Measurement of the production cross section of jets in association with a Z boson in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

Measurements of the production of jets of particles in association with a Z boson in pp collisions at sqrt(s) = 7 TeV are presented, using data corresponding to an integrated luminosity of 4.6/fb collected by the ATLAS experiment at the Large Hadron Collider. Inclusive and differential jet cross sections in Z events, with Z decaying into electron or muon pairs, are measured for jets with transverse momentum pT>30 GeV and rapidity |y|<4.4. The results are compared to next-to-leading-order perturbative QCD calculations, and to predictions from different Monte Carlo generators based on leading-order and next-to-leading-order matrix elements supplemented by parton showers.


Introduction
The production of jets of particles in association with a Z boson 1 at hadron colliders provides an important test of perturbative quantum chromodynamics (pQCD). Such events also constitute a non-negligible background for studies of the Higgs boson candidate [1,2] and searches for new phenomena. In these searches, the multiplicity and kinematics of jets in Z + jets events are exploited to achieve a separation of signal from background. This procedure often introduces scales larger than the mass of the Z boson, resulting in large logarithmic contributions in the calculation of higher-order QCD corrections to the predicted Z + jets cross section [3,4]. The measured Z + jets cross section can be compared 1 The notation Z refers to the complete Z/γ * interference.
-1 -directly to fixed-order predictions at next-to-leading-order (NLO) in pQCD [5][6][7] and to Monte Carlo (MC) generators based on next-to-leading-order or leading-order (LO) matrix elements supplemented by parton showers [8][9][10]. The simulations based on LO matrix elements are affected by large uncertainties in the factorization and renormalization scales and need to be tuned and validated using data.
Measurements of the Z + jets cross section have been reported for lower jet energies and lower jet multiplicities in proton-antiproton collisions at a center-of-mass energy of √ s = 1.96 TeV [11][12][13] and in proton-proton collisions based on a data set of 0.036 fb −1 collected at √ s = 7 TeV [14,15]. This article extends these measurements, using 4.6 fb −1 of proton-proton collision data collected by the ATLAS experiment in 2011 at √ s = 7 TeV. The large data set allows cross sections to be measured for the production of up to seven jets in association with a Z boson. Differential jet cross sections are accessible for large jet multiplicities and for energy regimes up to 1 TeV, which allows the modelling of the Z + jets process to be probed for typical phase-space regimes expected from new phenomena and from Higgs boson production, for example via vector-boson-fusion (VBF).
Selected events contain a Z boson decaying into a pair of electrons or muons. Associated jets are identified in a rapidity (y jet ) range of |y jet | < 4.4 and with transverse momentum (p jet T ) of p jet T > 30 GeV. The measurements comprise inclusive and exclusive jet multiplicities for different phase-space constraints and differential jet cross sections as a function of the transverse momentum and the rapidity of the four jets with the largest transverse momentum ('leading jets'). Cross sections for events with at least two jets in the final state are measured as a function of the invariant mass (m jj ) and the angular separation of the two leading jets. Differential cross sections in events with at least one jet are measured as a function of the scalar p T sum of the jets (S T ), of the scalar p T sum of the leptons and jets (H T ), and the transverse momentum of the Z boson candidate (p T ). The results of the measurements are unfolded for detector effects and quoted at the particle (hadron) level, where they are compared to predictions from fixed-order NLO pQCD programs and from several MC generators.
The paper is organized as follows. The detector and the data sample are described in the next section. Section 3 provides details of the simulations used in the measurements, while section 4 describes the lepton and jet reconstruction and the event selection. The estimation of background contributions is described in section 5 and selected uncorrected distributions are presented in section 6. The procedures used to unfold the measurements for detector effects and to combine electron and muon channels are detailed in section 7. Systematic uncertainties are discussed in section 8. The NLO pQCD predictions are described in section 9. Measured cross sections are presented in section 10 and compared to generator and NLO pQCD predictions. Finally, section 11 provides a summary. Table 1 summarizes the kinematic regions in which Z bosons and jets are selected. They are defined to provide a good experimental coverage for the reconstruction of electrons, muons and jets in the event. Events with less than three tracks associated to the hard scattering vertex, defined as the vertex with the highest p T sum of its associated tracks, are discarded.

