Measurement of the Z/γ* boson transverse momentum distribution in pp collisions at √s = 7 TeV with the ATLAS detector

: This paper describes a measurement of the Z/γ ∗ boson transverse momentum spectrum using ATLAS proton-proton collision data at a centre-of-mass energy of √ s = 7 TeV at the LHC. The measurement is performed in the Z/γ ∗ → e + e − and Z/γ ∗ → µ + µ − channels, using data corresponding to an integrated luminosity of 4.7 fb − 1 . Normalized diﬀerential cross sections as a function of the Z/γ ∗ boson transverse momentum are measured for transverse momenta up to 800 GeV. The measurement is performed inclusively for Z/γ ∗ rapidities up to 2.4, as well as in three rapidity bins. The channel results are combined, compared to perturbative and resummed QCD calculations and used to constrain the parton shower parameters of Monte Carlo generators.


Introduction
The transverse momentum distribution of W and Z bosons produced in hadronic collisions is a traditional probe of strong interaction dynamics. The low transverse momentum (p T ) range is governed by initial-state parton radiation (ISR) and the intrinsic transverse momentum of the initial-state partons inside the proton, and modeled using soft-gluon resummation [1] or parton shower models [2,3]. Quark-gluon scattering dominates at high p T and is described by perturbative QCD [4][5][6]. The correct modelling of the vector boson p T distribution is important in many physics analyses at the LHC for which the production of W or Z bosons constitutes a significant background. Moreover, it is crucial for a precise measurement of the W boson mass. The transverse momentum distribution also probes the gluon density of the proton [7]. Vector boson p T distribution measurements were published by ATLAS [8,9] and CMS [10] based on 35-40 pb −1 of proton-proton collisions at a centre-of-mass energy of √ s = 7 TeV. The typical precision of these measurements is 4% to 10%. This paper presents a measurement of the normalized Z boson transverse momentum distribution (p Z T ) with the ATLAS detector, in the Z/γ * → e + e − and Z/γ * → µ + µ − channels, using LHC proton-proton collision data taken in 2011 at a centre-of-mass energy of √ s = 7 TeV and corresponding to an integrated luminosity of 4.7 fb −1 [11]. The large integrated luminosity allows the measurement to be performed in three different Z boson rapidity (y Z ) bins, probing the transverse momentum dynamics over a wide range of the initial-state parton momentum fraction. With respect to previous results, the present analysis aims at reduced uncertainties, finer binning and extended measurement range.
Reconstructed from the final-state lepton kinematics, p Z T is affected by lepton energy and momentum measurement uncertainties. To minimize the impact of these uncertainties, the φ η observable 1 was introduced as an alternative probe of p Z T [12], pioneered at the Tevatron [13][14][15], and studied by ATLAS using the present data set [16] and LHCb [17]. The correlation between φ η and p Z T is, however, only partial and the good experimental resolution on φ η is counterbalanced by a reduced sensitivity to the underlying transverse momentum distribution; in addition, interpreting φ η as a probe of p Z T assumes that the final-state lepton angular correlations are correctly modeled. The measurement presented in this paper allows the effects of the Z boson transverse momentum and the lepton angular correlations to be disentangled unambiguously.
QCD predictions for the p Z T distribution are described in the next section. After a brief description of the experiment in section 3, the measurement is presented in sections 4-8. The results are compared to available QCD predictions in section 9 and used to constrain phenomenological models describing the low-p Z T region in section 10; the compatibility of the φ η measurement with the p Z T -constrained models is also tested. Section 11 concludes the paper.

QCD predictions
The measurements are compared to a representative set of theoretical predictions. They rely on perturbative QCD (pQCD) only, or include resummation of soft-gluon emissions. Resummation is treated either analytically, or using Monte Carlo methods.
