EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-301 LHCb-PAPER-2015-049

Measurement of forward $W$ and $Z$ boson production in $pp$ collisions

at $\sqrt{s}=8\mathrm{\,Te\kern-2.07413ptV}$

The LHCb collaboration†††Authors are listed at the end of this paper.

Measurements are presented of electroweak boson production using data from
$pp$ collisions at a centre-of-mass energy of
$\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$. The analysis is based on an
integrated luminosity of $2.0\mathrm{\,fb}^{-1}$ recorded with the LHCb
detector. The bosons are identified in the $W\rightarrow\mu\nu$ and
$Z\rightarrow\mu^{+}\mu^{-}$ decay channels. The cross-sections are measured
for muons in the pseudorapidity range $2.0<\eta<4.5$, with transverse momenta
$p_{\rm T}>20{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and, in the case of the $Z$
boson, a dimuon mass within
$60<M_{\mu^{+}\mu^{-}}<120{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The
results are

$\displaystyle\sigma_{W^{+}\rightarrow\mu^{+}\nu}$ $\displaystyle=1093.6\pm
2.1\pm 7.2\pm 10.9\pm 12.7{\rm\,pb}\,,$
$\displaystyle\sigma_{W^{-}\rightarrow\mu^{-}\overline{\nu}}$
$\displaystyle=\phantom{0}818.4\pm 1.9\pm
5.0\pm\phantom{0}7.0\pm\phantom{0}9.5{\rm\,pb}\,,$
$\displaystyle\sigma_{Z\rightarrow\mu^{+}\mu^{-}}$
$\displaystyle=\phantom{00}95.0\pm 0.3\pm
0.7\pm\phantom{0}1.1\pm\phantom{0}1.1{\rm\,pb}\,,$

where the first uncertainties are statistical, the second are systematic, the
third are due to the knowledge of the LHC beam energy and the fourth are due
to the luminosity determination. The evolution of the $W$ and $Z$ boson cross-
sections with centre-of-mass energy is studied using previously reported
measurements with $1.0\mathrm{\,fb}^{-1}$ of data at
$7\mathrm{\,Te\kern-1.00006ptV}$. Differential distributions are also
presented. Results are in good agreement with theoretical predictions at next-
to-next-to-leading order in perturbative quantum chromodynamics.

Published in JHEP 01 (2016) 155

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

Measurements of $W$ and $Z$ boson production cross-sections at hadron
colliders constitute important tests of the Standard Model (SM).111Throughout
this article $Z$ is used to denote the ${Z}/\gamma^{*}$ contributions.
Theoretical predictions for these cross-sections are available at next-to-
next-to-leading order (NNLO) in perturbative quantum chromodynamics [1, 2, 3,
4, 5]. The dominant uncertainty on these predictions reflects the
uncertainties on the parton density functions (PDFs). The forward acceptance
of the LHCb detector allows the PDFs to be constrained at Bjorken-$x$ values
down to $10^{-4}$ [6]. Ratios of the $W$ and $Z$ cross-sections provide
precise tests of the SM as the sensitivity to the PDFs in the theoretical
calculations is reduced and many of the experimental uncertainties cancel.

During LHC Run 1, data were collected at centre-of-mass energies, $\sqrt{s}$,
of 7$\mathrm{\,Te\kern-1.00006ptV}$ and 8$\mathrm{\,Te\kern-1.00006ptV}$,
providing two distinct samples for measurements of the electroweak boson
production cross-sections. The evolution of the cross-sections, and cross-
section ratios, may be used to infer the existence of physics beyond the
Standard Model (BSM) [7].

LHCb has measured the $W$ boson production cross-section at $\sqrt{s}$ =
7$\mathrm{\,Te\kern-1.00006ptV}$ using the muon channel [8], and that of $Z$
bosons decaying to muon [9], electron [10] and tau lepton [11] pairs, using a
data set of 1.0$\mbox{\,fb}^{-1}$. The $Z$ boson production cross-section at
$\sqrt{s}$ = 8$\mathrm{\,Te\kern-1.00006ptV}$ has also been measured using
decays to electron pairs [12]. Similar measurements have also been performed
by the ATLAS [13] and CMS [14, 15, 16] collaborations, although in different
kinematic regions.

The measurements of inclusive $W$ and $Z$ boson cross-sections at $\sqrt{s}$ =
8$\mathrm{\,Te\kern-1.00006ptV}$ described here are performed following the
same procedure as detailed in Refs. [8, 9]. The cross-sections are defined for
muons with transverse momentum $\mbox{$p_{\rm
T}$}>20{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and pseudorapidity in the range
$2.0<\eta<4.5$. In the case of the $Z$ boson measurements, the invariant mass
of the two muons is required to be in the range
$60<M_{\mu\mu}<120{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. These kinematic
requirements define the fiducial region of the measurement and are referred to
as the fiducial requirements in this article. Total cross-sections are
presented, as well as differential cross-sections as functions of $\eta$ of
the muons, and of the $Z$ boson rapidity, $y_{{Z}}$, transverse momentum,
$p_{\textrm{T},{Z}}$, and $\phi^{*}_{\eta}$ [17]. Here $\phi^{*}_{\eta}$ is
defined as222The $\phi^{*}_{\eta}$ definition in this article is equivalent to
the definitions in Refs. [9, 10, 12].

$\phi^{*}_{\eta}\equiv\frac{\tan{(\phi_{\rm
acop}/2)}}{\cosh{(\Delta\eta}/2)}\,,$ (1)

where the angle $\phi_{\rm acop}=\pi-|\Delta\phi|$ depends on the difference
$\Delta\phi$ in azimuthal angle between the two muon momenta, while the
difference between their pseudorapidities is denoted by $\Delta\eta$.
Differential cross-section ratios and the muon charge asymmetry, arising from
the W production charge asymmetry, are also determined as a function of the
muon pseudorapidity.

This article is organised as follows: Section 2 describes the LHCb detector;
Section 3 details the selection of $W$ and $Z$ boson candidate samples;
Section 4 defines the $W$ and $Z$ boson cross-sections and summarises the
relevant sources of systematic uncertainty, as well as their estimation;
Section 5 presents the results and Section 6 concludes the article. Appendices
A and B provide tables of differential cross-sections and correlations between
these measurements.

##  2 Detector and data set

The LHCb detector [18, 19] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, 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 $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream of the
magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex, the impact parameter (IP), is
measured with a resolution of $(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm m}$,
where $p_{\rm T}$ is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of a scintillating-pad detector (SPD), preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers. The online event selection is performed by a trigger [20], 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. A requirement that prevents events with high occupancy from
dominating the processing time of the software trigger is also applied. This
is referred to in this article as the global event cut (GEC).

The measurements presented here are based on $pp$ collision data collected at
a centre-of-mass energy of 8$\mathrm{\,Te\kern-1.00006ptV}$, the integrated
luminosity amounting to $1978\pm 23\mbox{\,pb}^{-1}$. The absolute luminosity
scale was measured during dedicated data-taking periods, using both van der
Meer scans [21] and beam-gas imaging methods [22]. Both methods give
consistent results, which are combined to give the final luminosity estimate
with an uncertainty of 1.16% [23].

Several samples of simulated events are produced to estimate contributions
from background processes, to verify efficiencies and to correct data for
detector-related effects. In the simulation, ${p}{p}$ collisions are generated
using Pythia 8 [24, 25] with a specific LHCb configuration [26]. Decays of
hadronic particles are described by EvtGen [27], in which final-state
radiation is generated using Photos [28]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [29, 30] as described in Ref. [31].

The $W$ boson yields are determined from fits to the data using signal
templates produced with the ResBos [32, 33, 34] generator configured with the
CT14 [35] PDF set. The ResBos generator includes an approximate NNLO
calculation, plus a next-to-next-to-leading logarithm approximation for the
resummation of the soft gluon radiation.

The results of the analysis are compared to theoretical predictions calculated
with the Fewz [36, 37] generator at NNLO for the PDF sets ABM12 [38], CT10
[39], CT14, HERA1.5 [40], MMHT14 [41] and NNPDF3.0 [42]. All calculations are
performed with the renormalisation and factorisation scales set to the
electroweak boson mass. Scale uncertainties are estimated by varying these
scales by factors of two around the boson mass [43]. Total uncertainties
correspond to those coming from the PDF and the strong force coupling
strength, $\alpha_{s}$, both at 68.3% confidence level (CL), added in
quadrature with the scale uncertainties.

##  3 Event yield

Events for this analysis must satisfy the selection criteria detailed in Refs.
[8, 9]. The trigger requires a single muon with $\mbox{$p_{\rm
T}$}>1.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ at the hardware stage, and
includes an upper threshold of 600 hits in the SPD to prevent high-particle
multiplicity events from dominating the processing time. A muon with
$\mbox{$p_{\rm T}$}>10{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ is required at the
software stage. In the offline analysis, particles are required to be well-
reconstructed, to be identified as muons, and also to pass the fiducial
requirements.

Additional selection criteria are applied to the $W$ boson candidates to
reduce the contributions of various sources of background. Muons from decays
of $W$ bosons are generally isolated from other particles. To define a degree
of isolation, a cone with radius $R=\sqrt{\Delta\eta^{2}+\Delta\phi^{2}}=0.5$
is constructed around the direction of the muon track. Excluding the candidate
muon momentum, requiring that there are small amounts of transverse momentum
($p_{\textrm{T}}^{\textrm{cone}}<2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$) and
transverse energy
($E_{\textrm{T}}^{\textrm{cone}}<2\mathrm{\,Ge\kern-1.00006ptV}$) in the cone
reduces background originating from generic QCD events. Requiring the
transverse momentum of all other muons in the event to be less than
2${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ reduces the contamination from
${Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}$ events. An upper limit on the IP of
40${\,\upmu\rm m}$ removes candidates in which the muon is not consistent with
originating from the primary vertex. Such candidates could be due to
electroweak boson decays to tau leptons, which in turn decay to muons, or
semileptonic decays of heavy flavour hadrons. Genuine muons are expected to
leave low-energy deposits in the electromagnetic and hadronic calorimeters. An
upper limit of 4% on the amount of energy that is deposited in the
calorimeters relative to the momentum of the track
($E_{\textrm{calo}}/\mbox{$p$}c$) reduces the background from energetic pions
and kaons punching through the calorimeters to the muon stations. A total of
$1\,733\,327$ ${W}\\!\rightarrow\mu{\nu}$ candidates are identified.