Event selection
Electrons are reconstructed from clusters of energy in the electromagnetic calorimeter matched to inner detector tracks. The electron candidates must have p T > 20 GeV and |η| < 2.47, excluding the transition region 1.37 < |η| < 1.52 between barrel and endcap electromagnetic calorimeter sections, and pass the 'medium' identification criteria described in ref.
[36], re-optimized for 2011 conditions. No additional isolation requirement is applied, since non-isolated electron candidates are already suppressed by the identification criteria. Muon candidates are identified as tracks in the inner detector matched and combined with track segments in the muon spectrometer [37]. They are required to have p T > 20 GeV and |η| < 2.4. In order to achieve a sufficient rejection of multi-jet events, muons are required to be isolated: the scalar sum of the transverse momenta of tracks within a cone of ∆R ≡ (∆φ) 2 + (∆η) 2 = 0.2 around the muon candidate must be less than 10% of the transverse momentum of the muon. All lepton pairs are required to have a separation of ∆R > 0.2. The Z candidates are selected by requiring exactly two oppositely charged leptons of the same flavour. Their invariant mass (m ) must be within the range 66 GeV ≤ m ≤ 116 GeV. With this selection, 1228767 Z (→ ee) and 1678500 Z (→ µµ) candidate events are identified.
Jets are reconstructed using the anti-k t algorithm [38] with a distance parameter R = 0.4. The inputs to the jet algorithm are topological clusters of energy in the calorimeter [39]. The energies and directions of reconstructed jets in data and simulated events are corrected for the presence of additional proton-proton interactions, the position of the primary interaction vertex, the measurement biases induced by calorimeter non-compensation, additional dead material, and out-of-cone effects, using detector simulation and a combination of in-situ methods [39,40]. Jets are required to have a transverse momentum above 30 GeV and a rapidity of |y jet | < 4.4. Jets closer than 0.5 in ∆R to a selected lepton are removed. In order to reject jets from additional proton-proton interactions, the 'jet vertex fraction' is used. This is defined as the p T sum of the tracks associated to the jet which are consistent with originating from the primary vertex divided by the p T sum of all tracks associated to the jet. The jet vertex fraction is required to be greater than 0.75 for jets with |η| < 2.4. The residual impact of additional proton-proton interactions on the distribution of the jet observables has been checked to be correctly simulated such that the unfolded cross sections are expected to be independent of the number of additional interactions. With this definition, 191566 Z (→ ee) and 257169 Z (→ µµ) candidate events are selected with at least one jet in the final state.

Background estimation
The selected data sample is expected to contain background events with two isolated leptons (tt, diboson and Z (→ τ τ ) events), with one isolated lepton (W → eν, W → µν and single-top-quark production) and without isolated leptons (multi-jet events). The total expected background fraction increases with the jet multiplicity (N jet ) from 2% (N jet ≥ 1) to 20% (N jet ≥ 6). It is dominated by multi-jet processes, tt and diboson events for Z (+ ≤ 1 jet) and by tt for larger jet multiplicities. The background is estimated using simulated samples, with the exception of the multi-jet and tt background contributions, which are derived from data. For these data-driven background estimates, the shape of the background contribution to each of the measured distributions is derived from a dedicated background-enriched sample in data. The background-enriched samples have been selected and normalized as described below. The multi-jet background contribution in the Z (→ ee) + jets channel is estimated using a multi-jet enriched data template with two electron candidates which both pass a 'loose' selection but fail to pass the medium identification requirements [36]. The dedicated trigger used for the selection of this sample requires two clusters of energy in the electromagnetic calorimeter with p T > 20 GeV. This sample is dominated by jets misidentified as electrons in the final state. The normalization of this sample to the multi-jet background expected with medium requirements is extracted from a template fit in the invariant mass distribution for medium electrons (m ee ) as follows: A single combined fit is performed of the multi-jet template and the standard simulated signal and non-multi-jet background templates to the measured spectrum of the invariant mass for medium electrons in the extended mass range 50 GeV < m ee < 150 GeV in the inclusive selection. Systematic uncertainties are assessed by varying the mass range and the binning in the fit, by using a different generator (SHERPA instead of ALPGEN) for the signal template, by varying the electron energy scale and resolution in the simulation and by allowing for a modification of the shape of the mass distribution in the multi-jet enriched sample. The multi-jet background to the measured inclusive jet multiplicities varies between (0.65 ± 0.23)% for N jet ≥ 1 and (1.20 ± 0.44)% for N jet ≥ 6.
In the Z (→ µµ) + jets channel, heavy flavour production (with muons originating from b-and c-quark decays) and decays-in-flight of pions and kaons are the primary source of the multi-jet background, which is highly suppressed by the isolation requirement applied to the muon candidates. The multi-jet template is derived from a data sample where both muons fail the isolation requirement. The normalization factor is obtained by fitting the multi-jet template together with a template composed of the simulated signal and the nonmultijet background events that pass the signal selection to the spectrum of the invariant mass of isolated muons (m µµ ) measured in data in the range 40 GeV < m µµ < 150 GeV. In contrast to the Z (→ ee) + jets channel, the creation of the template and the normalization is performed separately for N jet ≥ 0, N jet ≥ 1 and N jet ≥ 2. The normalization factor derived for N jet ≥ 2 is used for all higher jet multiplicities. The systematic uncertainty is assessed by replacing the multi-jet template with one formed from muons passing a loose isolation cut but failing the tight cut used to select signal muons. Multi-jet fractions vary between (0.25 ± 0.04)% for N jet ≥ 1 and (2.2 ± 2.2)% for N jet ≥ 6.
The tt background contributions in the Z (→ ) + jets samples are dominated by events where both W bosons decay leptonically. Since the kinematic properties of the jets in the final state are independent of the flavours of the two leptons, final states with one electron and one muon can be used to model the tt background contributions to Z (→ ee) and Z (→ µµ) selections. The tt-enriched sample is selected from data in the e ± µ ∓ final state with kinematic requirements analogous to the Z (→ ) + jets selection. The dedicated trigger used for the selection of this sample requires an electron with p T > 10 GeV and a muon with p T > 6 GeV. For each of the observables, the number of W + jets, Z + jets and diboson events expected from simulation in the tt-enriched sample is subtracted. The normalization from the e ± µ ∓ to the e + e − and µ + µ − final states is calculated from tt samples generated with MC@NLO+HERWIG and with POWHEG+PYTHIA, separately for each jet multiplicity. Systematic uncertainties on the normalization arise from the choice of the generator, uncertainty on the lepton trigger, reconstruction and identification efficiency (see section 8) and on the electroweak background subtraction. The tt fractions vary between (0.80 ± 0.05)% for Z (→ ee) + ≥ 1 jet and (18.6 ± 7.0)% for Z (→ ee) + ≥ 6 jets and between (0.74 ± 0.03)% for Z (→ µµ) + ≥ 1 jet and (18.1 ± 5.3)% for Z (→ µµ) + ≥ 6 jets.