Fully differential inclusive boson-production cross sections can be obtained to second order in the strong coupling constant α S (NNLO) using the Fewz3.1 [4][5][6] and Dynnlo1.3 [18,19] programs. The O(α 2 S ) cross-section predictions are valid at large p Z T , where the cross section is dominated by the radiation of high-p T gluons. At low p Z T , multiple soft-gluon emissions predominate and fixed-order pQCD predictions are not appropriate.
The ResBos calculation relies on soft-gluon resummation at low p Z T and matches the O(α 2 S ) cross section at high p Z T . It simulates the vector boson decays but does not include a description of the hadronic activity in the event. Two versions are used here, which differ in the non-perturbative parameterization used to perform the resummation. The original parameterization [1] and a recent development [20] are referred to as ResBos-Events are required to have at least one primary vertex reconstructed from at least three tracks with p T > 500 MeV, and to contain exactly two oppositely charged same flavour leptons, selected as described above, with invariant mass satisfying 66 GeV < m < 116 GeV ( = e, µ). This broad interval is chosen to minimize the impact of QED FSR on the signal acceptance. The total selected sample consists of 1228863 Z/γ * → e + e − and 1816784 Z/γ * → µ + µ − candidate events.
Monte Carlo events are corrected to take into account differences with data in lepton reconstruction, identification and trigger efficiencies, as well as energy and momentum scale and resolution. The efficiencies are determined using a tag-and-probe method based on reconstructed Z and W events [42]. The isolation requirement used in the muon channel induces significant p Z T dependence in the muon selection efficiency, and the efficiency determination is repeated in each p Z T bin. The energy resolution and scale corrections are obtained comparing the lepton pair invariant mass distribution in data and simulation [43,44].

Background estimation
The background to the observed Z signal includes contributions from Z/γ * → τ + τ − , W → ν, gauge boson pair production, single top quark and tt production, and multijet production. The electroweak and top quark background contributions are estimated from simulation and normalized using theoretical cross sections calculated at NNLO accuracy. For the multijet background, which dominates at low p Z T , the leptons originate from semileptonic decays or from hadrons or photons misidentified as electrons, which cannot be simulated accurately and are determined using data-driven methods.
In the electron channel, the multijet background fraction is determined from the electron isolation distribution observed in data. The isolation variable, x, is defined as the transverse energy contained in a cone of size ∆R = 0.3 around the electron energy cluster (excluding the electron itself), divided by the electron transverse energy. On average, isolated electrons from Z/γ * → e + e − decays are expected at lower values of x than multijet background events. The signal distribution, S(x), is given by the simulation and shifted to match the data in the signal-dominated low-x region. A jet-enriched sample is extracted from data by requiring electron candidates to fail the track-cluster matching or shower shape criteria in the first EM calorimeter layer, but otherwise pass the analysis selections, giving B(x). This distribution is corrected for the residual contribution from electroweak and top quark backgrounds, which are estimated using simulation. The multijet background normalization is then given by a fit of D(x) = qB(x) + (1 − q)S(x), where D(x) is the isolation distribution observed in data and q is the fitted background fraction. The above procedure is repeated, separating events with same charge sign (SS) and opposite charge sign (OS) leptons in the background-enriched sample, and varying ∆R between 0.2 and 0.4. The average of the results and their envelope define the multijet background fraction and its uncertainty, yielding q = (0.14 +0.10 −0.05 )%. The p Z T shape of the background is assumed to follow that of the background-enriched sample; this assumption is verified by repeating the procedure in three coarse p Z T bins. The uncertainty on the shape is defined from the difference between the SS and OS samples.
