Measurement of the Z boson production cross-section in pp collisions at √ s = 5 . 02 TeV

The first measurement of the Z boson production cross-section at centre-of-mass energy √ s = 5 . 02 TeV in the forward region is reported, using pp collision data collected by the LHCb experiment in year 2017, corresponding to an integrated luminosity of 100 ± 2 pb − 1 . The production cross-section is measured for final-state muons in the pseudorapidity range 2 . 0 < η < 4 . 5 with transverse momentum p T > 20 GeV/ c . The integrated cross-section is determined to be σ Z → µ + µ − = 39 . 6 ± 0 . 7 (stat) ± 0 . 6 (syst) ± 0 . 8 (lumi) pb for the di-muon invariant mass in the range 60 < M µµ < 120 GeV/ c 2 . This result and the differential cross-section results are in good agreement with theoretical predictions at next-to-next-to-leading order in the strong coupling constant. Based on a previous LHCb measurement of the Z boson production cross-section in p Pb collisions at √ s NN = 5 . 02 TeV, the nuclear modification factor R p Pb is measured for the first time at this energy. The measured values are 1 . 2 +0 . 5 − 0 . 3 (stat) ± 0 . 1 (syst) in the forward region (1 . 53 < y ∗ µ < 4 . 03) and 3 . 6 +1 . 6 − 0 . 9 (stat) ± 0 . 2 (syst) in the backward region ( − 4 . 97 < y ∗ µ < − 2 . 47), where y ∗ µ represents the muon rapidity in the centre-of-mass frame.


Introduction
The pp → Z → µ + µ − process1 is highly interesting for probing the quantum chromodynamics (QCD) and electroweak (EW) sectors.Particularly, precision measurements of the Z boson production cross-section at various experiments offer valuable insights for testing Standard Model predictions [1][2][3][4][5][6][7][8][9], which are obtained from precision perturbative QCD calculations up to the order of α 3 s [8,9].High precision measurements of the Z boson production cross-sections at different rapidities at LHCb have imposed important constraints on parton distribution functions (PDFs).Results from deep inelastic scattering and hadronic collisions [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], parameterized in terms of the Bjorken variable, x, indicating the fraction of the proton momentum carried by a single parton, are used in the global fits of the PDFs.However, these measurements provide limited information on the PDFs in the very large (x ∼ 0.8) or very small (x ∼ 10 −4 ) Bjorken-x regions.This leads to large uncertainties on the PDFs, and on the theoretical predictions that make use of them.Forward acceptance of the LHCb detector covers a unique region of phase space, allowing measurements of highly boosted Z boson candidates to be made.Measurements within this region are sensitive to both large and small Bjorken-x values.Previous measurements of single W and Z production by the LHCb collaboration [26][27][28][29][30][31][32] have been included in PDF determinations [33][34][35][36][37][38][39][40][41] and significantly contributed to the precision of the quark PDFs at large and small values of x.
In addition, the Z boson production cross-section is useful for constraining nuclear PDFs (nPDFs), providing a clean probe of nuclear-matter effects in the initial state.These effects are typically studied in terms of the nuclear modification factor, R pPb , defined as the ratio of the yield observed in pPb collisions to that in pp collisions, scaled by the mean number of nucleon-nucleon interactions.This quantity is used to study the modification of particle production in heavy-ion collisions compared to pp collisions.The LHCb experiment published the first inclusive Z production result in pPb collisions at a nucleon-nucleon centre-of-mass energy of √ s N N = 5.02 TeV [42].However, no nuclear modification factor has been reported so far for this collision energy due to the absence of a cross-section measurement in pp collisions.With this new measurement of the Z boson production cross-section in pp collisions at √ s = 5.02 TeV, the nuclear modification factors in the forward region and backward regions are reported here for the first time.The forward and backward regions, defined by the muon rapidity y * µ in the pPb centre-of-mass frame, are 1.53 < y * µ < 4.03 and −4.97 < y * µ < −2.47, as the pPb collision system experiences an asymmetric distribution of beam energy.
In this article, the integrated and differential Z boson production cross-sections in different kinematic bins are measured at the Born level in QED, using pp collision data collected by the LHCb detector at a centre-of-mass energy of √ s = 5.02 TeV in 2017, corresponding to an integrated luminosity of 100 pb −1 [43].The production cross-sections are measured in a fiducial region that closely matches the acceptance of the LHCb detector, following the analysis strategy developed in Ref. [32].The fiducial region is defined by requiring that both muons have a pseudorapidity in the range of 2.0 < η < 4.5 and transverse momentum p T > 20 GeV/c, and that the di-muon invariant mass is in the interval 60 < M µµ < 120 GeV/c 2 .

