Measurement of forward $\rm Z\rightarrow e^+e^-$ production at $\sqrt{s}=8$TeV

A measurement of the cross-section for Z-boson production in the forward region of pp collisions at 8TeV centre-of-mass energy is presented. The measurement is based on a sample of $\rm Z\rightarrow e^+e^-$ decays reconstructed using the LHCb detector, corresponding to an integrated luminosity of 2.0fb$^{-1}$. The acceptance is defined by the requirements $2.0<\eta<4.5$ and $p_{\rm T}>20$GeV for the pseudorapidities and transverse momenta of the leptons. Their invariant mass is required to lie in the range 60--120GeV. The cross-section is determined to be $$ \sigma({\rm pp\to Z\to e^+e^-})=93.81\pm0.41({\rm stat})\pm1.48({\rm syst})\pm1.14({\rm lumi})\;{\rm pb}\,,$$ where the first uncertainty is statistical and the second reflects all systematic effects apart from that arising from the luminosity, which is given as the third uncertainty. Differential cross-sections are presented as functions of the Z-boson rapidity and of the angular variable $\phi^*$, which is related to the Z-boson transverse momentum.


Introduction
Measurements of vector boson production in hadron collisions permit tests of electroweak physics and of QCD.The effective kinematic range of the LHCb detector [1], approximately 2.0 < η < 4.5 where η is the pseudorapidity, complements that of the general purpose LHC detectors whose acceptance for precise measurements extends to |η| ≈ 2.5.Measurements at LHCb are sensitive to knowledge of the proton structure functions at very low Bjorken x values, where the parton distribution functions (PDFs) are not well constrained by previous data, or by other LHC experiments [2].
The most straightforward decay mode in which LHCb can study the production of the Z boson is the channel Z → µ + µ − , since the experiment has a highly efficient trigger and precise reconstruction capabilities for high-momentum muons.However, it is also desirable to examine the channel Z → e + e − ,1 which offers a statistically independent sample, with substantially different sources of systematic uncertainties.The main difficulty with electron reconstruction in LHCb is the energy measurement.A significant amount of material is traversed by the particles before they reach the magnet, and their measured momenta are therefore frequently degraded by bremsstrahlung, which cannot be recovered fully using the calorimeters because of saturation at an energy corresponding to a transverse momentum of around 10 GeV per channel.Consequently the initial electron directions are well determined, but their measured momenta are degraded by ∼ 25% on average.Therefore the rapidity of the Z boson, y Z , is well determined while its transverse momentum, p T , is poorly measured and biased.Thus, as in Ref. [3], the distribution of the angular variable φ * , which is correlated with p T but less affected by bremsstrahlung, is studied.The φ * variable [4] is defined in terms of the directions of the particle momenta φ * ≡ tan(φ acop /2) cosh(∆η/2) where ∆η is the difference in pseudorapidity between the leptons, the acoplanarity angle φ acop = π − |∆φ| depends on the difference between the azimuthal directions of the lepton momenta, ∆φ, and M and p T are the invariant mass and transverse momentum of the lepton pair. 2n this paper, we present a measurement of the cross-section for pp → Z → e + e − using the data recorded by LHCb in 2012 at √ s = 8 TeV, corresponding to an integrated luminosity of 2.0 fb −1 .The approach is essentially the same as that used in a previous study of the same channel at √ s = 7 TeV [3].The current measurement, as well as being at a higher centre-of-mass energy, benefits from a significantly higher and more precisely determined integrated luminosity, and from stable trigger conditions.Futhermore, an improved Monte Carlo simulation of the detector and an improved modelling of electron bremsstrahlung are available.The determination is performed in the same kinematic region as the LHCb measurement of Z → µ + µ − [5], namely 60 < M (Z) < 120 GeV and 2.0 < η < 4.5 and p T > 20 GeV for the leptons.
Section 2 gives a brief description of the detector, triggers and software, after which Sect. 3 describes the event selection and the analysis procedure, and Sect. 4 explains the techniques used for determining the main uncertainties in the measurement.The results are presented in Sect. 5 followed by a brief summary in Sect.6.