In the muon channel, the multijet background is estimated using muon isolation information in signal-and background-dominated invariant-mass regions. Four two-dimensional regions are defined, characterized by a mass window and according to whether both muons pass or fail the isolation cut described in section 5. The signal region (region A), the two control regions (regions B and C) and the multijet region (region D) are defined as follows: Region A (signal region): 66 GeV < m µµ < 116 GeV, isolated Region B: 47 GeV < m µµ < 60 GeV, isolated Region C: 66 GeV < m µµ < 116 GeV, non-isolated Region D (multijet region): 47 GeV < m µµ < 60 GeV, non-isolated Assuming the m µµ and isolation distributions are not correlated, the number of multijet events in the signal region is determined from the number of events observed in regions B, C and D, as n A = n B × n C /n D , where n B , n C and n D are corrected for the residual contribution from electroweak and top processes. In an alternative method, the multijet background is assumed to be dominated by heavy-flavour decays, and its normalization is derived from the number of observed SS muon pairs, corrected by the expected OS/SS ratio in heavy-flavour jet events, as predicted by Pythia. Since the results of the two methods differ by more than their estimated uncertainty, the background normalization used for this channel is defined as the average of the two computations, and its uncertainty as their half difference, giving an expected fraction of (0.11 ± 0.06)%. The p Z T shape of the multijet background is defined from the control sample with the inverted isolation cut (region D); using that obtained from the SS sample instead has negligible impact on the measurement result. Figure 1 shows the p Z T distributions for data and Monte Carlo samples including the experimental corrections discussed in section 5 as well as the background estimates, in the electron and muon channels.

Unfolding and systematic uncertainties
The normalized differential cross section as a function of p Z T is defined as (1/σ fid )(dσ fid /dp Z T ), where σ fid is the inclusive pp → Z/γ * cross section measured within the fiducial acceptance defined by requiring p T > 20 GeV and |η| < 2.4 for the decay leptons; the invariant mass of the pair must satisfy 66 < m < 116 GeV. In addition to the rapidity-inclusive measurement, the measurement is performed for 0 ≤ |y Z | < 1, 1 ≤ |y Z | < 2 and 2 ≤ |y Z | < 2.4.
The measurement is performed for three definitions of the particle-level final-state kinematics. The Born and bare kinematics are defined from the decay lepton kinematics before and after FSR, respectively. The dressed kinematics are defined by combining the bare momentum of each lepton with that of photons radiated within a distance smaller than ∆R = 0. from the ratio of the corresponding particle-level p Z T distributions and denoted by k bare (p Z T ) and k dressed (p Z T ), respectively.
The Z/γ * transverse momentum is reconstructed from the measured lepton four-momenta. The p Z T range is divided into 26 bins of varying width between 0 GeV and 800 GeV, with finer granularity in the low-p Z T range, as shown in tables 1-3. The bin purity, defined as the fraction of reconstructed events for which p Z T falls in the same bin at reconstruction and particle level, is everywhere above 50%.
The total background is subtracted from the observed p Z T distribution. The electroweak background cross sections are assigned a 5% uncertainty derived by varying the PDFs within their uncertainties and from QCD renormalization and factorization scale variations; in addition, a relative uncertainty of 1.8% on the total integrated luminosity is taken into account. The normalization of the top background was verified comparing data and simulation at high missing transverse energy (E miss T ), defined for each event as the total transverse momentum imbalance of the reconstructed objects. An uncertainty of 12% is assigned comparing data and simulation for E miss T > 100 GeV and 20 < p Z T < 120 GeV, where this background contribution dominates. The multijet background uncertainty is discussed in section 6.
The p Z T distribution is subsequently corrected for resolution effects and QED final-state radiation back to the Born level, as well as for the differences between the reconstructionand particle-level fiducial acceptance, with an iterative Bayesian unfolding method [45][46][47]; three iterations are used. The response matrix used for the unfolding is defined as a twodimensional histogram correlating the Born-level and reconstructed p Z T distributions. The prior probability distribution for the Born-level p Z T distribution is defined from the modified Powheg+Pythia6 prediction described in section 4, and matches that of Pythia6-AMBT1.