Detector and simulation
The LHCb detector [45,46] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of hadrons containing b or c quarks.The detector includes a high-precision tracking system consisting of a siliconstrip vertex detector surrounding the pp interaction region [47], a large-area silicon-strip detector (TT) [48], 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 [49] placed downstream of the magnet.The tracking system provides a measurement of the momentum, p, of charged particles with a relative resolution that varies from 0.5 % at low momentum to 1.0 % at 200 GeV/c.The minimum distance of a track to a primary pp collision vertex, the impact parameter, is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of the momentum transverse to the beam, in GeV/c.Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic and a hadronic calorimeter.Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [50].The online event selection is performed by a trigger [51], which 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.
Simulation is used to model the effects of the detector acceptance and the imposed selection requirements.In the simulation, pp collisions are generated using Pythia [52,53] with a specific LHCb configuration [54].Final state radiation (FSR) is generated using Photos [55].The interactions of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [56] as described in Ref. [57].
In this paper, three generators are used to calculate the theoretical predictions.The ResBos [63] program performs resummation of large logarithms, achieving accuracy up to the next-to-next-to-leading-logarithm level, within the Collins-Soper-Sterman resummation formalism [65][66][67] and matches to next-to-leading-order (NLO) fixed order calculations.It also provides theoretical predictions for processes involving FSR corrections and event generation.The enhanced QCD prediction is obtained from the simulated Z → µ + µ − sample, generated with ResBos [63] using the CT18 PDFs [36] for all measurements.Powheg-BOX [68][69][70][71] is an NLO generator, and can be interfaced with Pythia for QCD and EW showering.Although Pythia is a leading-order (LO) generator, it approximates higher order effects in initial and final states via a parton showering algorithm [72].In this analysis, Powheg-BOX is used to generate Z → µ + µ − events, followed by hadronization using Pythia for all measurements.The MCFM package [58], a fixed-order next-tonext-to-leading-order (NNLO) generator, is used here to estimate the Z boson production cross-section as a function of y Z in the acceptance of the LHCb detector.For these three generators, different PDFs sets NNPDF3.1 [37], NNPDF4.0 [38], MSHT20 [39], and CT18 [36] are employed to provide theoretical predictions.