The $W^{\pm}$ sample purity ($\rho^{{W^{\pm}}}$), defined as the ratio of
signal to candidate event yield, is determined with a template fit to the
positively and negatively charged muon $p_{\rm T}$ distributions in eight bins
of muon pseudorapidity using the method of extended maximum likelihood. Only
muons with $p_{\rm T}$ smaller than 70${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
are considered. The $W^{\pm}$ boson signal and the
${Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}$ background templates are based on
distributions predicted by the ResBos generator. The
${Z}\,\\!\rightarrow{\tau^{+}}{\tau^{-}}$ and ${W}\\!\rightarrow\tau{\nu}$
templates are taken from Pythia 8 simulation. The overall fraction of the
electroweak background (${Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}$,
${Z}\,\\!\rightarrow{\tau^{+}}{\tau^{-}}$ and ${W}\\!\rightarrow\tau{\nu}$
decays) in the $W$ boson candidate sample is determined using a data-driven
method to be $(10.84\pm 0.21)\%$. A template for backgrounds due to
misidentified hadrons is taken from data using a sample of randomly triggered
pions and kaons that are weighted by their probability to be misidentified as
muons. This component is left free to vary in the fit, and is determined to
account for about 9.6% of the total candidates. Finally, a template of heavy-
flavour decays is obtained from data using muons with an IP of more than
100${\,\upmu\rm m}$. The fraction of this background is determined from a fit
to the muon IP distribution and is found to be $(1.31\pm 0.09)\%$ of the $W$
boson candidate sample. The momentum calibration for high-$p_{\rm T}$ muons is
performed using the data-driven technique outlined in Ref. [44]. A more
detailed description of the fit implementation is given in Ref. [8]. The fit
result in the full $\eta^{\mu}$ range is presented in Fig. 1 (left), where the
normalised residuals show an imperfect description of the data by the adopted
templates, similar to the 7$\mathrm{\,Te\kern-1.00006ptV}$ analysis. The
effect of this discrepancy on the signal yield is at the few per mille level.
The overall purities are $\rho^{{W^{+}}}=(78.91\pm 0.15)\%$ and
$\rho^{{W^{-}}}=(77.49\pm 0.18)\%$.

The invariant mass distribution of dimuon pairs passing the $Z$ candidate
requirements is shown in Fig. 1 (right). In total, $136\,702$
${Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}$ candidates are selected. The
background contamination is low. Five background sources are considered:
decays of heavy flavour hadrons, hadron misidentification,
${Z}\,\\!\rightarrow{\tau^{+}}{\tau^{-}}$ decays, ${t}{\overline{t}}$ and $W$
$W$ production. The largest sources of background are due to decays of heavy
flavour hadrons and hadron misidentification. These backgrounds are determined
from data using the techniques discussed in Ref. [9]. The heavy-flavour
background is estimated from a subset of the candidate sample by placing
additional requirements on muon isolation and dimuon vertex quality. The
background due to hadron misidentification is estimated using pairs of hadrons
from randomly triggered data. These are weighted by the momentum-dependent
probabilities for hadrons to be misidentified as muons. The other backgrounds
are determined using simulation and the purity is measured to be
$\rho^{Z}=(99.3\pm 0.2)\%$.

Figure 1: (left) Template fit to the (left panel) positive and (right panel)
negative muon $p_{\rm T}$ spectra in the full $\eta^{\mu}$ range for $W$
candidates. Data are compared to fitted contributions from
${W}\\!\rightarrow\mu{\nu}$ signal and QCD, electroweak and heavy flavour
backgrounds. (right) Invariant mass distribution of dimuon pairs in the $Z$
candidate sample.

##  4 Cross-section measurement

Cross-sections are determined in the specified kinematic ranges and are
corrected for quantum electrodynamic (QED) final-state radiation (FSR) in
order to compare measurements of electroweak boson production in different
decay modes and to provide a consistent comparison with next-to-leading order
and NNLO QCD predictions. No corrections are applied for initial-state
radiation or for electroweak effects and their interplay with QED effects.

The $W$ boson cross-sections are measured as a function of $\eta^{\mu}$ using
the equation

$\sigma_{{W^{\pm}}\rightarrow\mu^{\pm}\nu}(i)=\frac{\rho^{{W^{\pm}}}(i)}{\mathcal{L}}\cdot\frac{f_{\textrm{\mbox{{FSR}}}}^{{W^{\pm}}}(i)}{\varepsilon_{\textrm{\mbox{{GEC}}}}(i)}\cdot\frac{N^{{W^{\pm}}}(i)}{\varepsilon^{{W^{\pm}}}(i)\,\varepsilon_{\textrm{sel}}^{{W^{\pm}}}(i)\,\mathcal{A}^{{W^{\pm}}}(i)}\,,$
(2)

where all quantities except for the integrated luminosity, $\mathcal{L}$, are
determined in each bin $i$ of $\eta^{\mu}$. The number of observed $W^{\pm}$
boson candidates is denoted by $N^{{W^{\pm}}}(i)$. The correction factors for
QED final-state radiation are given by $f_{\textrm{\mbox{{FSR}}}}^{{W^{\pm}}}$
and the efficiency of the requirement on the number of SPD hits in the
hardware trigger is represented by $\varepsilon_{\textrm{\mbox{{GEC}}}}$. The
total muon reconstruction efficiency is denoted by $\varepsilon^{{W^{\pm}}}$
while the efficiency of the selection criteria is given by
$\varepsilon_{\textrm{sel}}^{{W^{\pm}}}$. The acceptance correction,
$\mathcal{A}^{{W^{\pm}}}$, accounts for the
70${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ experimental upper bound in the fit
to the muon $p_{\rm T}$.

The $Z$ boson cross-sections are measured in bins of $y_{{Z}}$,
$p_{\textrm{T},{Z}}$, $\phi^{*}_{\eta}$ and $\eta^{\mu}$, by integrating over
all but one of these variables. To account for bin migration effects, the
cross-section in bin $i$ is determined from the number of events in all bins
$j$ with an unfolding matrix $U$, as follows

$\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}(i)=\frac{\rho^{Z}}{\mathcal{L}}\cdot\frac{f_{\textrm{\mbox{{FSR}}}}^{{Z}}(i)}{\varepsilon_{\textrm{\mbox{{GEC}}}}(i)}\cdot\sum_{j}U(i,j)\left(\sum_{k}\frac{1}{\varepsilon^{Z}(\eta_{k}^{\mu^{+}},\eta_{k}^{\mu^{-}})}\right)_{j}\,.$
(3)

In this expression the index $k$ runs over all candidates contributing to bin
$j$ and $\varepsilon^{{Z}}$ is the pseudorapidity-dependent muon-
reconstruction efficiency for event $k$. The matrix $U$ is determined from
simulated data, as described in Section 4.6. The QED final-state radiation
corrections are denoted by $f_{\textrm{\mbox{{FSR}}}}^{Z}$. The components
that are common with the $W$ boson cross-sections defined in Eq. 2 are the
luminosity and the individual muon reconstruction efficiencies.

Although the beam energy does not enter in Eqs. 2 and 3, a related uncertainty
is assigned to all cross-sections. More details on these individual components
are given below.

###  4.1 Muon reconstruction efficiencies

The data are corrected for inefficiencies associated with track
reconstruction, muon identification, and trigger requirements. All
efficiencies are determined from data using the techniques detailed in Refs.
[8, 9], where the track reconstruction, muon identification, and muon trigger
efficiencies are obtained using tag-and-probe methods applied to the $Z$
candidates. The tag and the probe tracks are required to satisfy the fiducial
requirements. The tag must be identified as a muon and be consistent with
triggering the event, while the probe is defined so that it is unbiased with
respect to the requirement for which the efficiency is being measured. The
efficiency is studied as a function of several variables, which include both
the muon momenta and the detector occupancy. In this analysis, reconstruction,
identification and trigger efficiencies are applied as a function of the muon
pseudorapidity. The efficiency in each bin of $\eta^{\mu}$ is defined as the
fraction of tag-and-probe candidates where the probe satisfies the
corresponding track reconstruction, identification or trigger requirement. All
efficiencies are observed to be independent of the muon charge.

The tracking efficiency is determined using probe tracks that are
reconstructed by combining hits from the muon stations and the large-area
silicon-strip detector. The muon identification efficiency is determined using
probe tracks that are reconstructed without using the muon system. The single-
muon trigger efficiency is determined using reconstructed muons as probes.

###  4.2 GEC efficiency

The efficiency of the SPD multiplicity limit at 600 hits in the muon trigger
is evaluated from data using two independent methods. The first exploits the
fact that the SPD multiplicities of single $pp$ interactions involving a $Z$
boson are rarely above the 600 hit threshold. The expected SPD multiplicity
distribution of signal events is constructed by adding the multiplicities of
signal events in single $pp$ interactions to the multiplicities of randomly
triggered events, as in Ref. [45]. The convolution of the distributions
extends to values above 600 hits, and the fraction of events that the trigger
rejects can be determined. The second method consists of fitting the SPD
multiplicity distribution and extrapolating the fit function to determine the
fraction of events that are rejected, as in Ref. [9]. Both methods give
consistent results and $\varepsilon_{\textrm{\mbox{{GEC}}}}=(93.00\pm 0.32)\%$
is used in this analysis as the overall efficiency. This efficiency depends
linearly on $y_{{Z}}$ and $\eta^{\mu}$, with about 2% variation across the
full range. This is accounted for by applying a bin-dependent efficiency
correction.

###  4.3 Final-state radiation

The FSR correction is taken to be the mean of the corrections calculated with
Herwig++ [46] and Pythia 8\. The corrections are tabulated in Appendix A and
are about 2.5% on average.

###  4.4 Selection efficiencies

The efficiency of the additional selection requirements for the $W$ boson
candidate samples is evaluated using a sample of $Z$ bosons from data, where
one of the muons is excluded to mimic a ${W}\\!\rightarrow\mu{\nu}$ decay [8].
However, this introduces a bias because the $p_{\rm T}$ distribution of muons
from $Z$ bosons is harder than those from $W$ bosons. Simulation is used to
correct for this bias and for the fact that the $Z$ boson sample requires two
muons in the LHCb acceptance.

###  4.5 Acceptance

Only muons with $p_{\rm T}$ smaller than
70${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ are considered for the extraction of
the $W$ boson signal. A kinematic acceptance correction is required in order
to measure cross-sections without this restriction on muon $p_{\rm T}$. This
correction is evaluated using the ResBos simulated sample.

###  4.6 Unfolding the detector response

To correct for detector resolution effects, an unfolding is performed (matrix
$U$ of Eq. 3) using LHCb simulation and the RooUnfold [47] software package.
Only the $p_{\textrm{T},{Z}}$ and $\phi^{*}_{\eta}$ distributions are
unfolded. Since $y_{{Z}}$ and $\eta^{\mu}$ are well measured, no unfolding is
performed. The momentum resolution in the simulation is calibrated to the
data. The data are then unfolded using the iterative Bayesian approach
proposed in Ref. [48]. Other unfolding techniques [49, 50] give similar
results. Additionally, all unfolding methods are tested for model dependence
using underlying distributions from leading-order Pythia 8, leading-order
Herwig++, as well as next-to-leading order Powheg [51, 52, 53] showered with
both Pythia 8 and Herwig++ using the Powheg matching scheme. The corrections
are between 0.5–8.0$\%$ as a function of $p_{\textrm{T},{Z}}$, and between
0.1–7.0$\%$ as a function of $\phi^{*}_{\eta}$.

###  4.7 Systematic uncertainties

Sources of systematic uncertainty and their effects on the total cross-section
measurements from the $\sqrt{s}$ = 8$\mathrm{\,Te\kern-1.00006ptV}$ data set
are summarised in Table 1. The uncertainty due to the momentum correction is
negligible. Uncertainties from external input, e.g. the beam energy and
luminosity determinations, are quoted separately from the other contributions.