Detector-level results
Measured and expected distributions of the jet observables have been compared at the reconstruction level, separately in the electron and muon channels. As an example, figure 1 shows the dilepton invariant mass in events with at least one jet in the final state, as well as the inclusive jet multiplicity. For the signal, both ALPGEN and SHERPA expectations are shown. In this figure, W → eν, Z (→ τ τ ) and diboson processes are summarized as 'electroweak' background and tt and single-top processes are referred to as 'top' background. For figures 1(a) and 1(b), the selection has exceptionally been extended beyond the fiducial invariant mass range, in order to demonstrate in addition the reasonable agreement between data and expectations for dilepton mass sideband regimes with larger background fractions. Table 2 shows, for the electron and muon channels separately, the observed number of events for the different jet multiplicities in the final state compared to expectations  Table 2. Numbers of events expected and observed in data that pass the Z (→ ee) + jets and Z (→ µµ) + jets selections as a function of the inclusive jet multiplicity. The expected numbers are rounded according to the combined statistical and systematic uncertainty. ALPGEN has been used to simulate the signal events.
for signal (ALPGEN) and background processes. The combined statistical and systematic uncertainties on the total expectation increases from 6% to 30% with increasing jet multiplicity. The data are consistent with predictions by the generators ALPGEN and SHERPA, which gives confidence that the simulated samples, which are used in the unfolding, provide a reasonable description of the event kinematics and of the detector response.

Correction for detector effects and combination of channels
The cross sections in this article are quoted at the particle level, which corresponds to 'dressed' muons and electrons, calculated using final-state leptons from the Z decay for which collinear radiation in a cone of ∆R < 0.1 is added to the lepton four-momentum. Particle jets are clustered from all final-state particles (decay length cτ > 10 mm) excluding the dressed Z decay products. The phase-space requirements are the same as in the selection at reconstruction level (see table 1). After subtracting the expected background contributions, the data distributions in each channel are unfolded to the particle level using an iterative technique [41]. Response matrices are calculated for each observable, using Z + jets samples generated with ALPGEN. Before entering the iterative process, the data are corrected for the fraction of reconstructed events in the ALPGEN sample which do not match to a particle-level equivalent. The -8 -     Figure 1. Numbers of events observed in data and predicted in simulation that pass the Z (→ ee) + jets and Z (→ µµ) + jets selection as a function of the invariant mass of the Z candidate, (a) m ee and (b) m µµ , for events with at least one jet with p jet T > 30 GeV and |y jet | < 4.4, and as a function of the inclusive jet multiplicity, N jet , in (c) di-electron and (d) di-muon events. The individual contributions of the various backgrounds are also shown, as detailed in the legend. The hatched band corresponds to the combined statistical and systematic uncertainty on the prediction, obtained using ALPGEN to model the Z + jets process. The error bars on each data point show the statistical uncertainty. The bottom panel shows the corresponding MC/data ratio. The shaded band corresponds to the total systematic uncertainty and the error bars to the statistical uncertainty on the MC/data ratio. number of iterations, typically two or three, is optimized for each observable using a χ 2 comparison of generated and unfolded reconstructed Z + jets events from the generators -9 -SHERPA and MC@NLO.
The uncertainties from the limited number of events in data are propagated into the particle-level cross sections using a Monte Carlo method. One thousand pseudoexperimental spectra are generated by fluctuating the content of each bin according to the statistical uncertainty. The unfolding procedure is applied to each pseudo-experiment, and the r.m.s. of the results is taken as the statistical uncertainty. Systematic uncertainties arising from the unfolding procedure are estimated by comparing with an iterative unfolding based on response matrices and corrections derived from SHERPA. The statistical uncertainties of the response matrices are propagated into systematic uncertainties on the unfolded cross sections using pseudo-experiments.
The cross sections measured in the electron and muon channels are extrapolated to a common phase-space region, derived from table 1 by extending the η range of the leptons to |η lep | < 2.5, using global acceptance corrections derived from ALPGEN Z + jets Monte Carlo samples, reweighted to the CT10 PDF set. The corrections are of the order of 14% and 5% for the electron and muon channel, respectively. Systematic uncertainties are estimated by comparing with corrections obtained using the corresponding SHERPA Z + jets sample and the original ALPGEN sample. Total uncertainties on the corrections are calculated as the quadratic sum of the statistical and systematic uncertainties and amount to 0.2-0.3%. The extrapolated cross sections measured in the electron and muon channels are in agreement.
For each observable, the extrapolated cross sections are combined using the averaging procedure introduced in ref. [42], which accounts for systematic uncertainties (bin-to-bin correlated and uncorrelated) proportional to the central values of the respective cross sections. The weights of the individual cross-section measurements (µ i k ) in channel k (ee or µµ) and bin i in the combined cross sections (m i ) are derived by minimizing the following χ 2 function [42]: where b j denote the shift introduced by a correlated systematic error source j normalized to its respective standard deviation. The relative statistical and uncorrelated systematic uncertainties on µ i k are denoted by δ i stat,k and δ i uncor,k and the variable γ i j,k quantifies the influence of the correlated systematic error source j on the measurement i in the channel k.
The following bin-to-bin correlated systematic sources are taken into account: normalization of the multi-jet background, lepton energy scale and resolution, lepton reconstruction, identification and trigger efficiencies and normalization of tt, electroweak and single-top background contributions, the latter three treated as correlated between the channels. Bin-to-bin correlated systematic sources which have the same impact in both channels do not enter in the combination procedure. These are the individual components of the jet energy scale, the jet energy resolution, the luminosity, the unfolding procedure, and the extrapolation factor. The uncertainties from these sources on the combined result are taken as the weighted average of the corresponding uncertainties on the electron and muon measurements.