Event selection and background estimation
The muon triggers are responsible for the online event selection.At the hardware trigger stage, a muon candidate with high p T is required.The muon candidate is required to have p T > 6 GeV/c and p > 8 GeV/c, along with a good track fit quality in the first software trigger stage.In the second software trigger stage, an additional requirement of p T > 12.5 GeV/c is imposed on the muon candidate.For a Z → µ + µ − candidate, it is necessary for at least one of the muons to pass both the hardware and software trigger stages.
A high-purity Z → µ + µ − sample is reconstructed from a pair of opposite-signed tracks identified as muons.The invariant mass of the di-muon is required to be within the range 60 < M µµ < 120 GeV/c 2 .For each muon track, the fiducial requirements are p T > 20 GeV/c and pseudorapidity in the range 2.0 < η < 4.5.The muons are required to have momentum measurements with relative uncertainties below 10%.In total, 3265 Z → µ + µ − candidates meet these selection criteria, and the distribution of the di-muon invariant mass for the selected candidates is shown in Fig. 1.
The background contribution from decays of heavy-flavour hadrons is estimated using two control samples.These samples are used as two independent background determinations, which allow for cross-checking with each other.Tracks from heavyflavour decays degrade the primary vertex (PV) fit quality when included in the PV fit, since heavy-flavour hadrons travel a finite distance before decaying.Hence, the first control sample is obtained by applying a requirement that the selected candidate have a PV with a low fit quality (χ 2 > 95).Additionally, muons produced from semileptonic decays of heavy flavour hadrons are less isolated.The variable I µ is defined as the ratio of the muon p T to the vector sum of the p T of all charged particles in a cone of size R = (∆η) 2 + (∆ϕ) 2 < 0.5 around the muon.The second control sample is selected by requiring that the two muons are not spatially isolated (I µ < 0.91) from the rest of the event.
The yields of these two control samples are determined from a fit to the di-muon invariant mass distributions, using an exponential function.From the fitting results in Appendix A, it can be observed that statistical uncertainty is the primary source of uncertainty in this estimation.The heavy-flavour background is concentrated at low mass (50 < M µµ < 70 GeV/c 2 ), so to obtain a larger sample and a more stable fit, the background yield is determined in the region 50 < M µµ < 110 GeV/c 2 .The estimated background yield is corrected for the efficiency of vertex and isolation selections, and extrapolated to the signal region (60 < M µµ < 120 GeV/c 2 ).The efficiency of the muon isolation (vertex quality) selection is calculated separately by applying the muon isolation requirement (vertex quality requirement) to the first (second) control sample.The background contributions estimated using these two independent samples are consistent, and the average value is taken as the background contribution from the heavy flavour decay process, which is determined to be (2.0 ± 1.6) × 10 −2 for the selected Z → µ + µ − sample.
In summary, the total background contribution to the Z → µ + µ − sample in the mass range 60 < M µµ < 120 GeV/c 2 is determined to be (2.0 ± 1.6) × 10 −2 and the background composition of the candidate sample is summarised in Table 1.

Cross-section determination
Only single-differential cross-section measurements are performed due to the limited sample yields.The differential cross-section is measured as a function of y Z , p Z T and ϕ * η [44], which is defined as where ∆ϕ ℓℓ represents the difference in the azimuthal angle between the two muons in the laboratory frame.The variable θ * η is defined by cos(θ * η ) = tanh[(η − − η + )/2], with η − and η + denoting the pseudorapidities of the negatively and positively charged muons in the laboratory frame.The observable ϕ * η probes similar physics as the transverse momentum p Z T , but is measured with near-perfect resolution.
The integrated cross-section is obtained by integrating over all bins, which are chosen based on the detector resolution and sample size.The differential cross section in a generic variable a is defined as where the generic variable a represents the observable y Z , p Z T or ϕ * η , the index i indicates the bin of the variable under study, N Z (i) is the signal yield in bin i after background subtraction, f Z F SR (i) is the FSR correction factor (as discussed in Sec.4.3), L is the integrated luminosity, ∆a(i) is the bin width for the i-th bin (as presented in Tables 3 to 5 in Appendix B), and ε Z (i) is the total efficiency in the i-th bin.
To account for detector misalignment effects, the Z mass peak position and resolution in simulated events are corrected to be compatible with the data, using momentum scaling and smearing factors [59].The impact from this correction on the integrated cross-section measurement is found to be negligible.