Table 1: Summary of the relative uncertainties on the $W^{+}$, $W^{-}$ and $Z$ boson cross-sections. Source | Uncertainty [%]
---|---
| $\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}$ | $\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}$ | $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}$
Statistical | $0.19$ | $0.23$ | $0.27$
Purity | $0.28$ | $0.21$ | $0.21$
Tracking | $0.26$ | $0.24$ | $0.48$
Identification | $0.11$ | $0.11$ | $0.21$
Trigger | $0.14$ | $0.13$ | $0.05$
GEC | $0.40$ | $0.41$ | $0.34$
Selection | $0.24$ | $0.24$ | —
Acceptance and FSR | $0.16$ | $0.14$ | $0.13$
Systematic | $0.65$ | $0.61$ | $0.67$
Beam energy | $1.00$ | $0.86$ | $1.15$
Luminosity | $1.16$ | $1.16$ | $1.16$
Total | $1.67$ | $1.59$ | $1.79$

For the $W$ boson samples, the systematic uncertainty on the purity is
estimated by considering different shapes and normalisations of the templates,
refitting, and summing in quadrature the largest observed deviation in the
results corresponding to each source [8]. The uncertainty on the ResBos signal
template shape includes the effects of the PDF, the factorisation scale and
the renormalisation scale. An alternative definition for the QCD background
template, potential mismodelling of the lepton $p_{\rm T}$ shape in Pythia for
events that contain jets, and the normalisations of the background templates
are accounted for with additional uncertainties. The total uncertainties on
the $W^{+}$ and $W^{-}$ integrated cross-sections from the sample purity are
0.28% and 0.21%. For the $Z$ boson sample, the systematic uncertainty on the
purity is determined by considering alternative definitions of the heavy-
flavour background samples, and by varying by their uncertainties the
probabilities for hadrons to be misidentified as muons. In addition, an
uncertainty accounting for the assumption that the purity is the same for all
variables and bins of the analysis is evaluated by comparing to cross-section
measurements using a binned purity, rather than a global one. The
uncertainties on the differential cross-section measurements due to variations
in purity are typically less than 1%.

The systematic uncertainty associated with the trigger, identification and
tracking efficiencies is determined by re-evaluating all cross-sections with
the values of the individual efficiencies increased or decreased by one
standard deviation. The full covariance matrix of the differential cross-
section measurements is evaluated in this way for each source of uncertainty.
The covariance matrices for each source are added and the diagonal elements of
the result determine the total systematic uncertainty due to reconstruction
efficiencies. The total uncertainties on the $W^{+}$, $W^{-}$ and $Z$ boson
integrated cross-sections due to reconstruction efficiencies are 0.32%, 0.29%
and 0.53%.

The GEC efficiency for events containing a $Z$ boson is
$\varepsilon_{\textrm{\mbox{{GEC}}}}^{Z}=(93.00\pm 0.32)\%$. Differences
between this efficiency and those for events containing a $W^{+}$ or $W^{-}$
boson are expected to be small, and are thus accounted for with additional
systematic uncertainties, as explained in Ref. [9]. The values used for the
measurements of $W$ boson cross-sections are
$\varepsilon_{\textrm{\mbox{{GEC}}}}^{W^{+}}=(93.00\pm 0.37)\%$ and
$\varepsilon_{\textrm{\mbox{{GEC}}}}^{W^{-}}=(93.00\pm 0.38)\%$.

The uncertainties due to $W$ boson selection efficiencies result in
uncertainties on the $W^{+}$ and $W^{-}$ integrated cross-sections of 0.24%
and 0.23%. These include the uncertainties that arise due to the difference in
$W$ and $Z$ boson muon $p_{\rm T}$ spectra and the correction that accounts
for the fact that two muons are required to be inside the LHCb acceptance in
the $Z$ boson data sample.

As an estimate of the uncertainty due to the acceptance correction, half the
difference between the corrections evaluated using the ResBos generators and
Pythia 8 is taken. This results in uncertainties on the $W^{+}$ and $W^{-}$
integrated cross-sections of 0.06% and 0.09%.

The systematic uncertainty on the FSR correction is the quadratic sum of two
components. The first is due to the statistical precision of the Pythia 8 and
Herwig++ estimates and the second is half of the difference between their
central values, where the latter dominates.

The measurements are specified at a ${p}{p}$ centre-of-mass energy of
$\sqrt{s}$ = 8$\mathrm{\,Te\kern-1.00006ptV}$. The beam energy, and
consequently the centre-of-mass energy, is known to 0.65% [54]. The
sensitivity of the cross-section to the centre-of-mass energy is studied with
the DYNNLO [55] generator at NNLO. Cross-sections are calculated at 1 TeV
intervals in centre-of-mass energy and a functional form for the cross-section
is determined from a spline interpolation. A 0.65% uncertainty on the centre-
of-mass energy induces relative uncertainties of 1.00%, 0.86% and 1.15% on the
expected $W^{+}$, $W^{-}$ and $Z$ cross-sections.

The uncertainty on the luminosity determination is 1.16% [23], which
represents the largest contribution to the total uncertainty.

##  5 Results

###  5.1 Cross-sections at $\sqrt{s}$ = 8 TeV

The measured cross-section as a function of muon pseudorapidity in $W$ boson
decays is shown in Fig. 2 (top). Good agreement with the predictions of the
Fewz generator, with six different PDF sets, is observed. Similar conclusions
can be drawn from the comparisons of $Z$ boson cross-section measurements with
predictions as a function of rapidity, as shown in Fig. 2 (bottom). All
differential cross-sections are detailed in Tables 4, 5, 6, 7 and 8 of
Appendix A.

Figure 2: (top) Differential $W^{+}$ and $W^{-}$ boson production cross-
section in bins of muon pseudorapidity. (bottom) Differential $Z$ boson
production cross-section in bins of boson rapidity. Measurements, represented
as bands, are compared to (markers, displaced horizontally for presentation)
NNLO predictions with different parameterisations of the PDFs.

The total cross-sections are measured to be

$\displaystyle\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}$
$\displaystyle=1093.6\pm 2.1\pm 7.2\pm 10.9\pm 12.7\rm\,pb\,,$
$\displaystyle\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}$
$\displaystyle=\phantom{0}818.4\pm 1.9\pm
5.0\pm\phantom{0}7.0\pm\phantom{0}9.5\rm\,pb\,,$
$\displaystyle\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}$
$\displaystyle=\phantom{00}95.0\pm 0.3\pm
0.7\pm\phantom{0}1.1\pm\phantom{0}1.1\rm\,pb\,,$

where the first uncertainties are statistical, the second are systematic, the
third are due to the knowledge of the LHC beam energy and the fourth are due
to the luminosity measurement. The agreement of the measurements with NNLO
predictions given by the Fewz generator configured with various PDF sets is
illustrated in Fig. 3. Two-dimensional plots of electroweak boson cross-
sections are shown in Fig. 4, where the ellipses correspond to 68.3% CL
coverage.

A best linear unbiased estimator [56] is used to combine the $Z$ boson
production cross-section at $\sqrt{s}$ = 8$\mathrm{\,Te\kern-1.00006ptV}$
measured with the muon and the electron [12] channels. The combined result is

$\sigma_{{Z}\rightarrow{\ell^{+}}{\ell^{-}}}=94.9\pm 0.2\pm 0.6\pm 1.1\pm
1.1\rm\,pb\,.$

Uncertainties due to the GEC, the LHC beam energy and the luminosity
measurement are assumed to be fully correlated, while the other uncertainties
are assumed to be uncorrelated.

Figure 3: Summary of the $W$ and $Z$ cross-sections. Measurements, represented
as bands, are compared to (markers) NNLO predictions with different
parameterisations of the PDFs.

Figure 4: Two-dimensional plots of electroweak boson cross-sections compared
to NNLO predictions for various parameterisations of the PDFs. The
uncertainties on the theoretical predictions correspond to the PDF uncertainty
only. All ellipses correspond to uncertainties at 68.3$\%$ CL.

###  5.2 Ratios of cross-sections at $\sqrt{s}$ = 8 TeV

The ratios of electroweak boson production cross-sections are defined as

$\displaystyle R_{{W^{\pm}}}$
$\displaystyle=\frac{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}}{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}}\,,$
(4) $\displaystyle R_{{W^{+}}{Z}}$
$\displaystyle=\frac{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}}{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}}\,,$
(5) $\displaystyle R_{{W^{-}}{Z}}$
$\displaystyle=\frac{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}}{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}}\,,$
(6) $\displaystyle R_{{W}{Z}}$
$\displaystyle=\frac{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}+\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}}{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}}\,,$
(7)

and the muon charge asymmetry as a function of the muon pseudorapidity is
defined as

$\displaystyle
A_{\mu}(\eta_{i})=\frac{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}(\eta_{i})-\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}(\eta_{i})}{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}(\eta_{i})+\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}(\eta_{i})}\,.$
(8)

The sources of uncertainties contributing to the determination of the ratios
are summarised in Table 2. With respect to the systematic uncertainties on the
cross-sections, many sources cancel or are reduced. The luminosity uncertainty
completely cancels in the ratios, as do the correlated components of the GEC
efficiency uncertainty. The trigger used to select both samples is identical
and most of the uncertainty on the determination of the trigger efficiency
cancels. The uncertainties on the tracking and muon identification
efficiencies partially cancel in the ratios of $W$ and $Z$ boson cross-
sections, as do the uncertainties due to the proton beam energies. The
uncertainties on the purities of the $W$ and $Z$ boson selections are
uncorrelated and the FSR uncertainties are taken to be uncorrelated. The
dominant uncertainties on the ratios are due to the purity and the size of the
samples. The correlation coefficients used in the uncertainty calculations are
given in Tables 15–21 in Appendix B.

Table 2: Summary of the relative uncertainties on the $R_{{W^{\pm}}}$, $R_{{W^{+}}{Z}}$, $R_{{W^{-}}{Z}}$ and $R_{{W}{Z}}$ cross-section ratios. Source | Uncertainty [%]
---|---
| $R_{{W^{\pm}}}$ | $R_{{W^{+}}{Z}}$ | $R_{{W^{-}}{Z}}$ | $R_{{W}{Z}}$
Statistical | $0.30$ | $0.33$ | $0.36$ | $0.31$
Purity | $0.25$ | $0.35$ | $0.30$ | $0.30$
Tracking | $0.05$ | $0.22$ | $0.24$ | $0.23$
Identification | $0.01$ | $0.11$ | $0.11$ | $0.11$
Trigger | $0.04$ | $0.10$ | $0.09$ | $0.09$
GEC | $0.13$ | $0.22$ | $0.23$ | $0.21$
Selection | $0.10$ | $0.24$ | $0.24$ | $0.23$
Acceptance and FSR | $0.21$ | $0.21$ | $0.19$ | $0.17$
Systematic | $0.37$ | $0.59$ | $0.56$ | $0.54$
Beam energy | $0.14$ | $0.15$ | $0.29$ | $0.21$
Total | $0.50$ | $0.69$ | $0.73$ | $0.66$

The $W$ boson cross-section ratio is measured as

$R_{{W^{\pm}}}=1.336\pm 0.004\pm 0.005\pm 0.002\,,$

where the first uncertainty is statistical, the second is systematic and the
third is due to the knowledge of the LHC beam energy. The $W$ to $Z$ boson
production ratios are found to be

$\displaystyle R_{{W^{+}}{Z}}$ $\displaystyle=11.51\pm 0.04\pm 0.07\pm
0.02\,,$ $\displaystyle R_{{W^{-}}{Z}}$ $\displaystyle=\phantom{0}8.62\pm
0.03\pm 0.05\pm 0.02\,,$ $\displaystyle R_{{W}{Z}}$ $\displaystyle=20.13\pm
0.06\pm 0.11\pm 0.04\,.$

These measurements, as well as their predictions, are displayed in Fig. 5. The
data are well described by all PDF sets. The $W^{+}$ to $W^{-}$ boson ratio,
the charged $W$ to $Z$ boson ratios, and the muon charge asymmetry are
determined differentially as a function of muon $\eta$, and displayed in Figs.
6 and 7. Good agreement between measured and predicted values is observed. All
differential results are listed in Tables 9, 10 and 11 of Appendix A.