Systematic uncertainties
The kinematic ranges and the binning are chosen such that the statistical uncertainty of the measurement is comparable to or smaller than the systematic uncertainty. The relative systematic uncertainties on the cross sections measured in each channel are derived for each observable by propagating systematic shifts from a set of independent sources through the response matrices and the subtracted background contributions into the unfolded data. The resulting systematic uncertainties for each source in each channel are symmetrized in order to mitigate the impact of statistical fluctuations and are combined in the averaging procedure.
The uncertainty on the jet energy scale (JES), determined from the combination of methods based on MC and in-situ techniques used to determine the scale, constitutes the dominant component of the total systematic uncertainty. It is propagated through the analysis using 14 independent components fully correlated in p jet T [39, 40]. They account for uncertainties on the different in-situ measurements which enter the jet calibration, on the jet flavour and on the impact of pile-up and close-by jets. The uncertainty on the jet energy resolution, derived from a comparison of the resolution obtained in data and in simulated dijet events, is propagated into the final cross section by varying the energy resolution of the simulated jets. Uncertainties on the normalization of the background expectations, for simulated and data-driven background contributions respectively, are treated as correlated between bins and are propagated to the measured cross sections by unfolding the data distributions after the subtraction of the systematically shifted background. The statistical uncertainties of the background contributions are added quadratically to the statistical uncertainties of the data. The uncertainty from the unfolding process is derived from the different components discussed in section 7, which are considered to be uncorrelated. Systematic uncertainties on electron and muon trigger efficiencies, energy scale, resolution, reconstruction and identification efficiencies are derived from the comparison of tag-andprobe results in data and simulated events [36,37]. Table 3 summarizes the systematic uncertainties on the Z + jets cross sections as a function of the inclusive jet multiplicity and of p jet T of the leading jet separately for the electron and muon channels. The uncertainty on the integrated luminosity of 1.8% translates into comparable uncertainties on the measured cross sections. The total uncertainties on the inclusive jet cross sections range from 8% for N jet ≥ 1 to 16-17% for N jet ≥ 4, dominated by the JES uncertainty.
The uncertainty on cross-section ratios, R ≥(n+1)/≥n 3 , for successive jet multiplicities n is significantly reduced due to the strong correlations between the lepton and jet reconstruction and calibration uncertainties in neighbouring jet bins and amounts to a total of 3-4% for R ≥2/≥1 and higher multiplicities, which are of interest in this article, dominated by the residual JES uncertainty. The large JES uncertainties in the forward region propagate into uncertainties on the unfolded cross sections at the level of 20% (30%) for jet rapidities of |y jet | = 3.0 (4.0). This is reflected in large jet energy scale uncertainties on the cross section 3 For simplicity, n is used in the subscript instead of Njet  Table 3. Systematic uncertainties on the cross sections for Z (→ ee) + jets and Z (→ µµ) + jets as a function of the inclusive jet multiplicity and as a function of the transverse momentum, p jet T , of the leading jet for events with at least one jet with p jet T > 30 GeV and |y jet | < 4.4. The rows labelled 'electron reconstruction' and 'muon reconstruction' include uncertainties on trigger, reconstruction and identification, energy scale and resolution.