The statistical uncertainty on the unfolded spectrum is obtained by generating random replicas of the reconstruction-level p Z T distribution. For each trial, Poisson-distributed fluctuations are applied to the number of entries in each bin, and the measurement procedure is repeated. The obtained ensemble of fluctuated measurement results is used to fill a covariance matrix, including correlations between the bins introduced by the unfolding and normalisation procedure. The relative statistical uncertainty remains below 0.6% for p Z T < 30 GeV in both channels, and below 1.1% up to 150 GeV. The uncertainty induced by the size of the MC samples is determined by applying the same method to the response matrix, and stays below 0.4% and 0.5% up to p Z T = 150 GeV in the muon and electron channel, respectively, reaching 2% for the bin 300 < p Z T < 800 GeV.
Systematic uncertainties from experimental sources such as trigger, reconstruction and identification efficiency corrections, energy scale and resolution corrections, and the background normalization and p T distribution are evaluated by repeating the analysis varying the corresponding parameters within their uncertainties and comparing to the nominal result. For each channel, the impact of a given source of uncertainty is evaluated preserv-ing correlations across the measurement range. The uncertainty on the normalization of the electroweak and top quark backgrounds is treated as fully correlated between the two channels. The electron-and muon-specific uncertainties are uncorrelated between channels.
In the electron channel, the uncertainties on the trigger, reconstruction and identification efficiency corrections are propagated preserving their correlations across lepton η and p T . These sources contribute a relative uncertainty of the order of 10 −4 up to p Z T = 100 GeV and less than 0.2% over the full measurement range. The uncertainty induced by the background subtraction is typically 0.1%, except around p Z T = 100 GeV where it reaches 0.3% because of the top quark background contribution. The uncertainty induced by charge misidentification, estimated from the difference between the results obtained with and without an opposite-sign requirement on the leptons, amounts to less than 0.2% over the whole p Z T range. The dominant experimental uncertainties in the electron channel arise from the electron energy scale, resolution, mis-modelling of the electron energy tails caused by uncertainties in the treatment of electron multiple scattering in Geant4 and in passive detector material. The combined contribution from energy scale and resolution uncertainties to the total systematic uncertainty is typically 0.3% per bin between 4 GeV and 70 GeV, and reaches about 2% at the end of the spectrum. The uncertainty from the energy tails amounts to 0.8% at most, contributing mainly at very low p Z T and at very high p Z T where the statistical uncertainty dominates.
In the muon channel, the trigger, reconstruction and isolation efficiency corrections contribute an uncertainty of 0.6% on average, spanning 0.2% to 1.7% across the measurement range. The momentum scale and resolution uncertainties amount to 0.2%, except in the last three p Z T bins where they stay below 1.5%. The uncertainty contributed by the background subtraction is below 0.1% over the whole p Z T range except around p Z T = 100 GeV where it reaches 0.13% because of the top quark background contribution.
The dominant contribution to the systematic uncertainties for both channels comes from the unfolding method. Two effects are addressed: the bias of the result towards the prior, and the dependence of the result on the theoretical calculation used to determine the response matrix. The first item is evaluated by repeating the measurement using the nominal result as the prior. The difference between the nominal result and this iteration is less than 0.1% up to 100 GeV, and less than 1.3% for the rest of the distribution. The second effect is evaluated by unfolding the p Z T distribution using an alternative response matrix, constructed from a Z/γ * → + − sample obtained with Mc@nlo instead of Powheg, and modified to match the Pythia6-AMBT1 spectrum as it was done for Powheg. A systematic uncertainty of about 0.3% over the whole p Z T range is assigned from the difference between the two results. The PDF uncertainties are estimated by reweighting the baseline sample to each of the CT10 PDF error sets [30] and repeating the unfolding. In each bin, the sum in quadrature of deviations with respect to the nominal result is used to define the associated uncertainty, which is below 0.1% up to 60 GeV and below 0.3% over the remaining p Z T range. The unfolding systematic uncertainties are assumed to be fully correlated between the electron and muon channels.
