full selection. Despite the poor Monte-Carlo statistics for QCD events (giving rise to the observed spikiness), the figure clearly indicates the increasing importance of the QCD and t t backgrounds at higher jet E with respect to the steeply falling signal distribution. In Fig. 6, we can see the expected number of events as a function of the jet multiplicity in any given event, for an integrated luminosity of fb. Figure 6 also shows the corresponding cumulative jet multiplicity. A cut on the transverse energy of each jet of 0 gev is applied. he distributions show that the t t background dominates at large jet multiplicities, while QCD dijet production is the largest background for small multiplicities. As has been noted previously, however, the QCD background for this analysis is estimated by using PYHIA dijet processes, which are known to underestimate the level of multi-jet production. he real amount of QCD background can only be reliably estimated from LHC data. Whereas the W τν and Z e + e backgrounds can be reliably estimated by Monte Carlo tech- 9

Cross Section(pb) evatron LHC Process ZQ inclusive gb Zb. ± 0.9 ± 0.8 ± 0.8 0 +70+70+0 60 0 0 q q Zbb 6.8 9. gc Zc 0.. +.8 ± 0.+.. 90 ± 0 +60+0 70 80 q q Zc c.8 89.7 Zj inclusive gq Zq, q q Zg ++9+7 0 870 +900+60+00 600 00 00 able : he next-to-leading-order inclusive cross-sections (in pb) for Z + jets at the LHC ( s = evpp) and at the evatron ( s =.96eV p p). he calculations are for the case of a jet in a range p > GeV and η <. (LHC) or η <.0 (evatron). wo final-state partons are merged into a single jet if R j j < 0.7. No branching ratios or tagging efficiencies are included. he uncertainties are from the variation of the renormalization scale, the factorization scale, and the parton distribution functions and their sum are estimated to be of the order of about %. Cuts Z inclusive Z+b jets Z+c or light jets ttbar W at least µ + and µ 6.9 ± 0. 9 ± 9 ±. ± 0.. ± 0.09 p µ > GeV η µ <..6 ± 0. ± ±. ± 0.0 0.09 ± 0.0 R µ jet > 0. Mass Window 0.9 ± 0. 9 ± 0 ± 0.9 ± 0.0 0.00 ± 0.00 able 6: Efficiency after the cuts to identify the muons from Z decay, expressed in %. he last row corresponds to the efficiency after a mass window of 7 < m µµ < GeV. niques, the t t (to some extent) and especially the QCD dijet backgrounds can only be estimated by using LHC data. hus, to minimize the uncertainty on the amount of background, an alternative, mostly data driven, selection procedure is proposed. he /E cut is efficient in rejecting the backgrounds, but results in a loss of information of the QCD distribution shape. he amount and shape of the background under the signal area will be hard to estimate. herefore, a data driven approach to reject the background is developed (see the inclusive W/Z note for a detailed description of this technique). In this approach, Z e + e events are efficiently removed by cutting on the invariant mass of an e + e -pair, as shown in Fig. 6. he dominant QCD background can be parameterized and subsequently subtracted from the signal area by using a pure QCD dijet sample. o accomplish this, photon candidates are selected which pass a photon trigger and the same calorimeter-based identification as electrons. Photon candidates are distinguished from electrons as no good quality track is found to be associated with the electro-magnetic cluster. Applying some additional requirements on track isolation, this sample is largely dominated by QCD jets faking a photon and can be parameterized as a function of the cell-based /E. As the electron and photon samples are kinematically very similar, the /E spectrum for the QCD background has the same shape in both samples. he back- 0