Theoretical predictions
Fixed-order calculations at NLO pQCD for the production of Z (+ ≥ 1 jet) up to Z (+ ≥ 4 jets) are computed using the BlackHat+SHERPA program [5][6][7]. CT10 PDFs [25] are employed and renormalization and factorization scales are set to H T /2, where H T is defined event-by-event as the scalar sum of the p T of all stable particles/partons. The anti-k t algorithm with R = 0.4 is used to reconstruct jets at the parton level. Systematic uncertainties on the predictions related to PDF uncertainties are computed from the 52 CT10 eigenvectors at 68% confidence level [25]. The uncertainties on the cross sections increase from 1% for (N jet ≥ 1) to 3% for (N jet ≥ 4) and from 1% to 5% with p jet T of the leading jet between 30 GeV and 500 GeV. Additional changes in the PDFs due to the variation of the input value for the strong coupling constant α s at the Z-boson mass scale by ±0.001 around its nominal value α s (m Z ) = 0.118 introduce uncertainties on the predicted cross sections in the range of 1% to 3% for Z (+ (1 − 4) jets). These are added in quadrature to the PDF uncertainties. Scale uncertainties are estimated by variations of the renormalization and factorization scales to one half and two times the nominal scale. The scale uncertainties for different parton multiplicities are assumed to be uncorrelated. For inclusive calculations, the scale variations translate into variations of the cross section by 4% to 13% as N jet increases and by 2% to 18% with increasing p jet T of the leading jet. For exclusive final states, the scale uncertainties are calculated using the prescription of ref. [43]. For comparison, the theory/data ratios presented in section 10 also show the scale uncertainty resulting from a simple variation of the renormalization and factorization scales by a factor of two, assuming the uncertainties to be correlated for different parton multiplicities. The scale uncertainties constitute the dominant uncertainties in most kinematic regions.
The NLO fixed-order calculations at the parton level are corrected to the particle level for the underlying event and for effects of fragmentation and of QED final-state radiation (QED-FSR). Parton-to-hadron correction factors (δ had ) approximately account for nonperturbative contributions from the underlying event and fragmentation into particles. For each observable, the correction factor is estimated using simulated Z + jets samples, produced with ALPGEN with the HERWIG cluster fragmentation in which JIMMY models the underlying event using the AUET2-CTEQ61L [20] tune. It is calculated as the bin-bybin ratio of the nominal distribution at the particle level to the one obtained by turning off both the interactions between proton remnants and the fragmentation in the simulated samples. The non-perturbative corrections are also computed using ALPGEN samples, this time interfaced to PYTHIA, where the correction corresponds to the combined effect of string fragmentation and of the underlying event predicted by the PERUGIA2011C [22] tune. The difference is taken as a systematic uncertainty. The combined nominal correction is 7% in the low p jet T region and decreases with increasing p jet T towards zero. The correction factors for the inclusive N jet distributions are about 3-4%. Nonperturbative corrections for quantities calculated with several jets include implicitly the corrections for all jets. The statistical and the symmetrized systematic uncertainties on δ had are added in quadrature to the total uncertainty from the BlackHat+SHERPA calculation.
The QED-FSR correction factors (δ QED ) are determined using Z + jets samples produced with the ALPGEN generator, interfaced to PHOTOS [26], by calculating the expected cross sections both with the lepton four-momentum before final-state photon radiation ('Born level'), and with dressed leptons. The correction factors are about 2% for the electron and muon channels. They do not show a significant N jet dependence and are stable with respect to the jet rapidity and for large jet transverse momentum. Systematic uncertainties are derived by comparing with δ QED obtained using a Z + jets sample produced with the SHERPA generator [9] which generates QED-FSR using the YSF method [27]. The differences between the two predictions are usually at the per-mille level.

Results and discussion
For each observable, the spectrum measured in data is unfolded to the particle level. After extrapolation and combination of electron and muon channels, the results are compared with calculations from BlackHat+SHERPA, corrected to the particle level, and with predictions by ALPGEN, SHERPA and MC@NLO. Both ALPGEN and SHERPA employ matrix elements for up to five partons. Higher multiplicities are generated by the parton shower. In contrast, MC@NLO generates the Drell-Yan process at NLO precision, which includes the real emission of one additional parton. All higher parton multiplicities are generated by the parton shower. Inclusive and differential cross sections for Z (→ ) + ≥ n jets are compared with BlackHat+SHERPA fixed-order pQCD calculations for Z + ≥ n partons, which provide a NLO estimate for the respective parton multi--13 -plicity, including the real emission of one additional parton. Measured cross sections as a function of the jet multiplicity and their ratios are detailed in table 4. Tabulated values of all observed results are available in the Durham HEP database [44]. Figure 2(a) presents the absolute cross sections for inclusive jet multiplicities for up to seven hadronic jets in the final state. The ratios R ≥(n+1)/≥n of cross sections for two successive multiplicities, presented in figure 2(b), provide a more precise measurement of the QCD process, due to the cancellation of part of the systematic uncertainty. The data are consistent with BlackHat+SHERPA calculations and with predictions of the generators ALPGEN and SHERPA. The MC@NLO parton shower underestimates the observed rate for additional jet emission by a factor of two, which leads to large offsets to the data for higher jet multiplicities. For this reason, in subsequent figures the MC@NLO predictions are only shown for Z (→ ) + ≥ 1 jet selections, where the parton corresponding to the NLO real emission can be expected to yield a reasonable description of the kinematics.