Figure 5: Summary of the cross-section ratios. Measurements, represented as
bands, are compared to (markers) NNLO predictions with different
parameterisations of the PDFs.

Figure 6: (top) $W^{+}$ to $W^{-}$ cross-section ratio in bins of muon
pseudorapidity. (bottom) $W^{+}$ ($W^{-}$) to $Z$ cross-section ratio in bins
of $\mu^{+}$ ($\mu^{-}$) pseudorapidity. Measurements, represented as bands,
are compared to (markers, displaced horizontally for presentation) NNLO
predictions with different parameterisations of the PDFs. Figure 7: $W$
production charge asymmetry in bins of muon pseudorapidity. Measurements,
represented as bands, are compared to (markers, displaced horizontally for
presentation) NNLO predictions with different parameterisations of the PDFs.

###  5.3 Ratios of cross-sections at different centre-of-mass energies

The cross-section measurements detailed in the previous sections were also
performed using 1.0$\mbox{\,fb}^{-1}$ of data at
7$\mathrm{\,Te\kern-1.00006ptV}$ [9]. The two sets of measurements are used to
make measurements of ratios of quantities at different centre-of-mass
energies. The ratios of cross-sections are defined as

$\displaystyle R_{{W^{+}}}^{8/7}$
$\displaystyle=\frac{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}^{8\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}^{7\mathrm{\,Te\kern-0.70004ptV}}}\,,$
(9) $\displaystyle R_{{W^{-}}}^{8/7}$
$\displaystyle=\frac{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}^{8\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}^{7\mathrm{\,Te\kern-0.70004ptV}}}\,,$
(10) $\displaystyle R_{{Z}}^{8/7}$
$\displaystyle=\frac{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{8\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{7\mathrm{\,Te\kern-0.70004ptV}}}\,,$
(11)

and the double ratios of cross-sections are defined as

$\displaystyle R_{R_{{W^{\pm}}}}^{8/7}$
$\displaystyle=\frac{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}^{8\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}^{7\mathrm{\,Te\kern-0.70004ptV}}}\frac{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}^{7\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}^{8\mathrm{\,Te\kern-0.70004ptV}}}\,,$
(12) $\displaystyle R_{R_{{W^{+}}{Z}}}^{8/7}$
$\displaystyle=\frac{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}^{8\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}^{7\mathrm{\,Te\kern-0.70004ptV}}}\frac{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{7\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{8\mathrm{\,Te\kern-0.70004ptV}}}\,,$
(13) $\displaystyle R_{R_{{W^{-}}{Z}}}^{8/7}$
$\displaystyle=\frac{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}^{8\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}^{7\mathrm{\,Te\kern-0.70004ptV}}}\frac{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{7\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{8\mathrm{\,Te\kern-0.70004ptV}}}\,,$
(14) $\displaystyle R_{R_{{W}{Z}}}^{8/7}$
$\displaystyle=\frac{\sigma_{{W}\\!\rightarrow\mu{\nu}}^{8\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{W}\\!\rightarrow\mu{\nu}}^{7\mathrm{\,Te\kern-0.70004ptV}}}\frac{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{7\mathrm{\,Te\kern-0.70004ptV}}}{\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}^{8\mathrm{\,Te\kern-0.70004ptV}}}\
.$ (15)

The following assumptions are made in order to estimate uncertainties on these
ratios.

  * •

The uncertainties due to statistically independent samples are uncorrelated,
e.g. the uncertainties due to the number of candidates in each measured bin,
the uncertainties on the muon reconstruction efficiencies that are
uncorrelated between $\eta^{\mu}$ bins, and the uncertainty that arises from
corrections for having two muons inside the acceptance when measuring the
selection efficiencies of $W$ bosons and the $W$ boson purity.

  * •

The uncertainties reflecting common methods are correlated, e.g. the $Z$
candidate sample purity estimation, the components of the muon reconstruction
efficiencies that are correlated between muon $\eta$ bins, and the uncertainty
that arises when measuring selection efficiencies for $W$ bosons and all
aspects of the GEC efficiency.

  * •

The uncertainty due to the FSR correction is taken to be correlated in
identical measurement bins and uncorrelated between different measurement
bins.

  * •

The beam energy has been directly measured for
4$\mathrm{\,Te\kern-1.00006ptV}$ beams with a precision of 0.65%, but not for
3.5$\mathrm{\,Te\kern-1.00006ptV}$ beams [54]. No additional uncertainty is
expected to enter the energy measurement of 3.5$\mathrm{\,Te\kern-1.00006ptV}$
beams, so the relative uncertainty is taken to be the same, and fully
correlated between data sets with different centre-of-mass energies.

  * •

The uncertainties ($\delta_{i}^{\sqrt{s}}$) entering the luminosity estimates
are given in Ref. [23]. The degree of correlation between the luminosity
measurements at different centre-of-mass energies is determined by assigning
correlation coefficients ($c_{i}$) of 0, 1, [0,0.5], [0.5,1] or [0,1], where
the last three represent intervals within which the true correlation is
expected to lie. Pseudoexperiments are studied using correlation coefficients
that are sampled from both uniform and arcsin distributions across these
intervals. With this prescription, the total correlation is calculated using

$c=\frac{\sum_{i}c_{i}\,\delta_{i}^{8\mathrm{\,Te\kern-0.70004ptV}}\delta_{i}^{7\mathrm{\,Te\kern-0.70004ptV}}}{\delta^{8\mathrm{\,Te\kern-0.70004ptV}}\delta^{7\mathrm{\,Te\kern-0.70004ptV}}}$
(16)

and estimated to be $0.55\pm 0.06$. A correlation coefficient of 0.55 is used.

A summary of the uncertainties on ratios of quantities at different centre-of-
mass energies is given in Table 3.

Table 3: Summary of the relative uncertainties on the electroweak boson cross-section ratios at different centre-of-mass energies. Source | Uncertainty [%]
---|---
| $R_{{W^{+}}}^{8/7}$ | $R_{{W^{-}}}^{8/7}$ | $R_{{Z}}^{8/7}$ | $R_{R_{{W^{\pm}}}}^{8/7}$ | $R_{R_{{W^{+}}{Z}}}^{8/7}$ | $R_{R_{{W^{-}}{Z}}}^{8/7}$ | $R_{R_{{W}{Z}}}^{8/7}$
Statistical | 0.30 | 0.37 | 0.49 | 0.48 | 0.58 | 0.62 | 0.55
Purity | 0.41 | 0.45 | — | 0.65 | 0.41 | 0.45 | 0.29
Tracking | 0.33 | 0.27 | 0.53 | 0.09 | 0.23 | 0.26 | 0.24
Identification | 0.07 | 0.07 | 0.13 | 0.03 | 0.07 | 0.06 | 0.07
Trigger | 0.27 | 0.25 | 0.09 | 0.08 | 0.19 | 0.16 | 0.17
GEC | 0.15 | 0.14 | 0.09 | 0.07 | 0.09 | 0.09 | 0.08
Selection | 0.17 | 0.17 | — | 0.04 | 0.17 | 0.17 | 0.16
Acceptance and FSR | 0.05 | 0.06 | 0.04 | 0.08 | 0.07 | 0.07 | 0.06
Systematic | 0.64 | 0.63 | 0.56 | 0.66 | 0.55 | 0.59 | 0.46
Beam energy | 0.06 | 0.05 | 0.10 | — | 0.04 | 0.05 | 0.05
Luminosity | 1.45 | 1.45 | 1.45 | — | — | — | —
Total | 1.61 | 1.62 | 1.63 | 0.82 | 0.80 | 0.86 | 0.72

The cross-section ratios at different centre-of-mass energies, measured for
the same kinematic range as the total cross-sections, are

$\displaystyle R_{{W^{+}}}^{8/7}$ $\displaystyle=1.245\pm 0.004\pm 0.008\pm
0.001\pm 0.018\,,$ $\displaystyle R_{{W^{-}}}^{8/7}$ $\displaystyle=1.187\pm
0.004\pm 0.007\pm 0.001\pm 0.017\,,$ $\displaystyle R_{{Z}}^{8/7}$
$\displaystyle=1.250\pm 0.006\pm 0.007\pm 0.001\pm 0.018\,,$

where the first uncertainties are statistical, the second are systematic, the
third are due to the knowledge of the LHC beam energy and the fourth are due
to the luminosity measurement. The measurements and predictions are in
agreement, as shown in Fig. 8. Compared to Fig. 3, the variation in the
predictions is small. This indicates that the uncertainty due to the PDF is
very much reduced, which is also reflected in the calculated uncertainties on
the individual PDF predictions.

Figure 8: Summary of the $W$ and $Z$ cross-section ratios at different centre-
of-mass energies. Measurements, represented as bands, are compared to
(markers) NNLO predictions with different parameterisations of the PDFs.

Even more precise tests can be obtained through the following double ratios of
cross-sections, which are independent of the luminosities of either data set.
These double ratios are defined and measured as

$\displaystyle R_{R_{{W^{\pm}}}}^{8/7}$ $\displaystyle=1.049\pm 0.005\pm
0.007\,,$ $\displaystyle R_{R_{{W^{+}}{Z}}}^{8/7}$ $\displaystyle=0.996\pm
0.006\pm 0.005\,,$ $\displaystyle R_{R_{{W^{-}}{Z}}}^{8/7}$
$\displaystyle=0.950\pm 0.006\pm 0.006\,,$ $\displaystyle
R_{R_{{W}{Z}}}^{8/7}$ $\displaystyle=0.976\pm 0.005\pm 0.004\,,$

where the first uncertainties are statistical and the second are systematic.
The largest source of systematic uncertainty on these ratios is due to the
evaluation of the purity of the $W$ boson sample, which ranges between 0.3%
and 0.7%. The double ratios are shown in Fig. 9, where the uncertainties on
the predictions due to the PDF, scale, $\alpha_{s}$ and numerical integration
are of similar magnitude. Taking the uncertainty on the SM prediction to be
reflected by the spread of the PDF predictions, the maximal deviation between
the measured results and the theory is at the level of about 2 standard
deviations.

Figure 9: Summary of the cross-section double ratios at different centre-of-
mass energies. Measurements, represented as bands, are compared to (markers)
NNLO predictions with different parameterisations of the PDFs.

The ratios $R_{R_{{W^{+}}{Z}}}^{8/7}$, $R_{R_{{W^{-}}{Z}}}^{8/7}$ are also
measured differentially as a function of muon $\eta$. These measurements are
displayed in Fig. 10, where only uncertainties due to PDFs are included on the
predictions. Good agreement between measurement and prediction is observed,
especially for the $R_{R_{{W^{-}}{Z}}}^{8/7}$ ratio. The
$R_{R_{{W^{+}}{Z}}}^{8/7}$ ratio increases as a function of $\eta^{\mu}$,
while the $R_{R_{{W^{-}}{Z}}}^{8/7}$ ratio decreases as a function of
$\eta^{\mu}$. The PDF uncertainties are largest for the
$R_{R_{{W^{+}}{Z}}}^{8/7}$ ratio at high pseudorapidity, suggesting that these
measurements can improve the determination of the PDFs in this region.
Differential measurements are reported in Table 12 of Appendix A, along with
new differential measurements that were not published in Ref. [9] that are
required for this analysis (Tables 13 and 14).