The uncertainty arising from the accuracy of the theoretical description of QED FSR is obtained by comparing k bare (p Z T ) and k dressed (p Z T ) as predicted by Photos and Sherpa. The differences obtained for k bare (p Z T ) are representative of the QED uncertainty in the muon channel, and amount to 0.3% across the p Z T distribution. From the differences obtained for k dressed (p Z T ), a 0.1% uncertainty is assigned to the electron channel. Photon-induced dilepton production is significant only in the lowest p Z T bin (0-2 GeV), where it contributes 0.4%. The cross sections obtained for this process when evaluating the MRST2004qed PDFs in the current and constituent quark mass schemes differ by 30%, and contribute an uncertainty of 0.1% to the measurement in this bin.

Results
The inclusive normalized cross sections (1/σ fid )(dσ fid /dp Z T ) measured in the Z/γ * → e + e − and Z/γ * → µ + µ − channels are presented in table 1 including statistical, uncorrelated and correlated systematic uncertainties. The sizes of the correlated uncertainties depend on the channel because of different resolutions and background levels. The measurement results are reported at Born level and factors k bare and k dressed are given to translate to the bare and dressed levels. In each channel, the total uncertainty is between 0.5% and 1% for p Z T < 30 GeV, below 1.5% per bin up to p Z T = 150 GeV and rises to 7% at the end of the spectrum.
The electron-and muon-channel cross sections are combined using χ 2 minimization, following the best linear unbiased estimator prescription (BLUE) [48,49]. The combination is performed for the Born-level and dressed-level distributions. When building the χ 2 , the measurement uncertainties are categorized into uncorrelated and correlated sources. Table 2 presents the combined results for the inclusive measurement for Born level and dressed lepton kinematics. The combined precision is between 0.5% and 1.1% for p Z T < 150 GeV, rising to 5.5% towards the end of the spectrum. The combination has χ 2 /dof = 12.3/25 (χ 2 per degree of freedom). The individual channels are compared to the combined result in figure 3.
The measurements are repeated in three exclusive boson rapidity bins, namely 0 ≤ |y Z | < 1, 1 ≤ |y Z | < 2 and 2 ≤ |y Z | < 2.4. The combined results, corrected to the Born level, are given in table 3 with statistical, correlated and uncorrelated systematic uncertainties for the three rapidity bins. The measurement results in each channel and their combination are illustrated in figures 4-6.     Table 2. The measured normalized combined (electron and muon channels) cross section (1/σ fid )(dσ fid /dp Z T ), inclusive in rapidity. The cross sections at Born and dressed levels are given as well as the relative statistical (δ Stat ) and total systematic (δ Syst ) for uncorrelated and correlated sources.      1.08 Ldt=4.7 fb ∫ =7 TeV; s Figure 4. The measured normalized cross section (1/σ fid )(dσ fid /dp Z T ) for 0 ≤ |y Z | < 1, as a function of p Z T for the electron and muon channels and the combined result (top). Ratio of the electron and muon channels to the combined result (bottom). The uncertainty bands represent the statistical, total uncorrelated and total uncertainties, from light gray to dark gray respectively. 1.08 Ldt=4.7 fb ∫ =7 TeV; s Figure 5. The measured normalized cross section (1/σ fid )(dσ fid /dp Z T ) for 1 ≤ |y Z | < 2, as a function of p Z T for the electron and muon channels and the combined result (top). Ratio of the electron and muon channels to the combined result (bottom). The uncertainty bands represent the statistical, total uncorrelated and total uncertainties, from light gray to dark gray respectively. 1.08 Ldt=4.7 fb ∫ =7 TeV; s Figure 6. The measured normalized cross section (1/σ fid )(dσ fid /dp Z T ) for 2 ≤ |y Z | < 2.4, as a function of p Z T for the electron and muon channels and the combined result (top). Ratio of the electron and muon channels to the combined result (bottom). The uncertainty bands represent the statistical, total uncorrelated and total uncertainties, from light gray to dark gray respectively.