Detector and simulation
The LHCb detector [1,6] is a single-arm forward spectrometer designed for the study of particles containing b or c quarks.The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes, placed downstream of the magnet.The tracking system provides a measurement of momentum, p, with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV.The minimum distance of a track to a primary vertex, the impact parameter, is measured with a resolution of (15 + 29/p T ) µm, where p T is in GeV.Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors.Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad (SPD) and preshower (PRS) detectors, an electromagnetic calorimeter (ECAL) and a hadronic calorimeter (HCAL).Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.
The trigger consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction.Events are first required to pass the hardware trigger for electrons, which selects events having an electromagnetic cluster of high transverse energy geometrically associated with signals in the PRS and SPD detectors.This high-p T single-electron trigger is then refined by the software trigger.Global event cuts on the numbers of hits in several detectors, such as the SPD, are applied in order to prevent high-multiplicity events from dominating the processing time.
Simulated event samples of Z → e + e − with M (e + e − ) > 40 GeV are used in the analysis.Simulated samples of Z → τ + τ − , tt, W + W − and W ± Z are used to assess possible background contributions.In the simulation, pp collisions are generated using Pythia 8.1 [7] with a specific LHCb configuration [8].The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [9] as described in Ref. [10].

Data analysis
The reconstructed particles used as the basis of the analysis satisfy basic track quality requirements.The following criteria are applied in order to refine the sample of candidates for analysis: • either the electron or the positron candidate should satisfy a single-electron trigger at all stages of the trigger; • the reconstructed electron and positron candidates should have pseudorapidity and transverse momentum satisfying 2.0 < η < 4.5 and p T > 20 GeV respectively.The reconstructed e + e − invariant mass should be greater than 40 GeV; • the electron and positron candidates should have momenta measured with estimated fractional uncertainty smaller than 10%; • in order to identify the particles as electron candidates, both are required to show associated energy deposition in the calorimeters characteristic of high-energy electrons, namely E ECAL /p > 0.1, E HCAL /p < 0.05 and E PRS > 50 MeV where E ECAL , E HCAL and E PRS denote the energies recorded in the electromagnetic calorimeter, hadronic calorimeter and preshower detector respectively; • if more than one e + e − pair satisfies the above criteria in an event (which occurs in approximately 0.7% of cases), one is selected at random.
Applying these selection requirements, 65 552 Z → e + e − candidates are obtained.Most backgrounds are removed by subtracting a sample of same-sign e ± e ± candidates.Applying identical selection criteria, 4595 same-sign candidates are found.The cross-section is determined using the following expression: where N (e + e − ) is the number of signal candidates selected in data, N (e ± e ± ) is the number of same-sign candidates, N bg is the expected background not covered by same-sign candidates (predominantly Z → τ + τ − ) taken from simulation and Ldt is the integrated luminosity.The event detection efficiency, , is explained below, and the factor f MZ (determined from simulation) corrects for Z → e + e − candidates that pass the event selection whilst their true mass lies outside the range 60 < M (e + e − ) < 120 GeV.The correction procedure is applied for 17 bins in Z rapidity in the range 2.00 < y Z < 4.25. 3he analysis is also performed for 15 bins in φ * .The choice of binning takes account of the available sample size and the resolutions achieved on y Z and φ * .The luminosity is obtained with an overall uncertainty of 1.2% [11].
The efficiency of the event selection is factorised into several components, The efficiencies are determined such that the efficiency for each stage of the analysis is estimated for events that pass the preceding stages.Thus, track is the efficiency associated with the reconstruction of both electrons as tracks satisfying the quality requirements and kin gives the efficiency that both these reconstructed electron tracks satisfy the kinematic acceptance requirements on p T and η.Similarly, PID is the efficiency for identification of the tracks as electrons, GEC is the estimated efficiency of the global event cuts for these events and trig is the trigger efficiency.The determination of these contributions to the efficiency is performed separately in each bin of y Z or of φ * .The contributions that the terms in the efficiency make to the systematic uncertainty on the measurement are summarised in Sect. 4.
The tracking efficiency, track , gives the probability that, in events in which the electrons satisfy 2.0 < η < 4.5, p T > 20 GeV and 60 < M (e + e − ) < 120 GeV at the particle level, both of them correspond to reconstructed tracks satisfying the track quality requirements.In order to characterise accurately the dependence of the efficiency on y Z and φ * , the efficiency is taken from simulation.A consistency check using data allows a systematic uncertainty to be assigned.The efficiency shows a significant dependence on y Z , but almost no variation with φ * .
The kinematic efficiency, kin , accounts for the possibility that a Z → e + e − decay in which the electron momenta at particle level satisfy the kinematic requirements on p T and η may not do so for the reconstructed momenta, even though the tracks are reconstructed.This is a sizeable correction because of bremsstrahlung.The efficiency is determined using simulated events, with data used to assess the systematic uncertainty.In contrast to the earlier analysis [3], the particle-level electron momentum used here is the momentum before final-state radiation (FSR), so that the kinematic efficiency also includes the effect of FSR as implemented in Pythia 8.1, and an additional correction is no longer applied.
The particle identification efficiency, PID , accounts for the possibility that a signal event passing all track finding and kinematic requirements fails the electron identification requirements, either because the track falls outside the calorimeter acceptance, or because the requirements on calorimeter energies are not satisfied.The overall efficiency is taken from simulation to model accurately the acceptance effect, which leads to a significant variation with y Z ; this part of the efficiency is modelled reliably.The efficiency of the calorimeter energy requirements is validated using data, leading to a systematic uncertainty.
The global event cut that has the greatest effect on the Z → e + e − channel is a requirement in the electron triggers that the number of hits in the SPD be less than 600.In order to assess the consequent loss of events, use is made of Z → µ + µ − events that satisfy the dimuon trigger, for which the number of SPD hits, N SPD , is required to be less than 900.The distribution of N SPD in dielectron events should be the same as that in dimuon events apart from the contribution from the leptons.In the region N SPD < 600 it is observed that the distribution for Z → e + e − is consistent with that for Z → µ + µ − with an upward shift of 10 ± 5 hits associated with showering of the electron and positron.Accordingly, we use the fraction of Z → µ + µ − dimuon triggers in the range 590 ≤ N SPD < 900 to estimate the loss of dielectron events in the range 600 ≤ N SPD < 910.The small fraction of dimuon events having N SPD ≥ 900 is estimated to be 0.7% by extrapolation using an empirical fit to the distribution.The efficiency shows a weak dependence on Z rapidity and φ * .The trigger efficiencies for events passing the selection cuts are determined from data using a "tag-and-probe" method.The principle is to use events in which the electron satisfies the trigger to determine the efficiency for the positron to satisfy the trigger and vice versa.
The values of the various correction factors, averaged over all values of y Z , are summarised in Table 1.The uncorrelated components of the uncertainties are generally related to the statistical uncertainty associated with each efficiency.These can be sizeable in individual bins, but become small when their effect on the integrated cross-section is considered.The correlated components are taken to be fully correlated between bins, and therefore have roughly the same effect on individual bins and on the integrated cross-section.The principal systematic uncertainties are discussed in greater detail in Sect. 4. The overall efficiency is shown as a function of y Z and φ * in Fig. 1.