Jet multiplicities
Exclusive jet multiplicities at the LHC are expected to be described by means of two benchmark patterns, 'staircase scaling' with R (n+1)/n constant and 'Poisson scaling' with R (n+1)/n inversely proportional to n [3,45], which provide limiting cases for certain kinematic conditions. While for high multiplicities a flat exclusive jet multiplicity ratio is derived from the non-abelian nature of QCD FSR, at low multiplicity the jet multiplicity ratio is flat due to the combined effect of a Poisson-distributed multiplicity distribution and parton density suppression [3]. The emission of the first parton should be suppressed more strongly than the subsequent parton emissions. The underlying Poisson scaling is expected to emerge after introducing large scale differences between the core process (Z (+1 jet)) and the p jet T of the second leading jet. Two selections are chosen to test the two benchmark scenarios: (a) the standard Z + jets selection and (b) events where the leading jet has a transverse momentum in excess of 150 GeV. Figure 3(a) presents the ratios R (n+1)/n of cross sections for two successive exclusive multiplicities for the standard Z + jets selection. The comparitatively large scale uncertainties on the pQCD predictions result from the prescription of ref. [43], assuming the scale variations to be uncorrelated across the jet multiplicities. For comparison, the total uncertainty calculated using a naive scale variation, and a reduced uncertainty that does not include any scale uncertainty are also shown. The data are consistent with the central values of the BlackHat+SHERPA calculations and with predictions by the generators ALPGEN and SHERPA. The cross-section ratios show an approximately linear dependence on the jet multiplicity with a small slope. A linear fit R (n+1)/n = R 0 + dR dn · n of the observed multiplicity ratio starting with R 2/1 yields R 0 = 0.232 ± 0.009 and dR/dn = −0.011 ± 0.003. The uncertainties include a systematic contribution, derived from a series of fits to systematic variations of the multiplicity ratio. The flat staircase pattern provides an acceptable approximation of the observed scaling behaviour for the standard Z + jets selection. The observation is consistent with results presented in [15] on the smaller data set collected in 2010.
-14 -    Figure 3(b) presents the exclusive jet multiplicity ratio for events where the leading jet has a transverse momentum in excess of 150 GeV. The observed ratio R (n+1)/n is now steeply increasing towards low jet multiplicities, a pattern described by the central values of the BlackHat+SHERPA calculations, by the generator ALPGEN and approximately also by SHERPA. The observed cross-section ratios have been fitted with a pattern expected from a Poisson-distributed jet multiplicity with the expectation valuen, R (n+1)/n =n n . The Poisson scaling provides a good overall description of the jet multiplicity observed in data for the selected kinematic regime, withn = 1.02 ± 0.04, where the uncertainty includes statistical and systematic components.
The scaling pattern is also investigated for a preselection typically employed in the selection of particles produced via vector boson fusion (VBF). Figure 4 presents the absolute cross section as a function of the exclusive jet multiplicity and R (n+1)/n after requiring two jets with m jj > 350 GeV and |∆y jj | > 3.0, in the following referred to as 'VBF preselection'. The data are consistent with the BlackHat+SHERPA prediction. SHERPA describes the multiplicity well whereas ALPGEN overestimates R 3/2 .
-15 - The data are compared to NLO pQCD predictions from BlackHat+SHERPA corrected to the particle level, and the ALPGEN, SHERPA and MC@NLO event generators (see legend for details). The error bars indicate the statistical uncertainty on the data, and the hatched (shaded) bands the statistical and systematic uncertainties on data (prediction) added in quadrature. The shaded bands on the theory calculations show the systematic uncertainty excluding the scale uncertainty (dark shaded) and the total systematic uncertainties using the naive approach (medium shaded) and the nominal approach (light shaded) to derive the scale uncertainty (see section 9). The figures include (a) a linear fit R (n+1)/n = R o + dR dn · n in the range R 2/1 < R (n+1)/n < R 5/4 and (b) a Poisson fit R (n+1)/n =n n to the data points, with the free parameters R o , dR dn andn.

Jet transverse momentum
Differential cross sections with respect to the jet transverse momentum, p jet T , provide a test of pQCD over a large kinematic range. In particular, when p jet T exceeds the scale given by the gauge boson mass, NLO/LO K-factors can be large due to the presence of QCD corrections of the order of α s ln 2 (p jet T /m Z ) [4]. In addition, higher-order electroweak corrections are expected to reduce the cross section with increasing transverse momentum of the Z boson candidate, by 5-20% for 100 GeV < p T < 500 GeV [46]. Figures 5 and 6 show the cross section as a function of p jet T of the first, the second, the third and the fourth leading jet (in descending order of p jet T ) for events with at least one, two, three and four jets in the final state, respectively. The cross sections are normalized to  For the leading jet, the precision of the measurement exceeds the precision of the theory prediction. While ALPGEN predictions for the p jet T spectrum of the second to fourth leading jet are consistent with the data, the p jet T spectrum of the leading jet is predicted to be too hard for larger values of p jet T . SHERPA is characterized by offsets to the data at the level of 5-15%, consistent with the observations presented in figure 2(a) for the inclusive jet cross section. MC@NLO predicts a too soft p jet T spectrum, resulting in a discrepancy with the data by one order of magnitude for large p jet T . This is attributed to the fact that the fraction of events with a second resolved jet, which in MC@NLO is modelled via the parton shower, increases considerably with p jet T of the leading jet (see figures 3(a) and 3(b) for small and larger p jet T (leading jet)). A too soft p jet T spectrum of the parton shower will hence result in an increasing discrepancy between the MC@NLO prediction and the data. agreement between the predicted and observed cross-sections is observed. For events with at least two jets, figure 7(b) shows cross section as a function of the p jet T ratio of the two leading jets, normalized to the inclusive Z (→ ) cross section. ALPGEN overestimates the cross section for events with a p jet T ratio of the leading jets in the range of 0.1-0.2. SHERPA underestimates the cross section as a function of the p jet T ratio by ≈15%, consistent with the results presented in figure 2(a).
In a complementary approach, the cross section is measured as a function of the p T of the recoiling Z boson, reconstructed from the momenta of the two leptons. The results are presented in figure 8 for both the inclusive and the exclusive Z (+1 jet) selection, normalized to the inclusive Z (→ ) cross section. Both ALPGEN and SHERPA predict a too hard p T spectrum, in particular in the inclusive case. The discrepancy with the data is comparable to the expected higher-order electroweak corrections [46] although higher-order QCD corrections could equally account for this. The BlackHat+SHERPA Z (+ ≥ 1 jet) fixed-order calculation for the inclusive final state is too soft whereas for the exclusive final state the central predictions are closer to the observed spectrum. This result is attributed to missing higher jet multiplicities in the fixed-order calculation and will be discussed in more -18 - detail in section 10.5. The comparison with BlackHat+SHERPA yields no indication for missing higher-order electroweak corrections in the large-p T region. Consistent with the results presented for the p jet T spectrum of the leading jet, MC@NLO describes the exclusive Z (+1 jet) final state better than the corresponding inclusive final state. Figures 9 and 10 show the rapidity spectrum of the four leading jets, normalized to the inclusive Z (→ ) cross section. Both BlackHat+SHERPA and SHERPA predict rapidity spectra for the leading jet that are somewhat wider than observed in the data. ALPGEN predictions are compatible with the measurements. Figure 11 presents the separation in rapidity, |∆y jj |, and the invariant mass, m jj , of the two leading jets, normalized to the inclusive Z (→ ) cross section. The predictions by BlackHat+SHERPA and ALPGEN are consistent with the data. SHERPA overestimates the cross section for large |∆y jj |, consistent with the too wide rapidity spectra.