Comparison to QCD predictions
In figure 7, the Born-level combined result is compared to theoretical predictions at fixed order from Fewz and Dynnlo, to ResBos and to the NLO+NNLL calculation. Fewz, Dynnlo and ResBos use the CT10 PDFs, while the NLO+NNLL calculation uses the CTEQ6m PDFs [50].
The uncertainty on the predictions, estimated from the PDF uncertainties and renormalization and factorization scale variations, are in all cases much larger than the measurement uncertainties. The disagreement between the data and the Fewz and Dynnlo predictions is larger than the data uncertainties, reaching 10% around 50 GeV and diverging at low p Z T as expected from the absence of resummation effects in these calculations. Fewz and Dynnlo agree with each other when using QCD renormalization and factorization scales, µ R and µ F , defined as µ R = µ F = m Z and leading-order electroweak perturbative accuracy. The influence of the QCD scale choice is studied with Dynnlo by using the alternative dynamic scale E Z T , defined as the sum in quadrature of m Z and p Z T . The resulting p Z T shape is in better agreement with the data for p Z T > 30 GeV, but the normalization remains low by 10% in this region. NLO electroweak corrections to Z+jet production [51] are applied to the dynamic-scale Dynnlo prediction and lead to a decrease of the cross section of 10% in the highest p Z T bin.
The ResBos-GNW prediction agrees with the data within 5-7%; the prediction uncertainties are defined from PDF, renormalization scale and factorization scale variations. The ResBos-BLNY prediction, to which the previous ATLAS measurements [8,9,16] were compared, is included for reference. The NLO+NNLL calculation matches the data within 10-12%. The uncertainties on this prediction are defined from resummation, renormalization and factorization scale variations; PDF uncertainties are neglected following Ref. [21]. In both cases, the prediction uncertainties are almost sufficient to cover the difference with the data. Figure 8 shows the ratio of the p Z T distributions predicted by different generators to the combined measurements performed inclusively in Z rapidity, and in the three exclusive Z rapidity bins described above. The Pythia and Powheg generators agree with the data to within 5% in the 2 < p Z T < 60 GeV range, and to within 20% over the full range. Mc@nlo shows a similar level of agreement with the data for p Z T < 30 GeV but develops a discrepancy up to around 40% at the end of the spectrum. Sherpa and Alpgen agree with the data to within about 5% for 5 < p Z T < 200 GeV, but tend to overestimate the distribution near the end of the spectrum.

Tuning of Pythia8 and Powheg+Pythia8
The parton shower tunes presented below are performed to determine the sensitivity of the measured p Z T cross sections presented here to parton shower model parameters in state-of- the-art MC generators, and to constrain the models by trying to achieve precise predictions of vector boson production. The ATLAS φ η measurement [16] is also exploited as it is highly correlated to p Z T and is hence sensitive to the same model components.
The Pythia8 generator with the p T -ordered, interleaved parton shower is chosen for these studies. Pythia8 is used in standalone mode and in a configuration interfaced to Powheg.
To minimize dependence on QED final-state corrections, the tunes use the dressed-level  Figure 8. Ratio of the p Z T distribution predicted by different MC generators to the Born-level combined measurement, for the inclusive measurement and for 0 ≤ |y Z | < 1, 1 ≤ |y Z | < 2 and 2 ≤ |y Z | < 2.4. measurement results. The study is restricted to the low p Z T range, where parton shower effects dominate. The tunes are performed for p Z T < 26 GeV, which is found to be most sensitive to the model parameters described below, and φ η < 0.29, which covers a similar transverse momentum range. The measurement inclusive in rapidity is used for the tuning, and the compatibility of the tuned predictions with the data in the separate rapidity bins is then evaluated.
For Pythia8, the parton shower model components under consideration include the strong coupling constant used for the parton shower evolution α ISR S (m Z ), and the parton shower lower cut-off p T0 in the non-perturbative regime, implemented as a smooth damping factor p 2 T /(p 2 T0 +p 2 T ). To populate the region below p T0 , the partons initiating the hard scattering process are assumed to have a primordial transverse momentum k T following a Gaussian distribution with tunable width. The Pythia8 parton shower also includes QED emissions, but the corresponding cut-off values and coupling strength are left to the program defaults. The steerable parameters not used in the tuning are set to the values defined by the tune 4C [35].