Systematic uncertainties
The tracking efficiency is evaluated using simulation and checked using data.The principle is to search for events where a track appears to be missing, so that the signature of a Z becomes a high-p T electron track accompanied by a high-energy ECAL cluster with no associated track.An efficiency is determined by comparison with the corresponding number of events in which two tracks are reconstructed.To reduce background, more stringent particle identification requirements are imposed on the tag electron, and isolation requirements are imposed on both the electron and the ECAL cluster.This cannot be regarded as a direct measurement of the efficiency of the main analysis selection because more stringent requirements are employed.Instead, the same procedure is applied to the simulated event sample.The ratio between the two, 0.990 ± 0.004, is taken as a correction to track obtained from simulation, with the full size of the correction taken as a systematic  1)) averaged over the experimental acceptance by integrating over y Z .The fractional uncertainties on the overall factors are also given, separated into components that are assumed to be correlated and uncorrelated between bins of the differential distributions.The kinematic efficiency is also evaluated from simulation.Accurate simulation of the detector material is necessary in order that energy losses through bremsstrahlung be correctly modelled, and any inaccuracy would lead to a scaling of the measured momenta.This is tested by examining the modelling of the p T distributions by simulation, particularly in the neighbourhood of the 20 GeV threshold.Figure 2 shows the distribution of min(p T (e + ), p T (e − )) for data compared with simulation.In order to quantify the uncertainty in kin , the p T values in data are scaled by a global factor α to represent the effect of an uncertainty in the detector material.The χ 2 between data and simulation is examined as α is varied.The resulting uncertainty in α translates into a relative uncertainty in kin of 0.6% (or 1.2% for y Z > 3.75), which is taken to be a systematic uncertainty fully correlated between bins.