Figure 10: Double ratios of cross-sections at different centre-of-mass
energies as a function of muon pseudorapidity. Measurements, represented as
bands, are compared to (markers, displaced horizontally for presentation) NNLO
predictions with different parameterisations of the PDFs.

##  6 Conclusions

Measurements of forward electroweak boson production at $\sqrt{s}$ =
8$\mathrm{\,Te\kern-1.00006ptV}$ are presented and found to be in agreement
with NNLO calculations in perturbative quantum chromodynamics. The large
degree of correlation between the uncertainties allows for sub-percent
determination of the cross-section ratios. These represent the most precise
determinations to date of electroweak boson production at the LHC. Using
previous results from the $\sqrt{s}$ = 7$\mathrm{\,Te\kern-1.00006ptV}$ data
set, the evolution with the centre-of-mass energy is studied. Good agreement
between measured and predicted cross-section ratios is observed. The
experimental uncertainties are dominated by luminosity uncertainties of about
1.5%. Double ratios of cross-sections at different centre-of-mass energies are
independent of the luminosity and are thus a more precise class of
observables, determined with precision of between 0.7% and 0.9%. In the cross-
section ratios, the predictions deviate slightly from the measurements. Such
deviations can be expected in BSM extensions that feature new sources of $W$
and $Z$ production. This motivates the extension of this analysis to higher
energies, as will be possible with future data.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM
and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI (Russia),
CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC
(USA). We are indebted to the communities behind the multiple open source
software packages on which we depend. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received support from AvH
Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC
(European Union), Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU,
Région Auvergne (France), RFBR (Russia), GVA, XuntaGal and GENCAT (Spain), The
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

Appendices

##  Appendix A Differential measurements

Differential production cross-section measurements as functions of the
pseudorapidities of the muons from the decay of the $Z$ boson were not
included in the previous publication that describes the analysis of the
$\sqrt{s}$ = 7 TeV data set [9]. They are provided in this appendix in Table
13, along with the related measurements of the differential $W$ to $Z$ boson
cross-section ratios in Table 14.

Table 4: Cross-section for (top) $W^{+}$ and (bottom) $W^{-}$ boson production
in bins of muon pseudorapidity. The first uncertainties are statistical, the
second are systematic, the third are due to the knowledge of the LHC beam
energy and the fourth are due to the luminosity measurement. The last column
lists the final-state radiation correction.

$\eta^{\mu}$ |  $\sigma_{{W^{+}}\\!\rightarrow{\mu^{+}}{\nu}}$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{W^{+}}}$
---|---|---
2.00 – 2.25 | $236.5\pm 1.2\pm 3.2\pm 2.4\pm 2.7$ | $1.0188\pm 0.0047$
2.25 – 2.50 | $208.4\pm 0.9\pm 2.2\pm 2.1\pm 2.4$ | $1.0163\pm 0.0028$
2.50 – 2.75 | $182.0\pm 0.8\pm 1.8\pm 1.8\pm 2.1$ | $1.0158\pm 0.0025$
2.75 – 3.00 | $153.3\pm 0.7\pm 1.6\pm 1.5\pm 1.8$ | $1.0148\pm 0.0028$
3.00 – 3.25 | $119.5\pm 0.6\pm 1.3\pm 1.2\pm 1.4$ | $1.0152\pm 0.0032$
3.25 – 3.50 | $\phantom{0}84.4\pm 0.5\pm 1.0\pm 0.8\pm 1.0$ | $1.0150\pm 0.0046$
3.50 – 4.00 | $\phantom{0}86.4\pm 0.5\pm 1.2\pm 0.9\pm 1.0$ | $1.0175\pm 0.0045$
4.00 – 4.50 | $\phantom{0}23.0\pm 0.4\pm 0.7\pm 0.2\pm 0.3$ | $1.0211\pm 0.0087$

$\eta^{\mu}$ |  $\sigma_{{W^{-}}\\!\rightarrow{\mu^{-}}{\overline{\nu}}}$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{W^{-}}}$
---|---|---
2.00 – 2.25 | $134.0\pm 0.9\pm 1.8\pm 1.2\pm 1.6$ | $1.0172\pm 0.0026$
2.25 – 2.50 | $119.8\pm 0.7\pm 1.4\pm 1.0\pm 1.4$ | $1.0155\pm 0.0027$
2.50 – 2.75 | $110.6\pm 0.6\pm 1.2\pm 1.0\pm 1.3$ | $1.0153\pm 0.0028$
2.75 – 3.00 | $102.4\pm 0.6\pm 1.2\pm 0.9\pm 1.2$ | $1.0162\pm 0.0030$
3.00 – 3.25 | $\phantom{0}92.5\pm 0.6\pm 1.1\pm 0.8\pm 1.1$ | $1.0160\pm 0.0031$
3.25 – 3.50 | $\phantom{0}79.9\pm 0.5\pm 0.9\pm 0.7\pm 0.9$ | $1.0176\pm 0.0033$
3.50 – 4.00 | $119.3\pm 0.6\pm 1.5\pm 1.0\pm 1.4$ | $1.0200\pm 0.0033$
4.00 – 4.50 | $\phantom{0}60.0\pm 0.7\pm 1.6\pm 0.5\pm 0.7$ | $1.0243\pm 0.0053$

Table 5: Cross-section for $Z$ boson production in bins of boson rapidity. The first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity measurement. The last column lists the final-state radiation correction. $y_{{Z}}$ |  $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{Z}}$
---|---|---
2.000 – 2.125 | 1.223 $\pm$ 0.033 $\pm$ 0.055 $\pm$ 0.014 $\pm$ 0.014 | $1.0466\pm 0.0395$
2.125 – 2.250 | 3.263 $\pm$ 0.051 $\pm$ 0.060 $\pm$ 0.038 $\pm$ 0.038 | $1.0305\pm 0.0119$
2.250 – 2.375 | 4.983 $\pm$ 0.062 $\pm$ 0.064 $\pm$ 0.057 $\pm$ 0.058 | $1.0277\pm 0.0069$
2.375 – 2.500 | 6.719 $\pm$ 0.070 $\pm$ 0.072 $\pm$ 0.077 $\pm$ 0.078 | $1.0252\pm 0.0061$
2.500 – 2.625 | 8.051 $\pm$ 0.076 $\pm$ 0.074 $\pm$ 0.093 $\pm$ 0.094 | $1.0264\pm 0.0048$
2.625 – 2.750 | 8.967 $\pm$ 0.079 $\pm$ 0.074 $\pm$ 0.103 $\pm$ 0.105 | $1.0257\pm 0.0032$
2.750 – 2.875 | 9.561 $\pm$ 0.081 $\pm$ 0.076 $\pm$ 0.110 $\pm$ 0.112 | $1.0258\pm 0.0038$
2.875 – 3.000 | 9.822 $\pm$ 0.082 $\pm$ 0.071 $\pm$ 0.113 $\pm$ 0.115 | $1.0252\pm 0.0027$
3.000 – 3.125 | 9.721 $\pm$ 0.081 $\pm$ 0.074 $\pm$ 0.112 $\pm$ 0.114 | $1.0282\pm 0.0035$
3.125 – 3.250 | 9.030 $\pm$ 0.078 $\pm$ 0.071 $\pm$ 0.104 $\pm$ 0.105 | $1.0264\pm 0.0030$
3.250 – 3.375 | 7.748 $\pm$ 0.072 $\pm$ 0.074 $\pm$ 0.089 $\pm$ 0.090 | $1.0261\pm 0.0066$
3.375 – 3.500 | 6.059 $\pm$ 0.063 $\pm$ 0.051 $\pm$ 0.070 $\pm$ 0.071 | $1.0248\pm 0.0040$
3.500 – 3.625 | 4.385 $\pm$ 0.054 $\pm$ 0.041 $\pm$ 0.050 $\pm$ 0.051 | $1.0258\pm 0.0060$
3.625 – 3.750 | 2.724 $\pm$ 0.042 $\pm$ 0.027 $\pm$ 0.031 $\pm$ 0.032 | $1.0228\pm 0.0053$
3.750 – 3.875 | 1.584 $\pm$ 0.032 $\pm$ 0.020 $\pm$ 0.018 $\pm$ 0.019 | $1.0180\pm 0.0079$
3.875 – 4.000 | 0.749 $\pm$ 0.022 $\pm$ 0.012 $\pm$ 0.009 $\pm$ 0.009 | $1.0207\pm 0.0100$
4.000 – 4.250 | 0.383 $\pm$ 0.016 $\pm$ 0.008 $\pm$ 0.004 $\pm$ 0.004 | $1.0183\pm 0.0140$
4.250 – 4.500 | 0.011 $\pm$ 0.003 $\pm$ 0.001 $\pm$ 0.000 $\pm$ 0.000 | $1.0177\pm 0.0761$
Table 6: Cross-section for $Z$ boson production in bins of boson transverse momentum. The first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity measurement. The last column lists the final-state radiation correction. $p_{\textrm{T},{Z}}$ [${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ] |  $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{Z}}$
---|---|---
00.0 – 002.2 | 7.903 $\pm$ 0.082$\pm$ 0.130 $\pm$ 0.091 $\pm$ 0.092 | $1.0962\pm 0.0045$
02.2 – 003.4 | 7.705 $\pm$ 0.080$\pm$ 0.108 $\pm$ 0.089 $\pm$ 0.090 | $1.0788\pm 0.0055$
03.4 – 004.6 | 7.609 $\pm$ 0.078$\pm$ 0.080 $\pm$ 0.088 $\pm$ 0.089 | $1.0620\pm 0.0039$
04.6 – 005.8 | 7.073 $\pm$ 0.075$\pm$ 0.078 $\pm$ 0.081 $\pm$ 0.083 | $1.0472\pm 0.0035$
05.8 – 007.2 | 7.379 $\pm$ 0.078$\pm$ 0.069 $\pm$ 0.085 $\pm$ 0.086 | $1.0290\pm 0.0044$
07.2 – 008.7 | 6.813 $\pm$ 0.076$\pm$ 0.074 $\pm$ 0.078 $\pm$ 0.080 | $1.0165\pm 0.0060$
08.7 – 010.5 | 6.751 $\pm$ 0.075$\pm$ 0.064 $\pm$ 0.078 $\pm$ 0.079 | $1.0044\pm 0.0037$
10.5 – 012.8 | 7.204 $\pm$ 0.078$\pm$ 0.073 $\pm$ 0.083 $\pm$ 0.084 | $0.9953\pm 0.0060$
12.8 – 015.4 | 6.270 $\pm$ 0.073$\pm$ 0.053 $\pm$ 0.072 $\pm$ 0.073 | $0.9852\pm 0.0035$
15.4 – 019.0 | 6.534 $\pm$ 0.072$\pm$ 0.064 $\pm$ 0.075 $\pm$ 0.076 | $0.9830\pm 0.0042$
19.0 – 024.5 | 6.953 $\pm$ 0.071$\pm$ 0.066 $\pm$ 0.080 $\pm$ 0.081 | $0.9853\pm 0.0044$
24.5 – 034.0 | 6.999 $\pm$ 0.069$\pm$ 0.062 $\pm$ 0.080 $\pm$ 0.082 | $1.0109\pm 0.0031$
34.0 – 063.0 | 7.602 $\pm$ 0.070$\pm$ 0.072 $\pm$ 0.087 $\pm$ 0.089 | $1.0380\pm 0.0034$
63.0 – 270.0 | 2.176 $\pm$ 0.037$\pm$ 0.025 $\pm$ 0.025 $\pm$ 0.025 | $1.0604\pm 0.0059$
Table 7: Cross-section for $Z$ boson production in bins of boson $\phi^{*}_{\eta}$. The first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity measurement. The last column lists the final-state radiation correction. $\phi^{*}_{\eta}$ |  $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{Z}}$
---|---|---
0.00 – 0.01 | 10.442 $\pm$ 0.077 $\pm$ 0.118 $\pm$ 0.120 $\pm$ 0.122 | $1.0367\pm 0.0028$
0.01 – 0.02 |  09.704 $\pm$ 0.076 $\pm$ 0.116 $\pm$ 0.112 $\pm$ 0.113 | $1.0346\pm 0.0031$
0.02 – 0.03 |  08.510 $\pm$ 0.071 $\pm$ 0.130 $\pm$ 0.098 $\pm$ 0.099 | $1.0323\pm 0.0031$
0.03 – 0.05 | 13.749 $\pm$ 0.089 $\pm$ 0.151 $\pm$ 0.158 $\pm$ 0.161 | $1.0288\pm 0.0024$
0.05 – 0.07 | 10.085 $\pm$ 0.076 $\pm$ 0.119 $\pm$ 0.116 $\pm$ 0.118 | $1.0254\pm 0.0036$
0.07 – 0.10 | 10.662 $\pm$ 0.077 $\pm$ 0.159 $\pm$ 0.123 $\pm$ 0.125 | $1.0211\pm 0.0030$
0.10 – 0.15 | 10.575 $\pm$ 0.077 $\pm$ 0.133 $\pm$ 0.122 $\pm$ 0.123 | $1.0196\pm 0.0029$
0.15 – 0.20 |  06.322 $\pm$ 0.059 $\pm$ 0.074 $\pm$ 0.073 $\pm$ 0.074 | $1.0177\pm 0.0034$
0.20 – 0.30 |  06.681 $\pm$ 0.061 $\pm$ 0.085 $\pm$ 0.077 $\pm$ 0.078 | $1.0188\pm 0.0039$
0.30 – 0.40 |  03.213 $\pm$ 0.042 $\pm$ 0.064 $\pm$ 0.037 $\pm$ 0.038 | $1.0210\pm 0.0064$
0.40 – 0.60 |  02.837 $\pm$ 0.040 $\pm$ 0.055 $\pm$ 0.033 $\pm$ 0.033 | $1.0251\pm 0.0065$
0.60 – 0.80 |  01.030 $\pm$ 0.024 $\pm$ 0.027 $\pm$ 0.012 $\pm$ 0.012 | $1.0258\pm 0.0114$
0.80 – 1.20 |  00.670 $\pm$ 0.020 $\pm$ 0.030 $\pm$ 0.008 $\pm$ 0.008 | $1.0269\pm 0.0110$
1.20 – 2.00 |  00.263 $\pm$ 0.013 $\pm$ 0.022 $\pm$ 0.003 $\pm$ 0.003 | $1.0276\pm 0.0210$
2.00 – 4.00 |  00.094 $\pm$ 0.008 $\pm$ 0.023 $\pm$ 0.001 $\pm$ 0.001 | $1.0345\pm 0.0396$
Table 8: Cross-section for $Z$ boson production in bins of muon
pseudorapidity. The first uncertainties are statistical, the second are
systematic, the third are due to the knowledge of the LHC beam energy and the
fourth are due to the luminosity measurement. The last column lists the final-
state radiation correction.