Efficiency
The selection efficiencies are determined for the muon tracking, identification and trigger requirements.These are derived using the Z → µ + µ − data and a tag-and-probe method [60].
In the determination of the tracking efficiency, a particle reconstructed in all the tracking subdetectors, and fulfilling the muon trigger and muon identification requirements, is used as the tag.An object reconstructed by combining hits in the muon stations and the TT downstream tracking stations, denoted as a MuonTT track, then acts as the probe.As described in Ref. [60], the tracking efficiency is calculated as the fraction of probe candidates matched with a reconstructed track.However, the precision of the measured tracking efficiency is limited by the low number of Z boson candidates in the data sample.In this analysis, we therefore use the tracking efficiency ε MC, 5.02  Tracking found from the 5.02 TeV Z → µ + µ − simulation, and apply a correction to this using a scale factor determined using the tag-and-probe method in the 13 TeV analysis [32], as Tracking . ( The muon identification efficiency determination is affected by statistical fluctuations similarly to the tracking efficiency, and the same treatment is applied.
The efficiency of the muon trigger is determined with the tag-and-probe method, where a tag particle is chosen from a particle reconstructed in all tracking subdetectors, which must be identified and triggered as a muon.The probe particle must pass all selection requirements used in the analysis apart from the trigger requirements.The invariant mass of tag and probe particles is further required to be within the range [60,120] GeV/c 2 , and the azimuthal separation, |∆ϕ|, greater than 2.7 radians.The efficiency is computed as the ratio of the number of probes meeting the muon trigger criteria to the total number of probes.
After correcting the muon tracking efficiency using Eq. 3 and applying this correction method to the muon identification efficiency in a similar way, the determined muon tracking reconstruction efficiency ε µ ± Track , identification efficiency ε µ ± ID and trigger efficiency ε µ ± Trig vary between 94% and 98%, 90% and 97%, 62% and 85% respectively.The efficiencies measured as a function of muon pseudorapidity are presented in Appendix C.This measurement follows the efficiency correction method employed in the 13 TeV analysis [32], which involved a one-dimensional efficiency correction based solely on the muon pseudorapidity.To investigate whether any additional dependencies of efficiencies were overlooked or if the results could be entirely attributed to the 1-D correction, a so-called closure test was performed: the number of reconstructed events in simulation is corrected using the efficiencies determined in simulation, then compared to the true number of events for each of the differential distributions.The differences between this correction method and the true information from the simulation is considered as a source of systematic uncertainty (as discussed in Sec. 5).
The Z event selection efficiency is derived from the muon efficiencies

Bin migration correction
The detector resolution causes migration between kinematic bins.Due to the good angular resolution of the LHCb detector, negligible migration effects are observed among y Z and ϕ * η bins.Hence, it is unnecessary to correct for migration effects on the number of events in each bin of y Z and ϕ * η for the cross-section measurement.To assess the necessity of correcting the p Z T measurement for bin migrations at the reconstruction level, the ratio of the p Z T distribution before and after applying a Bayesian unfolding procedure [61,62] is calculated from data.This ratio is then compared to the ratio of the reconstructed to the generated p Z T distribution obtained from the simulated sample.As noticeable migration is detected, corrections for migration effects on the p Z T distribution are implemented using the Bayesian unfolding approach mentioned earlier.

Final state radiation correction
The measured cross-section is corrected to the Born level in QED, so that it can be directly compared with theoretical predictions.The final-state radiation (FSR) correction is developed and applied to the measurements, by comparing the ResBos [63] predictions with and without the implementation of Photos [55], which corrects the quantities of muons after final state radiation to the Born level.The FSR corrections in bins of y Z , p Z T and ϕ * η are shown in Fig. 2. The corrections for single-differential cross-section measurements are also presented in Appendix B.