Angular distributions
Differential jet cross sections as a function of angular distances (∆φ jj and ∆R jj ) between the two leading jets are presented in figures 12(a) and 12(b), respectively, normal- ized to the inclusive Z (→ ) cross section. The azimuthal distance is well modelled by ALPGEN and by BlackHat+SHERPA. The tendencies observed in the modelling of the distance in φ and in rapidity are reflected in the measurement of the ∆R spectrum of the leading jets. SHERPA models a too flat spectrum for both ∆φ and ∆R. The offset of 15% of the SHERPA prediction from the observed cross section in the bulk of the data in figures 11 and 12 is consistent with the results presented in figure 2(a) for the inclusive Z (→ ) + ≥ 2 jets cross section.

Distributions after VBF preselection
A veto on a third jet is used to reject Z + jets background in selections of Higgs boson candidates produced by VBF. Figure 13 shows the transverse momentum and rapidity distributions of the third jet after the VBF preselection, as defined in section 10.1, normalized to the inclusive Z (→ ) cross section. The predictions by BlackHat+SHERPA, ALP-GEN and SHERPA are consistent with the measurements. Figure 14 shows the fraction of events which have fulfilled the requirements of a VBF preselection that pass in addition a veto on a third jet in the central region (|η| < 2.4) as a function of the minimum trans- verse momentum of the veto jet, referred to as 'jet veto efficiency' in the following. The results are shown at detector level, separately for the Z → ee and the Z → µµ channel. The overestimate of R 3/2 in ALPGEN (see figure 4) leads to an underestimate of the veto efficiency, particularly for the low-p jet T regime. SHERPA predicts the veto efficiencies better.

Inclusive quantities
Quantities based on inclusive p T sums of final-state objects, such as H T or S T , are often employed in searches in order to enrich final states resulting from the decay of heavy particles. Reference [47] reports a discrepancy between fixed-order pQCD calculations and data for moderate energy regimes in W + jets events which can be mitigated by including higher jet multiplicities in the theoretical calculations by means of 'exclusive sums' [48]. Differential cross sections of Z (+ ≥ 1 jet) events as a function of H T and S T , normalized to the inclusive Z (→ ) cross section, are presented in figure 15. ALPGEN predicts slightly too hard spectra for both variables in line with the too hard spectrum for p jet T . SHERPA predictions show an offset of 10-15% to the data. The softer spectra from BlackHat+SHERPA, based on a Z (+ ≥ 1 jet) fixed-order NLO calculation, deviate -21 - increasingly from the data for larger values of H T and S T , which confirms and extends the results in reference [47] to a higher energy regime. The discrepancy is attributed to missing higher jet multiplicities in the fixed-order calculation. This interpretation is investigated further in what follows. Figure 16(a) shows, at reconstruction level, the average jet multiplicity as a function of H T for the Z → ee channel. Compatible results have been obtained in the muon channel. Predictions by ALPGEN and SHERPA are consistent with the data. For values of H T ≈ 350 GeV, where data and NLO calculation start to deviate significantly, the average jet multiplicity exceeds two. A similar measurement is performed as a function of the p T in the Z → µµ channel and shown in figure 16(b). Compatible results have been obtained in the electron channel. For values of p T ≈ 200 GeV, where the NLO predictions underestimate the measured cross section (see figure 8), on average two jets are resolved, typically one hard jet that carries most of the Z recoil, accompanied by a soft jet. In both cases, the kinematic regions where the NLO fixed-order calculations perform poorly are characterized by average jet multiplicities in excess of the fixed order used in the NLO calculation. and p T in figures 15 and 8 with the 'exclusive sum' of the cross sections for the first two jets: (Z (+1 jet)) + (Z (+ ≥ 2 jets)). The exclusive sum is consistent with the observed H T and p T spectra in the phase space considered. These results support the interpretation of the poor performance of the fixed-order calculation for inclusive quantities like H T , S T and p T as a sign of missing higher jet multiplicities. Agreement with the data can be restored by adding explicitly higher jet multiplicities via exclusive sums.