$\eta^{\mu}$ |  $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}(\eta^{\mu^{+}})$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{Z}}$
---|---|---
2.00 – 2.25 | 15.28 $\pm$ 0.11 $\pm$ 0.18 $\pm$ 0.18 $\pm$ 0.18 | $1.0293\pm 0.0036$
2.25 – 2.50 | 14.39 $\pm$ 0.10 $\pm$ 0.13 $\pm$ 0.17 $\pm$ 0.17 | $1.0250\pm 0.0027$
2.50 – 2.75 | 13.39 $\pm$ 0.10 $\pm$ 0.11 $\pm$ 0.15 $\pm$ 0.16 | $1.0244\pm 0.0044$
2.75 – 3.00 | 12.37 $\pm$ 0.09 $\pm$ 0.10 $\pm$ 0.14 $\pm$ 0.14 | $1.0240\pm 0.0033$
3.00 – 3.25 | 10.93 $\pm$ 0.09 $\pm$ 0.09 $\pm$ 0.13 $\pm$ 0.13 | $1.0234\pm 0.0037$
3.25 – 3.50 |  09.02 $\pm$ 0.08 $\pm$ 0.08 $\pm$ 0.10 $\pm$ 0.11 | $1.0246\pm 0.0046$
3.50 – 4.00 | 12.94 $\pm$ 0.09 $\pm$ 0.10 $\pm$ 0.15 $\pm$ 0.15 | $1.0269\pm 0.0033$
4.00 – 4.50 |  06.67 $\pm$ 0.07 $\pm$ 0.07 $\pm$ 0.08 $\pm$ 0.08 | $1.0365\pm 0.0038$

$\eta^{\mu}$ |  $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}(\eta^{\mu^{-}})$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{Z}}$
---|---|---
2.00 – 2.25 | 14.07 $\pm$ 0.10 $\pm$ 0.18 $\pm$ 0.16 $\pm$ 0.16 | $1.0291\pm 0.0056$
2.25 – 2.50 | 13.68 $\pm$ 0.10 $\pm$ 0.13 $\pm$ 0.16 $\pm$ 0.16 | $1.0254\pm 0.0028$
2.50 – 2.75 | 13.09 $\pm$ 0.10 $\pm$ 0.10 $\pm$ 0.15 $\pm$ 0.15 | $1.0251\pm 0.0028$
2.75 – 3.00 | 12.43 $\pm$ 0.09 $\pm$ 0.11 $\pm$ 0.14 $\pm$ 0.15 | $1.0239\pm 0.0033$
3.00 – 3.25 | 11.01 $\pm$ 0.09 $\pm$ 0.10 $\pm$ 0.13 $\pm$ 0.13 | $1.0227\pm 0.0041$
3.25 – 3.50 |  09.49 $\pm$ 0.08 $\pm$ 0.08 $\pm$ 0.11 $\pm$ 0.11 | $1.0246\pm 0.0042$
3.50 – 4.00 | 13.85 $\pm$ 0.10 $\pm$ 0.11 $\pm$ 0.16 $\pm$ 0.16 | $1.0268\pm 0.0036$
4.00 – 4.50 |  07.35 $\pm$ 0.07 $\pm$ 0.07 $\pm$ 0.09 $\pm$ 0.09 | $1.0353\pm 0.0055$

Table 9: (Top) $W^{+}$ and (bottom) $W^{-}$ to $Z$ cross-section ratios in
bins of muon pseudorapidity. The first uncertainties are statistical, the
second are systematic, the third are due to the knowledge of the LHC beam
energy and the fourth are due to the luminosity measurement.

$\eta^{\mu^{+}}$ | $R_{{W^{+}}{Z}}$
---|---
2.00 – 2.25 | 15.478 $\pm$ 0.134 $\pm$ 0.174 $\pm$ 0.024 $\pm$ 0.001
2.25 – 2.50 | 14.490 $\pm$ 0.119 $\pm$ 0.136 $\pm$ 0.022 $\pm$ 0.001
2.50 – 2.75 | 13.593 $\pm$ 0.112 $\pm$ 0.137 $\pm$ 0.020 $\pm$ 0.001
2.75 – 3.00 | 12.406 $\pm$ 0.108 $\pm$ 0.126 $\pm$ 0.019 $\pm$ 0.001
3.00 – 3.25 | 10.937 $\pm$ 0.102 $\pm$ 0.115 $\pm$ 0.016 $\pm$ 0.001
3.25 – 3.50 |  09.353 $\pm$ 0.097 $\pm$ 0.114 $\pm$ 0.015 $\pm$ 0.001
3.50 – 4.00 |  06.677 $\pm$ 0.063 $\pm$ 0.093 $\pm$ 0.010 $\pm$ 0.001
4.00 – 4.50 |  03.444 $\pm$ 0.072 $\pm$ 0.103 $\pm$ 0.005 $\pm$ 0.000

$\eta^{\mu^{-}}$ | $R_{{W^{-}}{Z}}$
---|---
2.00 – 2.25 | 9.521 $\pm$ 0.095 $\pm$ 0.117 $\pm$ 0.028 $\pm$ 0.001
2.25 – 2.50 | 8.754 $\pm$ 0.080 $\pm$ 0.090 $\pm$ 0.025 $\pm$ 0.001
2.50 – 2.75 | 8.449 $\pm$ 0.076 $\pm$ 0.086 $\pm$ 0.025 $\pm$ 0.001
2.75 – 3.00 | 8.235 $\pm$ 0.077 $\pm$ 0.089 $\pm$ 0.024 $\pm$ 0.000
3.00 – 3.25 | 8.400 $\pm$ 0.082 $\pm$ 0.096 $\pm$ 0.024 $\pm$ 0.001
3.25 – 3.50 | 8.414 $\pm$ 0.088 $\pm$ 0.096 $\pm$ 0.024 $\pm$ 0.000
3.50 – 4.00 | 8.615 $\pm$ 0.075 $\pm$ 0.107 $\pm$ 0.025 $\pm$ 0.001
4.00 – 4.50 | 8.166 $\pm$ 0.130 $\pm$ 0.215 $\pm$ 0.023 $\pm$ 0.000

Table 10: $W^{+}$ to $W^{-}$ cross-section ratio in bins of muon pseudorapidity. The first uncertainties are statistical, the second are systematic and the third are due to the knowledge of the LHC beam energy. $\eta^{\mu}$ | $R_{{W^{\pm}}}$
---|---
2.00 – 2.25 | $1.765\pm 0.015\pm 0.018\pm 0.003$
2.25 – 2.50 | $1.740\pm 0.012\pm 0.018\pm 0.002$
2.50 – 2.75 | $1.645\pm 0.011\pm 0.013\pm 0.002$
2.75 – 3.00 | $1.499\pm 0.011\pm 0.011\pm 0.002$
3.00 – 3.25 | $1.292\pm 0.010\pm 0.010\pm 0.002$
3.25 – 3.50 | $1.057\pm 0.009\pm 0.009\pm 0.002$
3.50 – 4.00 | $0.724\pm 0.006\pm 0.014\pm 0.001$
4.00 – 4.50 | $0.383\pm 0.009\pm 0.016\pm 0.001$
Table 11: Lepton charge asymmetry in bins of muon pseudorapidity. The first uncertainties are statistical, the second are systematic and the third are due to the knowledge of the LHC beam energy. $\eta^{\mu}$ |  $A_{\mu}$ (%)
---|---
2.00 – 2.25 | $\phantom{-}27.67\pm 0.39\pm 0.48\pm 0.07$
2.25 – 2.50 | $\phantom{-}27.02\pm 0.33\pm 0.47\pm 0.07$
2.50 – 2.75 | $\phantom{-}24.39\pm 0.32\pm 0.37\pm 0.07$
2.75 – 3.00 | $\phantom{-}19.96\pm 0.35\pm 0.34\pm 0.07$
3.00 – 3.25 | $\phantom{-}12.74\pm 0.38\pm 0.37\pm 0.07$
3.25 – 3.50 | $\phantom{-0}2.75\pm 0.43\pm 0.42\pm 0.07$
3.50 – 4.00 | $-15.99\pm 0.39\pm 0.96\pm 0.07$
4.00 – 4.50 | $-44.63\pm 0.89\pm 1.64\pm 0.06$

Table 12: Ratios of (top) $W^{+}$ and (bottom) $W^{-}$ to $Z$ cross-section
ratios at different centre-of-mass energies in bins of muon pseudorapidity.
The first uncertainty is statistical and the second is systematic.