Systematic uncertainties
The systematic uncertainties considered in the present measurement include the background estimation, the calibration of the momentum scale, the efficiency determination, the bin migration correction, the results of efficiency closure tests, the FSR correction, and the measurement of the integrated luminosity.
The determination of the heavy flavour background uses the averaged yield between two methods as the background contribution.The associated uncertainty is calculated as the discrepancy between the background yields obtained from the two control samples.Additionally, a systematic uncertainty is introduced by varying the mass region and selection requirements of the control samples.The hadron misidentification and other backgrounds are estimated from the data and simulation, with the statistical uncertainties being treated as systematic uncertainties that depend on the limited size of the same-sign data and simulation samples.The systematic uncertainties on the tt, W + W − , W ± Z, ZZ, and Z → τ + τ − components derive from the statistical uncertainties and theoretical uncertainties on the LO to NNLO correction factors.To estimate the uncertainty due to inadequate calibration of the detector, the momentum scaling and smearing correction for the simulation are studied in order to improve the modeling of the Z → µ + µ − data.Only a small fraction, less than 0.01% of events, exhibits changes when comparing the simulation before and after studying the momentum scaling and smearing.This value is conservatively assigned as the systematic uncertainty related to the detector alignment.The impact from momentum calibration uncertainty on the integrated cross-section measurement is found to be negligible.However, the alignment uncertainty is considered and added for the p Z T distribution.The track reconstruction and identification efficiencies for high p T muons are calculated using simulation and data taking at √ s = 13 TeV.The systematic uncertainties are determined by the size of the 5.02 TeV simulation samples and the uncertainties are propagated from the 13 TeV results.For the trigger efficiency, which is directly measured using control samples in the 5.02 TeV data, a systematic uncertainty is assigned for variations due to the limited size of the samples studied.As studied in Ref. [32], an additional systematic uncertainty is evaluated, based on the method used to determine the tracking efficiency.This is evaluated to be 0.47% which is already considered in the systematic uncertainty of the muon tracking efficiency.
To examine whether it is sufficient to perform efficiency corrections only as a function of the muon pseudorapidity variable or if the efficiency also depends on other variables such as muon p T , a closure test is performed.The reconstructed event yields in simulation are adjusted using the efficiencies determined solely based on the muon pseudorapidity obtained from the simulation samples and then compared with the generated yield.The differences, which do not exhibit any systematic pattern across the differential cross-section measurement regions, are attributed as an additional source of uncertainty.
To estimate the uncertainty attributed to the bin migration correction, the p Z T distribution is unfolded using the so-called Invert Approach [64], which employs a simple inversion of the response matrix without regularisation.The deviation of the results from the Bayesian Approach [61,62] is taken as a systematic uncertainty on the p Z T differential cross-section.The systematic uncertainty arising from the FSR correction is evaluated by comparing the default correction with one determined using the Powheg generator showered using Pythia.The differences in FSR corrections between ResBos with Photos and Powheg with Pythia are then taken into consideration as a systematic uncertainty.Regarding the data sample used, the luminosity is determined with a precision of 2.0% [43], which is quoted separately to the other sources of systematic uncertainty.The statistical and systematic uncertainties in the integrated cross-section measurement are listed in Table 2.The different sources of systematic uncertainty for each bin of the differential cross-sections are summarised in Tables 7 to 9 in Appendix D.

Differential cross-section results
The single differential cross-sections in regions of y Z , p Z T and ϕ * η are shown in Fig. 3, together with the ratios of theoretical predictions to data.The numerical results of single differential cross-section within each bin are summarised in  in Appendix E.
Measurements are in reasonable agreement with the different theoretical predictions.In both the lower and higher p Z T and ϕ * η region, the measurements agree with predictions from both ResBos and Powheg.For the measurement of y Z , the theoretical predictions from the three generators are also compatible with the experimental results within the uncertainty range.

Correlation matrices
The event migration between bins causes statistical correlations, which are determined using simulation.Large correlations are found in the low-p Z T region and small correlations in the high-p Z T region, while the statistical correlations are negligible for both the y Z and ϕ * η distributions.
For the differential cross-section measurements, background, alignment, efficiency closure test, and FSR uncertainties are assumed to be 50% correlated between different bins, while the luminosity uncertainty is considered to be 100% correlated.The calculated correlation matrices for the efficiencies are presented in Appendix F. Large correlations between different bins are present in the p Z T differential cross-section measurement, but small correlations are also present between most bins for the y Z and ϕ * η measurements.

Integrated cross-section results
Using the LHCb 2017 pp collision data at √ s = 5.02 TeV, the integrated Born-level Z boson production cross-section, with two muons in the final state and within the LHCb acceptance is σ Z→µ + µ − = 39.6 ± 0.7 (stat) ± 0.6 (syst) ± 0.8 (lumi) pb (5) where the uncertainties are due to statistical effects, systematic effects, and the luminosity measurement, respectively.In this article, the Z boson is defined to also include contributions from virtual photons, and the interference between them since they cannot be distinguished experimentally.The measured results obtained for the total cross-section of the pp → Z → µ + µ − process at 5.02 TeV in the fiducial region of the LHCb detector have been compared to the predictions obtained using MCFM with CT18NNLO and other theoretical models, including Powheg-Box with NNPDF3.1,NNPDF4.0,MSHT20, CT18, and ResBos with CT18, all of which account for both statistical and PDF uncertainties.These theoretical predictions are compared to the results in Fig. 4, which demonstrate a reasonable agreement.
By comparing the theoretical predictions at different center-of-mass energies provided by MCFM, with the experimental measurements previously obtained by LHCb at √ s = 7, 8 and 13 TeV, as illustrated in Fig. 5, a good level of consistency can be observed overall.