Fractional uncertainty
The contribution to PID resulting from the calorimeter acceptance is purely geometrical and is assumed to be modelled reliably in simulation.To assess the reliability of simulation for the calorimeter energy requirements, events are selected in which one electron is tagged using the standard criteria, while a second probe track is found that satisfies all the requirements apart from that on the energy recorded in one of the calorimeters.By examining the distributions of calorimeter energy in the neighbourhood of the threshold applied, an estimate of any correction needed and its uncertainty is made.The test is repeated for each part of the calorimeter in turn.As a result of these studies, a systematic uncertainty of 0.7% on PID is assigned, independent of y Z and φ * , and treated as fully correlated between bins.
The statistical uncertainty in the determination of GEC is taken as part of the systematic uncertainties.The uncertainty in the 10 ± 5 hit offset leads to an additional systematic uncertainty of 0.4% overall, while an uncertainty of 0.2% is assigned based on comparing various extrapolation techniques.The value of GEC is determined as a function of y Z and φ * .The statistical uncertainty on the determination of trig is treated as a systematic uncertainty.
The principal background to the selected Z → e + e − sample is expected to arise from failures of particle identification, typically where one or two high-p T hadrons interact early and exhibit a shower profile in the calorimeters similar to electrons.Such backgrounds are addressed by the subtraction of the same-sign Z → e ± e ± candidates.To check whether this procedure is reliable, event samples are studied in which one electron is tagged using the standard requirements, while the second electron satisfies the same criteria except that the requirement on HCAL energy is not satisfied, suggesting that the probe is likely to be a hadron.The numbers of same-sign and opposite-sign pairs satisfying these criteria agree within 5.5%.Treating this as an uncertainty on the background corresponds to an uncertainty of 0.4% in the signal yield, which is taken as the systematic uncertainty on the cross-section.There is no significant variation with y Z or φ * , so the uncertainty is taken to be the same in all bins and fully correlated between bins.
Physics backgrounds that could give correlated pairs of genuine electron and positron are not necessarily removed by the same-sign subtraction.Production of heavy quark pairs, cc or bb, followed by semileptonic decay could mimic the signal.This contribution is expected to be small, and is found to be negligible using studies of the distribution of the vertex-fit χ 2 for the candidates in data and simulation.The decay Z → τ + τ − provides a background if both τ -leptons decay to electrons.After the selection, the background from this source is estimated to be 0.15% of the signal using simulated samples, and the prediction is subtracted in each bin of y Z and φ * as indicated in Eq. ( 1) with its statistical uncertainty included in the statistical error.The background arising from production of pairs of gauge bosons, such as W + W − or W ± Z, or of tt pairs, is neglected, being well below the 0.1% level, based on expectations from simulation.

Results
The measured differential cross-sections as functions of y Z and φ * are tabulated in Tables 2 and 3.The uncertainties in the bins of these distributions are significantly correlated because the luminosity uncertainty and some of the systematic uncertainties are assumed to be common between bins.The correlation matrices between bins of the distributions are presented in Tables 4 and 5 of the Appendix.The results are given as Born-level cross-sections, which do not include the effects of final-state radiation.Tables 2 and 3 also include the factors f FSR that permit the measurements to be converted to the particle level after FSR.These are determined using the true momenta of the electrons before and after the generation of FSR in the simulation.
The overall cross-section, obtained by integration of the rapidity distribution, is σ(pp → Z → e + e − ) = 93.81± 0.41(stat) ± 1.48(syst) ± 1.14(lumi) pb , where the first uncertainty is statistical, the second includes all experimental systematic effects apart from the contribution from the luminosity, which forms the third uncertainty.
When combining the experimental systematic uncertainties, those associated with trig , and those parts of track , kin and PID arising from the size of the Monte Carlo sample, are treated as uncorrelated between bins and therefore combined quadratically; other contributions are treated as fully correlated, as is the luminosity uncertainty, and combined linearly.
The measured cross-section is compared in Fig. 3 with next-to-next-to-leading order (NNLO; O(α s 2 )) QCD predictions, based on Fewz version 3.1.b2[12] using five different PDF sets, MSTW08 [13], CTEQ10 [14], ABM12 [15], NNPDF23 [16] and NNPDF30 [17].Of these, MSTW08 and CTEQ10 predate the start of LHC data-taking, while ABM12 and NNPDF have included some LHC measurements in their analyses.The uncertainties in the predictions include the effect of varying the renormalisation and factorisation scales by factors of two around the nominal values (set to the Z mass), combined in quadrature with the PDF uncertainties evaluated at 68% confidence level.All predictions are in good agreement with the data.
The differential distribution with respect to y Z is presented in Fig. 4 and compared with the NNLO calculations based on Fewz, all of which are compatible with the integrated cross-section, and model the rapidity distribution as well.In comparing the shapes of the differential cross-sections with theoretical predictions it can be beneficial to normalise them to the integrated cross-section in the acceptance, since most of the correlated systematic uncertainties in the data cancel.This is useful when comparing with models based on LO or NLO calculations, which may predict the integrated cross-section well.The normalised differential distribution with respect to y Z is presented in Fig. 4 and compared with calculations that partially take account of higher-order effects.A QCD calculation that takes multiple soft gluon emissions into account through resummation is provided by ResBos [18]. 4Alternatively, Powheg [19] provides a framework whereby a NLO (O(α s )) calculation can be interfaced to a parton shower model such as Pythia, which can approximate higher-order effects.The parton shower model of Pythia 8.1 [7] is also compared with the data.All approaches reproduce the main features of the rapidity distribution.
Studies at 7 TeV [3] showed that the NNLO calculations based on Fewz fail to model the φ * distribution.It is expected that the φ * distribution, like that of p T , is significantly affected by multiple soft gluon emissions, which are not sufficiently accounted for in fixed-order calculations.The normalised distribution with respect to φ * presented in Fig. 5 is therefore compared with the ResBos, Powheg and Pythia 8.1 calculations.These all model the data reasonably well, especially at lower φ * .To show this more clearly, the ratios between the calculations that include higher orders and the data for the φ * distribution are also shown in Fig. 5.The data tend to fall between the different models, indicating no clear preference for any of them.
Table 2: Differential cross-section for Z → e + e − as a function of Z-boson rapidity.The first error is statistical, the second the uncorrelated experimental systematic, the third the correlated experimental systematic and the last error is the uncertainty in luminosity.The cross-sections are at the Born level, i.e. before FSR.The rightmost column gives values of the additional factor, f FSR , by which the results should be multiplied in order to give the cross-sections after FSR.