$\eta^{\mu^{+}}$ | $R_{R_{{W^{+}}{Z}}}^{8/7}$
---|---
2.00 – 2.25 | 1.022 $\pm$ 0.015 $\pm$ 0.016
2.25 – 2.50 | 0.997 $\pm$ 0.014 $\pm$ 0.016
2.50 – 2.75 | 0.993 $\pm$ 0.014 $\pm$ 0.013
2.75 – 3.00 | 1.027 $\pm$ 0.016 $\pm$ 0.013
3.00 – 3.25 | 0.981 $\pm$ 0.017 $\pm$ 0.014
3.25 – 3.50 | 1.085 $\pm$ 0.020 $\pm$ 0.017
3.50 – 4.00 | 1.055 $\pm$ 0.018 $\pm$ 0.016
4.00 – 4.50 | 1.077 $\pm$ 0.041 $\pm$ 0.043

$\eta^{\mu^{-}}$ | $R_{R_{{W^{-}}{Z}}}^{8/7}$
---|---
2.00 – 2.25 | 1.022 $\pm$ 0.017 $\pm$ 0.018
2.25 – 2.50 | 0.969 $\pm$ 0.015 $\pm$ 0.017
2.50 – 2.75 | 0.977 $\pm$ 0.015 $\pm$ 0.013
2.75 – 3.00 | 0.925 $\pm$ 0.015 $\pm$ 0.017
3.00 – 3.25 | 0.928 $\pm$ 0.016 $\pm$ 0.016
3.25 – 3.50 | 0.906 $\pm$ 0.017 $\pm$ 0.020
3.50 – 4.00 | 0.912 $\pm$ 0.014 $\pm$ 0.014
4.00 – 4.50 | 0.922 $\pm$ 0.026 $\pm$ 0.033

Table 13: Cross-section for $Z$ boson production in bins of muon
pseudorapidity at $\sqrt{s}$ = 7 TeV. The first uncertainties are statistical,
the second are systematic, the third are due to the knowledge of the LHC beam
energy and the fourth are due to the luminosity measurement. The last column
lists the final-state radiation correction.

$\eta^{\mu}$ |  $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}(\eta^{\mu^{+}})$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{Z}}$
---|---|---
2.00 – 2.25 | 12.69 $\pm$ 0.13 $\pm$ 0.16 $\pm$ 0.16 $\pm$ 0.22 | $1.0290\pm 0.0038$
2.25 – 2.50 | 12.31 $\pm$ 0.13 $\pm$ 0.13 $\pm$ 0.15 $\pm$ 0.21 | $1.0246\pm 0.0031$
2.50 – 2.75 | 11.27 $\pm$ 0.12 $\pm$ 0.10 $\pm$ 0.14 $\pm$ 0.19 | $1.0237\pm 0.0040$
2.75 – 3.00 | 10.16 $\pm$ 0.11 $\pm$ 0.10 $\pm$ 0.13 $\pm$ 0.18 | $1.0242\pm 0.0044$
3.00 – 3.25 |  08.44 $\pm$ 0.10 $\pm$ 0.08 $\pm$ 0.11 $\pm$ 0.15 | $1.0235\pm 0.0033$
3.25 – 3.50 |  07.15 $\pm$ 0.10 $\pm$ 0.07 $\pm$ 0.09 $\pm$ 0.12 | $1.0258\pm 0.0045$
3.50 – 4.00 |  09.48 $\pm$ 0.11 $\pm$ 0.08 $\pm$ 0.12 $\pm$ 0.16 | $1.0286\pm 0.0032$
4.00 – 4.50 |  04.49 $\pm$ 0.08 $\pm$ 0.05 $\pm$ 0.06 $\pm$ 0.08 | $1.0386\pm 0.0044$

$\eta^{\mu}$ |  $\sigma_{{Z}\,\\!\rightarrow{\mu^{+}}{\mu^{-}}}(\eta^{\mu^{-}})$ [$\rm\,pb$ ] | $f_{\textrm{\mbox{{FSR}}}}^{{Z}}$
---|---|---
2.00 – 2.25 | 11.93 $\pm$ 0.13 $\pm$ 0.19 $\pm$ 0.15 $\pm$ 0.21 | $1.0294\pm 0.0047$
2.25 – 2.50 | 11.61 $\pm$ 0.12 $\pm$ 0.14 $\pm$ 0.15 $\pm$ 0.20 | $1.0251\pm 0.0026$
2.50 – 2.75 | 11.12 $\pm$ 0.12 $\pm$ 0.12 $\pm$ 0.14 $\pm$ 0.19 | $1.0245\pm 0.0030$
2.75 – 3.00 |  09.93 $\pm$ 0.11 $\pm$ 0.10 $\pm$ 0.12 $\pm$ 0.17 | $1.0238\pm 0.0031$
3.00 – 3.25 |  08.91 $\pm$ 0.11 $\pm$ 0.11 $\pm$ 0.11 $\pm$ 0.15 | $1.0236\pm 0.0044$
3.25 – 3.50 |  07.39 $\pm$ 0.10 $\pm$ 0.08 $\pm$ 0.09 $\pm$ 0.13 | $1.0253\pm 0.0048$
3.50 – 4.00 | 10.16 $\pm$ 0.11 $\pm$ 0.11 $\pm$ 0.13 $\pm$ 0.18 | $1.0269\pm 0.0047$
4.00 – 4.50 |  04.95 $\pm$ 0.08 $\pm$ 0.09 $\pm$ 0.06 $\pm$ 0.09 | $1.0376\pm 0.0055$

Table 14: (Top) $W^{+}$ and (bottom) $W^{-}$ to $Z$ cross-section ratios in
bins of muon pseudorapidity at $\sqrt{s}$ = 7 TeV. The first uncertainties are
statistical, the second are systematic, the third are due to the knowledge of
the LHC beam energy and the fourth are due to the luminosity measurement.

$\eta^{\mu^{+}}$ | $R_{{W^{+}}{Z}}$
---|---
2.00 – 2.25 | 15.152 $\pm$ 0.182 $\pm$ 0.231 $\pm$ 0.029 $\pm$ 0.001
2.25 – 2.50 | 14.529 $\pm$ 0.167 $\pm$ 0.230 $\pm$ 0.028 $\pm$ 0.001
2.50 – 2.75 | 13.689 $\pm$ 0.164 $\pm$ 0.176 $\pm$ 0.026 $\pm$ 0.001
2.75 – 3.00 | 12.079 $\pm$ 0.153 $\pm$ 0.153 $\pm$ 0.023 $\pm$ 0.001
3.00 – 3.25 | 11.176 $\pm$ 0.157 $\pm$ 0.151 $\pm$ 0.021 $\pm$ 0.001
3.25 – 3.50 |  08.623 $\pm$ 0.134 $\pm$ 0.132 $\pm$ 0.016 $\pm$ 0.001
3.50 – 4.00 |  06.330 $\pm$ 0.091 $\pm$ 0.076 $\pm$ 0.012 $\pm$ 0.001
4.00 – 4.50 |  03.198 $\pm$ 0.101 $\pm$ 0.093 $\pm$ 0.006 $\pm$ 0.000

$\eta^{\mu^{-}}$ | $R_{{W^{-}}{Z}}$
---|---
2.00 – 2.25 | 9.314 $\pm$ 0.126 $\pm$ 0.162 $\pm$ 0.032 $\pm$ 0.001
2.25 – 2.50 | 9.030 $\pm$ 0.115 $\pm$ 0.151 $\pm$ 0.031 $\pm$ 0.001
2.50 – 2.75 | 8.647 $\pm$ 0.112 $\pm$ 0.112 $\pm$ 0.029 $\pm$ 0.001
2.75 – 3.00 | 8.907 $\pm$ 0.121 $\pm$ 0.150 $\pm$ 0.030 $\pm$ 0.001
3.00 – 3.25 | 9.054 $\pm$ 0.129 $\pm$ 0.156 $\pm$ 0.031 $\pm$ 0.001
3.25 – 3.50 | 9.285 $\pm$ 0.143 $\pm$ 0.202 $\pm$ 0.032 $\pm$ 0.001
3.50 – 4.00 | 9.443 $\pm$ 0.124 $\pm$ 0.126 $\pm$ 0.032 $\pm$ 0.001
4.00 – 4.50 | 8.858 $\pm$ 0.212 $\pm$ 0.243 $\pm$ 0.030 $\pm$ 0.001

##  Appendix B Correlation Matrices

Table 15: Correlation coefficients between the differential $W^{+}$ and
$W^{-}$ cross-sections in bins of muon $\eta$. The LHC beam energy and
luminosity uncertainties, which are fully correlated between cross-section
measurements, are excluded.

| $\eta^{\mu}$ | 2–2.25 | 2.25–2.5 | 2.5–2.75 | 2.75–3 | 3–3.25 | 3.25–3.5 | 3.5–4 | 4–4.5 |
---|---|---|---|---|---|---|---|---|---|---
|  2–2.25 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | $W^{+}$
| 0.67 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  | $W^{-}$
|  2.25–2.5 | 0.20 | 0.10 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  | $W^{+}$
| 0.07 | 0.21 | 0.54 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  | $W^{-}$
|  2.5–2.75 | 0.13 | 0.24 | 0.12 | 0.23 | 1.00 |  |  |  |  |  |  |  |  |  |  |  | $W^{+}$
| 0.05 | 0.18 | 0.03 | 0.22 | 0.64 | 1.00 |  |  |  |  |  |  |  |  |  |  | $W^{-}$
|  2.75–3 | 0.06 | 0.22 | 0.03 | 0.28 | 0.26 | 0.27 | 1.00 |  |  |  |  |  |  |  |  |  | $W^{+}$
| 0.04 | 0.21 | 0.00 | 0.25 | 0.25 | 0.31 | 0.70 | 1.00 |  |  |  |  |  |  |  |  | $W^{-}$
|  3–3.25 | 0.07 | 0.22 | 0.03 | 0.28 | 0.25 | 0.26 | 0.33 | 0.30 | 1.00 |  |  |  |  |  |  |  | $W^{+}$
| 0.06 | 0.22 | 0.03 | 0.28 | 0.26 | 0.27 | 0.32 | 0.32 | 0.68 | 1.00 |  |  |  |  |  |  | $W^{-}$
|  3.25–3.5 | 0.03 | 0.23 |  $-$0.01 | 0.28 | 0.28 | 0.27 | 0.35 | 0.33 | 0.34 | 0.32 | 1.00 |  |  |  |  |  | $W^{+}$
| 0.07 | 0.23 | 0.04 | 0.23 | 0.30 | 0.29 | 0.28 | 0.32 | 0.27 | 0.28 | 0.63 | 1.00 |  |  |  |  | $W^{-}$
|  3.5–4 |  $-$0.00 | 0.26 |  $-$0.06 | 0.33 | 0.31 | 0.32 | 0.41 | 0.39 | 0.40 | 0.38 | 0.45 | 0.36 | 1.00 |  |  |  | $W^{+}$
| 0.14 |  $-$0.06 | 0.20 |  $-$0.04 |  $-$0.13 |  $-$0.04 |  $-$0.08 |  $-$0.11 |  $-$0.07 |  $-$0.07 |  $-$0.17 |  $-$0.19 |  $-$0.04 | 1.00 |  |  | $W^{-}$
|  4–4.5 |  $-$0.07 | 0.14 |  $-$0.14 | 0.24 | 0.14 | 0.23 | 0.32 | 0.29 | 0.32 | 0.26 | 0.35 | 0.22 | 0.45 |  $-$0.15 | 1.00 |  | $W^{+}$
| 0.12 |  $-$0.09 | 0.17 |  $-$0.11 |  $-$0.18 |  $-$0.14 |  $-$0.17 |  $-$0.19 |  $-$0.15 |  $-$0.18 |  $-$0.23 |  $-$0.24 |  $-$0.31 | 0.48 | 0.05 | 1.00 | $W^{-}$
|  | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ |

Table 16: Correlation coefficients between the differential $Z$ cross-section
in bins of $y_{{Z}}$. The LHC beam energy and luminosity uncertainties, which
are fully correlated between cross-section measurements, are excluded.