Nuclear modification factors
The nuclear modification factors are determined based on the present measurements and those in Ref. [42].Here, the statistical and systematic uncertainties (including uncertainties due to integrated luminosity) of the cross-sections measured between pp and pPb collisions are assumed to be fully uncorrelated when being propagated to the nuclear modification factors.Efficiency and background modeling uncertainties are also treated as fully uncorrelated, owing to the very different running conditions between pp and pPb collisions such as the heavier detector contamination from the higher charged hadron multiplicities in case of pPb.All other sources of systematic uncertainty are considered to be uncorrelated, an assumption that has negligible effect to the reported results.
The unique forward geometry coverage allows the LHCb detector to probe nPDFs at very small Bjorken-x (10 −4 < x < 10 −3 ).The nuclear modification factors can be calculated using the pp cross-section measured here together with the Z boson production cross-section in pPb collisions measured in Ref. [42].The nuclear modification factors are defined as the ratio of the Z boson production cross-sections between pPb and pp collisions under the same muon rapidity acceptance.Due to the asymmetric beam energy in the pPb centre-of-mass frame, the muon rapidity acceptance (2.0 < η < 4.5) becomes 1.53 < y * µ < 4.03 in case of the forward collisions, and −4.97 < y * µ < −2.47 in case of backward collisions, where y * µ represents the muon rapidity in the centre-of-mass frame.The two rapidity quantities are identical in pp collisions, η µ ≡ y * µ , due to the symmetric beam energy.Forward collisions refer to the proton beam entering the LHCb detector along the positive direction of the z axis, while backward collisions correspond to the proton beam going in the opposite direction.
The cross-sections of the pPb collisions measured under different rapidity acceptances need to be corrected before being used to calculate the nuclear modification factors.The k pPb factor corrects for the different η acceptance between pPb and pp collisions and can be calculated using Powheg with the proton PDF set CTEQ6.1 [73], and for forward and backward collisions, respectively.The integrated nuclear modification factors can then be defined as follows and for forward and backwards pPb collisions, respectively, with 208 being the number of binary nucleon-nucleon collisions in pPb collisions.The quantity σ (pPb, 1.53<y * µ <4.03) is measured to be 13.5 +5.4  −4.0 (stat) ± 1.2 (syst) nb, and σ (pPb, −4.97<y * µ <−2.47) is measured to be 10.7 +8.4  −5.1 (stat) ± 1.0 (syst) nb [42].
The nuclear modification factors are calculated to be for the forward collisions, and for the backward collisions.The large statistical uncertainties are due to the small size of the pPb data sample.
pP b = 0.929 +0.011 −0.028 for the forward and backward collisions, respectively.The measurement and theoretical prediction agree within the uncertainties in the forward region, whereas a 2.86 σ tension between the measured result and the prediction is seen in the backward region.However, due to the limited size of the pPb sample, the tension could be caused by a statistical fluctuation.

Conclusion
This paper reports the first measurement of Z boson production cross-section at the centreof-mass energy √ s = 5.02 TeV, using the LHCb pp collision dataset collected in 2017.The techniques employed in this analysis closely follow those established in a previous LHCb Run 2 analysis [32].The results show reasonable agreement with various predictions in the Standard Model.Combining this measurement with the previous inclusive Z production result in pPb collisions at √ s N N = 5.02 TeV [42] the nuclear modification factors in the forward and backward regions are obtained for the first time.

Appendices A Invariant mass fitting results for background
To estimate the signal yield for heavy-flavour background-dominated samples, an exponential function is used to fit the dimuon invariant mass distributions in the region of 50 − 110 GeV/c 2 , using a binned likelihood method.The distribution of selected candidates and fitted results are shown in Fig. 6.The fit result is then extrapolated to determine the background contribution in the mass region of 60 − 120 GeV/c 2 .

B Final state radiation corrections
Tabulated results of final state radiation corrections used in the single differential crosssection measurements are presented in Tables 3 to 5.