Figure 1 :
Figure 1: Overall detection efficiency, , determined from a combination of data and simulation as described in the text, shown as a function of (left) y Z and (right) φ * .

Figure 2 :
Figure2: Comparison between data and simulation for the distribution of min(p T (e + ), p T (e − )), used in the assessment of uncertainties in kin .The data are shown as points with error bars, the background obtained from same-sign data is shown in red (dark shading), to which the expectation from Z →e + e − simulation is added in yellow (light shading).The simulated distribution is normalised to the background-subtracted data.The τ + τ − background is also included (green), though barely visible.The dashed line indicates the threshold applied in the event selection.The small plot at the top shows the pulls (i.e.deviations divided by statistical uncertainties) between the data and the expectation.

Figure 3 :Figure 4 :Figure 5 :
Figure 3: Measured cross-section for Z → e + e − shown as the shaded band, with the inner (orange) band indicating the statistical error and the outer (yellow) band the total uncertainty.For comparison, the NNLO predictions of Fewz are shown using five different sets of PDFs.The uncertainties on these predictions include the PDF uncertainties and the variation of the factorisation and normalisation scales, as well as the errors arising from numerical integration.

Table 1 :
Efficiencies and other factors used for the cross-section determination (see Eq. (

Table 3 :
Differential cross-section for Z → e + e − as a function of φ * .The first error is statistical, the second the uncorrelated experimental systematic, the third the correlated experimental systematic and the last error is the uncertainty in luminosity.The cross-sections are at the Born level, i.e. before FSR.The rightmost column gives values of the additional factor, f FSR , by which the results should be multiplied in order to give the cross-sections after FSR.

Table 5 :
Correlation matrix between bins of φ * .The bin numbering follows the same sequence as Table 3. Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil b P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia c Università di Bari, Bari, Italy d Università di Bologna, Bologna, Italy e Università di Cagliari, Cagliari, Italy f Università di Ferrara, Ferrara, Italy g Università di Firenze, Firenze, Italy h Università di Urbino, Urbino, Italy i Università di Modena e Reggio Emilia, Modena, Italy j Università di Genova, Genova, Italy k Università di Milano Bicocca, Milano, Italy l Università di Roma Tor Vergata, Roma, Italy m Università di Roma La Sapienza, Roma, Italy n Università della Basilicata, Potenza, Italy o AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland p LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain q Hanoi University of Science, Hanoi, Viet Nam r Università di Padova, Padova, Italy s Università di Pisa, Pisa, Italy t Scuola Normale Superiore, Pisa, Italy a u Università degli Studi di Milano, Milano, Italy v Politecnico di Milano, Milano, Italy