Conclusions
Cross sections for jets produced in association with a Z boson have been measured in proton-proton collisions at √ s = 7 TeV with 4.6 fb −1 of data observed with the ATLAS detector at the LHC, using electron and muon decay modes of the Z boson. The data have been unfolded to the particle level and compared with predictions from the SHERPA generator, from MC@NLO interfaced with HERWIG, from the ALPGEN generator, interfaced with HERWIG, and with fixed-order calculations from BlackHat+SHERPA. The cross sections are quoted with respect to a phase-space region defined by Z candidates -23 - constructed from opposite-sign leptons with p T > 20 GeV, |η| < 2.5, ∆R > 0.2 and 66 GeV ≤ m ≤ 116 GeV and for jets with p jet T > 30 GeV, |y jet | < 4.4 and ∆R j > 0.5. Cross sections as a function of the inclusive and exclusive jet multiplicities and their ratios have been compared, as well as differential cross sections as a function of transverse momenta and rapidity of the jets, angular separation between the leading jets and the inclusive variables H T and S T . Compared with previous publications, the sensitivity has been extended to regimes with larger jet multiplicities and larger jet transverse momenta. In addition, the sample has been compared to theory in specific kinematic regions governed by large logarithmic corrections.
In general, the predictions of the matrix element plus parton shower generators and the fixed-order calculations are consistent with the measured values over a large kinematic range. MC@NLO fails to model not only higher jet multiplicities but also the transverse momentum of the leading jet. The transition from staircase to Poisson scaling of the exclusive jet multiplicity ratio, expected from theory when introducing a large scale difference, is observed in the data.
In events where two jets have passed a VBF preselection, the cross sections for higher -24 - jet multiplicities are overestimated by ALPGEN. This leads to a small underestimation of the probability for Z + jets events to survive a veto on a soft third jet.
ALPGEN predicts a too hard spectrum of the transverse momentum of the leading jet, of p T , H T and S T in a regime where large corrections from higher-order electroweak and higher-order QCD processes are expected. The jet rapidity distribution is predicted to be too wide in BlackHat+SHERPA and in SHERPA. BlackHat+SHERPA underestimates the cross section for large p T where more than one jet can be resolved. The H T or S T spectra predicted by BlackHat+SHERPA fixed order NLO calculations deviate by several standard deviations from the measured spectra in the hard H T and S T regime characterized by large average jet multiplicities. The observed spectra of H T and p T can be described by an exclusive sum of BlackHat+SHERPA fixed-order calculations for Z (+1 parton) and Z (+ ≥ 2 partons).

Acknowledgements
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.
We    Figure 14. Fraction of events that pass a veto on a central (|η| < 2.4) third jet after VBF preselection (at least two jets with p jet T > 30 GeV and |y jet | < 4.4, m jj > 350 GeV and |∆y jj | > 3.0 for the two leading jets) as a function of the third jet p jet T threshold, min p jet T , (a) in the electron channel and (b) in the muon channel, measured in data and predicted by the generators ALPGEN and SHERPA (see legend for details). The data points indicate the measured distribution after subtraction of electroweak and multi-jet background. The hatched bands correspond to the combined statistical and systematic uncertainty on the Z + jets prediction, using ALPGEN to derive the systematic uncertainties. The error bars on each data point show the combined statistical and systematic uncertainty on the data. The bottom panel shows the MC/data ratio. The shaded band corresponds to the total systematic uncertainty and the error bars to the statistical uncertainty on the MC/data ratio.    Figure 17. (a) Measured cross section for Z (→ ) + jets as a function of the scalar p T sum of the leptons and the jets, H T , and (b) as a function of the transverse momentum of the Z candidate, p T , in events with at least one jet with p jet T > 30 GeV and |y jet | < 4.4 in the final state. The cross sections are normalized to the inclusive Z (→ ) cross section. The unfolded data are compared to NLO pQCD predictions from BlackHat+SHERPA, obtained by adding the exclusive Z (→ ) +1 jet and the inclusive Z (→ ) + ≥ 2 jets calculations and corrected to the particle level. The error bars indicate the statistical uncertainty on the data, and the hatched (shaded) bands the statistical and systematic uncertainties on data (prediction) added in quadrature.  Table 4. Combined inclusive Z (→ ) + jets cross sections per lepton flavour and their ratios and exclusive cross-section ratios for various preselections measured in data together with the corresponding non-perturbative corrections δ had and δ QED . The cross sections are quoted with respect to a phase-space region defined by Z candidates constructed from opposite-sign leptons with p T > 20 GeV, |η| < 2.5, ∆R > 0.2 and 66 GeV ≤ m ≤ 116 GeV and for jets with p jet T > 30 GeV, |y jet | < 4.4 and ∆R j > 0.5.