C Efficiency
Results of muon efficiencies used in the total Z boson efficiency calculation are presented in Fig. 7 and Table 6.

D Summary of systematic uncertainties
The summarised systematic uncertainties for single differential cross-sections are shown in Tables 7 to 9.

E Numerical results of single differential crosssections
The measured single differential cross-sections in bins of y Z , p Z T and ϕ * η are presented in Tables 10 to 12.

Figure 1 :
Figure 1: Mass distribution of the Z → µ + µ − signal candidates.The data are overlaid with model of the signal and background models.The signal component is scaled such that the sum of the signal and background matches the integral of the data.

Figure 2 :
Figure 2: Final state radiation correction estimated for the (top-left) y Z , (top-right) p Z T , and (bottom) ϕ * η differential cross-section measurements.The error bars represent the total (statistical and systematic) uncertainties.

Figure 3 :
Figure 3: (Left) Measured single differential cross-section as a function of y Z , p Z T and ϕ * η compared with different theoretical predictions.(Right) Ratio of theoretical predictions to measured values, with the horizontal bars showing the uncertainty from the PDFs.The green band, centered at unity, shows the uncertainty of the measurement.

Figure 4 :
Figure 4: Comparison of the integrated cross-section, σ Z→µ + µ − , between data and theoretical predictions.The bands correspond to the data, with the inner band corresponding to the statistical uncertainty and the outer bands corresponding to the systematic uncertainty and total uncertainty.

Figure 5 :
Figure 5: Measured σ Z→µ + µ − for pp collisions, as a function of √ s.The uncertainty on the data is smaller than the marker size.The data are overlaid with a curve showing the theoretical prediction.

Figure 6 :
Figure 6: Invariant mass distributions of heavy-flavour samples with (left) PV fit quality χ 2 > 95 and (right) I µ < 91% applied to both muons.Only statistical uncertainties are shown.

Figure 7 :
Figure 7: Muon tracking, identification and trigger efficiency as a function of pseudorapidity, estimated from the data and simulation at 5.02 TeV and 13 TeV.

Figure 8 :Table 13 :
Figure 8: Statistical correlation matrices for the differential cross-section measurements as functions of (top-left) y Z , (top-right) p Z T and (bottom) ϕ * η .

Figure 9 :
Figure 9: Correlation matrices for the efficiency uncertainties as functions of (top-left) y Z , (top-right) p Z T and (bottom) ϕ * η .

Table 1 :
Summary of the background composition in the Z → µ + µ − data sample of candidates satisfying the signal selection.

Table 2 :
The uncertainties for the integrated Z → µ + µ − cross-section measurement.

Table 3 :
Final state radiation correction used in the y Z cross-section measurement.The first uncertainty is statistical and the second is systematic.

Table 4 :
Final state radiation correction used in the p Z T cross-section measurement.The first uncertainty is statistical and the second is systematic.

Table 5 :
Final state radiation correction used in the ϕ * η cross-section measurement.The first uncertainty is statistical and the second is systematic.

Table 6 :
The muon tracking, muon identification and trigger efficiency in each pseudorapidity bin.

Table 7 :
Systematic uncertainties on the single differential cross-sections in bins of y Z , presented in percentage.

Table 8 :
Systematic uncertainties on the single differential cross-sections in bins of p Z

Table 9 :
Systematic uncertainties on the single differential cross-sections in bins of ϕ * η , presented in percentage.

Table 10 :
Measured single differential cross-sections in bins of y Z .The first uncertainty is statistical, the second systematic, and the third is from the uncertainty on the integrated luminosity.

Table 11 :
Measured single differential cross-sections in bins of p Z T .The first uncertainty is statistical, the second systematic, and the third is due to the luminosity.

Table 12 :
Measured single differential cross-sections in bins of ϕ * η .The first uncertainty is statistical, the second systematic, and the third is due to the luminosity.

Table 14 :
Statistical correlation matrix for the one-dimensional p Z

Table 15 :
Statistical correlation matrix for the one-dimensional ϕ * η measurement.

Table 17 :
Correlation matrix for the efficiency uncertainty of the one-dimensional p Z T measurement.