Powheg calculates the hardest (highest p T ) QCD radiation provided that it is above a Powheg cut-off [GeV 2 ] -4.0 Table 4. Parameter ranges and model switches used in the tuning of Pythia8 and Pythia8+Powheg described in section 10.
transverse momentum threshold p 2 T,min , which is a steerable parameter in the program. Below p 2 T,min , Powheg generates events without extra radiation and the phase space is populated by Pythia8. Therefore, the upper limit of the Pythia8 parton shower should match the Powheg cut-off value. The tunes are performed using p 2 T,min = 4 GeV 2 , corresponding to p Z T = 2 GeV. In addition, in order to avoid discontinuities in the matched spectrum, the α S (m Z ) value used to calculate the QCD radiation in Powheg should match α ISR S (m Z ) in Pythia; α S (m Z ) = 0.118 is used as in the CT10 PDFs. Correspondingly the running of α S in the parton shower calculation is set to NLO. The tuning of Powheg+Pythia8 hence only varies the shower cut-off and the primordial k T in Pythia8. The other steerable parameters not used in the tuning are set to the values defined by the 4C tune.
The tunes are performed using the Professor [52] package, which interpolates the dependence of MC predictions on the model parameters as originally proposed in ref. [53]. Predictions for the p Z T distribution are generated at randomly chosen parameter settings (anchor points) in the ranges indicated in table 4. A fourth-order polynomial is used to approximate the generator predictions between the anchor points. The optimal parameter values are determined using a χ 2 minimization between the interpolated generator response and the data.
The sensitivity of the generator parameters to the p Z T and φ η measurements is probed by performing tunes of Pythia8 and Powheg+Pythia8 to each measurement separately. As shown in table 5 both measurements have comparable sensitivity and yield compatible tuned parameter values. As a further check of the compatibility between the p Z T and φ η measurements, the p Z T -tuned and φ η -tuned predictions are compared to the measured p Z T distribution. The tuning uncertainty is obtained from variations of the eigenvector components of the parameters error matrix over a range covering ∆χ 2 = χ 2 min /dof. Figure 9 shows that the tuned predictions agree with the measured cross sections within 2% for p Z T < 50 GeV, and with each other within the tuned parameter uncertainties.
Since the p Z T and φ η observables provide similar sensitivity to the parton shower parameters and to avoid correlations between these measurements, the final tune optimally combines

Pythia8
Powheg+Pythia8  the most precise independent single measurements, namely the muon channel p Z T measurement, and the electron channel φ η measurement. The same tuning range is used. Table 6 shows the tune results and figure 10 shows the comparison of the tuned predictions to the data. The final tunes are referred to as AZ and AZNLO for Pythia8 and Powheg+Pythia8 respectively. The tuned predictions agree with the measurement to better than 2% in the range used for the tuning, and below p Z T = 50 GeV. The primordial k T and ISR cut-off parameters are essentially constrained by the data in the region p Z T < 12 GeV and not affected by the choice of upper bound for the tuning range. In contrast, α ISR S (m Z ) is tightly constrained for a given choice of range but its tuned value varies by 2% when increasing the upper bound to 50 GeV. At higher transverse momentum, discrepancies of around 15% for Pythia8 and 20% for Powheg+Pythia8 remain, indicating the limited accuracy of the NLO signal matrix element and suggesting the need for contributions from higher parton multiplicity.
Tuned predictions based on the parameter values given in table 6 are produced in the different Z rapidity bins and compared to the measured cross sections with the aim of assessing how accurately the tune based on the inclusive measurement reproduces the data in each Z rapidity bin. The results are shown in figure 11. A satisfactory description across rapidity is obtained in the case of Pythia8; in the case of Powheg+Pythia8, the prediction at low p Z T undershoots the data for 0 ≤ |y Z | < 1, and overshoots the data for 2 ≤ |y Z | < 2.4. The inclusive tune thus appears as a compromise between the different |y Z | regions in this case. The sensitivity of the parton shower tune to other model components provided in Pythia8, such as multiple parton interactions (MPI), which affect the event overall hadronic activity, was studied by varying the corresponding parameters. No effect on the parton shower parameters is found. In order to compensate for the changes in energy and particle flow induced by the modifications in the parton shower and primordial k T parameters, the p T threshold for the QCD 2 → 2 scattering processes used in MPI is changed from 2.085 GeV (tune 4C) to 2.18 GeV for Pythia8, following the underlying event data measured in Drell-Yan events by ATLAS [54]. For the Powheg+Pythia8 configuration, the interleaving of MPI in the parton shower model in Pythia8 is adapted to also properly take into account the Powheg emissions. It is tuned in the same way as Pythia8 in standalone mode and an optimized value of 2.00 for the low-p T regularization of MPI is found. Finally, comparing tunes based on the native Pythia8 QED final-state corrections with Pythia8 results using Photos for QED final-state radiation, the results are found insensitive to the differences in the QED FSR implementations.
A consistent description of the p Z T and φ η data is reached with a single tune. Both observables are also found to provide similar sensitivity to the parameters of interest. The inclusive tune provides an accurate description of the different rapidity bins in the case of Pythia8, while the agreement versus |y Z | is slightly worse in the case of Powheg+Pythia8.

Conclusion
A measurement of the Z/γ * transverse momentum spectrum in the Z/γ * → e + e − and Z/γ * → µ + µ − channels with the ATLAS detector is presented, using 4.7 fb −1 of LHC proton-proton collision data at a centre-of-mass energy of √ s = 7 TeV. Normalized differential cross sections as a function of p Z T are measured for the range 0 < p Z T < 800 GeV and the individual channel results are combined. The measurement is performed inclusively in rapidity, and for 0 ≤ |y Z | < 1, 1 ≤ |y Z | < 2 and 2 ≤ |y Z | < 2.4. The large data sample allows a fine binning in p Z T with a typical uncertainty on the combined result better than 1% for p Z T < 100 GeV, rising to 5% towards the end of the spectrum.
The cross-section measurements are compared to pQCD and resummed predictions. While Fewz and Dynnlo do not include resummation and the observed disagreement at low p Z T is expected, ResBos and the NLO+NNLL prediction marginally agree with the data given the large uncertainties on these predictions. The data are also compared to predictions from Pythia6-AUET2B, Powheg+Pythia6-AUET2B, MC@NLO, Alpgen and Sherpa. The Pythia and PowHeg generators agree with the data to within 5% in the range 2 < p Z T < 60 GeV and to within 20% over the full range, whereas Mc@nlo shows a deficit of about 40% at the end of the measured spectrum. Alpgen and Sherpa provide good agreement over a larger range, p Z T < 200 GeV, but overestimate the high end of the distribution. These patterns are compatible with what was observed for the φ η measurement. Electroweak corrections and the choice of a dynamic QCD scale were found to have a significant impact on the predictions at high p Z T ; incorporating these improvements provides a better description of the measured distribution in the high p Z T region.
The p Z T and φ η measurements were used to tune the Pythia8 and Powheg+Pythia8 generators. Both measurements can be interpreted consistently in terms of the Z/γ * bosons transverse momentum distribution and provide similar sensitivity to parton shower model parameters. The tuned predictions are in agreement with the data within 2% for p Z T below 50 GeV. The best description is provided by Pythia8, which is also able to describe the different rapidity intervals with a single tune. [17] LHCb collaboration, Measurement of the cross-section for Z → e + e − production in pp collisions at √ s = 7 TeV, JHEP 02 (2012) 106, [arXiv:1212.4620].