$y_{{Z}}$ | 2–2.125 | 2.125–2.25 | 2.25–2.375 | 2.375–2.5 | 2.5–2.625 | 2.625–2.75 | 2.75–2.875 | 2.875–3 | 3–3.125 | 3.125–3.25 | 3.25–3.375 | 3.375–3.5 | 3.5–3.625 | 3.625–3.75 | 3.75–3.875 | 3.875–4 | 4–4.25 | 4.25–4.5
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
2–2.125 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.125–2.25 | 0.19 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.25–2.375 | 0.17 | 0.27 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.375–2.5 | 0.16 | 0.26 | 0.28 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.5–2.625 | 0.16 | 0.25 | 0.28 | 0.29 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
2.625–2.75 | 0.15 | 0.24 | 0.27 | 0.29 | 0.30 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
2.75–2.875 | 0.14 | 0.23 | 0.26 | 0.28 | 0.29 | 0.30 | 1.00 |  |  |  |  |  |  |  |  |  |  |
2.875–3 | 0.14 | 0.21 | 0.25 | 0.27 | 0.29 | 0.30 | 0.30 | 1.00 |  |  |  |  |  |  |  |  |  |
3–3.125 | 0.13 | 0.20 | 0.23 | 0.25 | 0.27 | 0.28 | 0.29 | 0.29 | 1.00 |  |  |  |  |  |  |  |  |
3.125–3.25 | 0.11 | 0.17 | 0.20 | 0.23 | 0.25 | 0.26 | 0.27 | 0.28 | 0.27 | 1.00 |  |  |  |  |  |  |  |
3.25–3.375 | 0.09 | 0.14 | 0.16 | 0.18 | 0.20 | 0.22 | 0.22 | 0.23 | 0.23 | 0.23 | 1.00 |  |  |  |  |  |  |
3.375–3.5 | 0.08 | 0.12 | 0.15 | 0.17 | 0.19 | 0.20 | 0.21 | 0.22 | 0.22 | 0.22 | 0.20 | 1.00 |  |  |  |  |  |
3.5–3.625 | 0.07 | 0.10 | 0.12 | 0.14 | 0.16 | 0.17 | 0.18 | 0.19 | 0.19 | 0.20 | 0.18 | 0.19 | 1.00 |  |  |  |  |
3.625–3.75 | 0.06 | 0.08 | 0.10 | 0.11 | 0.13 | 0.14 | 0.15 | 0.16 | 0.16 | 0.17 | 0.16 | 0.16 | 0.15 | 1.00 |  |  |  |
3.75–3.875 | 0.05 | 0.07 | 0.08 | 0.09 | 0.10 | 0.11 | 0.11 | 0.12 | 0.13 | 0.13 | 0.12 | 0.13 | 0.12 | 0.11 | 1.00 |  |  |
3.875–4 | 0.03 | 0.05 | 0.06 | 0.06 | 0.07 | 0.08 | 0.08 | 0.09 | 0.09 | 0.10 | 0.09 | 0.10 | 0.09 | 0.08 | 0.07 | 1.00 |  |
4–4.25 | 0.03 | 0.04 | 0.04 | 0.05 | 0.05 | 0.06 | 0.06 | 0.06 | 0.07 | 0.07 | 0.07 | 0.08 | 0.07 | 0.07 | 0.06 | 0.05 | 1.00 |
4.25–4.5 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 | 0.01 | 1.00

Table 17: Correlation coefficients between the differential $Z$ cross-section
in bins of $p_{\textrm{T},{Z}}$. The LHC beam energy and luminosity
uncertainties, which are fully correlated between cross-section measurements,
are excluded.

$p_{\textrm{T},{Z}}$ [GeV/c] | 0.0–2.2 | 2.2–3.4 | 3.4–4.6 | 4.6–5.8 | 5.8–7.2 | 7.2–8.7 | 8.7–10.5 | 10.5–12.8 | 12.8–15.4 | 15.4–19 | 19–24.5 | 24.5–34 | 34–63 | 63–270
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
0.0–2.2 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
2.2–3.4 | 0.06 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
3.4–4.6 | 0.08 | 0.16 | 1.00 |  |  |  |  |  |  |  |  |  |  |
4.6–5.8 | 0.13 | 0.09 | 0.20 | 1.00 |  |  |  |  |  |  |  |  |  |
5.8–7.2 | 0.15 | 0.16 | 0.12 | 0.19 | 1.00 |  |  |  |  |  |  |  |  |
7.2–8.7 | 0.14 | 0.16 | 0.18 | 0.11 | 0.17 | 1.00 |  |  |  |  |  |  |  |
8.7–10.5 | 0.14 | 0.16 | 0.20 | 0.19 | 0.14 | 0.15 | 1.00 |  |  |  |  |  |  |
10.5–12.8 | 0.14 | 0.16 | 0.19 | 0.19 | 0.21 | 0.14 | 0.12 | 1.00 |  |  |  |  |  |
12.8–15.4 | 0.15 | 0.17 | 0.20 | 0.19 | 0.22 | 0.20 | 0.17 | 0.11 | 1.00 |  |  |  |  |
15.4–19 | 0.14 | 0.16 | 0.20 | 0.19 | 0.21 | 0.19 | 0.21 | 0.18 | 0.11 | 1.00 |  |  |  |
19–24.5 | 0.15 | 0.17 | 0.21 | 0.20 | 0.22 | 0.20 | 0.21 | 0.21 | 0.21 | 0.13 | 1.00 |  |  |
24.5–34 | 0.16 | 0.18 | 0.22 | 0.21 | 0.23 | 0.21 | 0.22 | 0.22 | 0.23 | 0.22 | 0.17 | 1.00 |  |
34–63 | 0.16 | 0.18 | 0.22 | 0.21 | 0.23 | 0.21 | 0.22 | 0.22 | 0.23 | 0.22 | 0.23 | 0.21 | 1.00 |
63–270 | 0.11 | 0.12 | 0.15 | 0.14 | 0.16 | 0.15 | 0.15 | 0.15 | 0.16 | 0.15 | 0.16 | 0.17 | 0.15 | 1.00

Table 18: Correlation coefficients between the differential $Z$ cross-section
in bins of $\phi^{*}_{\eta}$. The LHC beam energy and luminosity
uncertainties, which are fully correlated between cross-section measurements,
are excluded.

$\phi^{*}_{\eta}$ | 0.00–0.01 | 0.01–0.02 | 0.02–0.03 | 0.03–0.05 | 0.05–0.07 | 0.07–0.10 | 0.10–0.15 | 0.15–0.20 | 0.20–0.30 | 0.30–0.40 | 0.40–0.60 | 0.60–0.80 | 0.80–1.20 | 1.20–2.00 | 2.00–4.00
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
0.00–0.01 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
0.01–0.02 | 0.50 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
0.02–0.03 | 0.42 | 0.39 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
0.03–0.05 | 0.57 | 0.55 | 0.44 | 1.00 |  |  |  |  |  |  |  |  |  |  |
0.05–0.07 | 0.52 | 0.50 | 0.41 | 0.55 | 1.00 |  |  |  |  |  |  |  |  |  |
0.07–0.10 | 0.44 | 0.42 | 0.34 | 0.47 | 0.42 | 1.00 |  |  |  |  |  |  |  |  |
0.10–0.15 | 0.50 | 0.48 | 0.40 | 0.54 | 0.49 | 0.41 | 1.00 |  |  |  |  |  |  |  |
0.15–0.20 | 0.49 | 0.47 | 0.38 | 0.52 | 0.48 | 0.40 | 0.46 | 1.00 |  |  |  |  |  |  |
0.20–0.30 | 0.47 | 0.45 | 0.37 | 0.50 | 0.45 | 0.39 | 0.44 | 0.43 | 1.00 |  |  |  |  |  |
0.30–0.40 | 0.31 | 0.30 | 0.24 | 0.33 | 0.30 | 0.26 | 0.29 | 0.29 | 0.27 | 1.00 |  |  |  |  |
0.40–0.60 | 0.31 | 0.29 | 0.24 | 0.33 | 0.30 | 0.25 | 0.29 | 0.28 | 0.27 | 0.18 | 1.00 |  |  |  |
0.60–0.80 | 0.21 | 0.20 | 0.16 | 0.23 | 0.20 | 0.17 | 0.20 | 0.19 | 0.19 | 0.12 | 0.12 | 1.00 |  |  |
0.80–1.20 | 0.13 | 0.13 | 0.10 | 0.14 | 0.13 | 0.11 | 0.13 | 0.12 | 0.12 | 0.08 | 0.08 | 0.05 | 1.00 |  |
1.20–2.00 | 0.07 | 0.07 | 0.06 | 0.08 | 0.07 | 0.06 | 0.07 | 0.07 | 0.06 | 0.04 | 0.04 | 0.03 | 0.02 | 1.00 |
2.00–4.00 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 | 1.00

Table 19: Correlation coefficients between differential $W$ and $Z$ cross-
sections in bins of muon $\eta$ and $y_{{Z}}$, respectively. The LHC beam
energy and luminosity uncertainties, which are fully correlated between cross-
section measurements, are excluded.

|  | $y_{{Z}}$ |
---|---|---|---
|  | 2–2.125 | 2.125–2.25 | 2.25–2.375 | 2.375–2.5 | 2.5–2.625 | 2.625–2.75 | 2.75–2.875 | 2.875–3 | 3–3.125 | 3.125–3.25 | 3.25–3.375 | 3.375–3.5 | 3.5–3.625 | 3.625–3.75 | 3.75–3.875 | 3.875–4 | 4–4.25 | 4.25–4.5 |
$\eta^{\mu}$ |  2–2.25 | 0.23 | 0.30 | 0.28 | 0.27 | 0.26 | 0.25 | 0.24 | 0.23 | 0.21 | 0.18 | 0.15 | 0.13 | 0.11 | 0.10 | 0.07 | 0.05 | 0.04 | 0.01 | $W^{+}$
0.21 | 0.28 | 0.26 | 0.25 | 0.24 | 0.24 | 0.22 | 0.21 | 0.20 | 0.17 | 0.14 | 0.12 | 0.11 | 0.09 | 0.07 | 0.05 | 0.04 | 0.01 | $W^{-}$
2.25–2.5 | 0.05 | 0.15 | 0.21 | 0.20 | 0.20 | 0.20 | 0.20 | 0.19 | 0.18 | 0.16 | 0.14 | 0.12 | 0.10 | 0.08 | 0.06 | 0.04 | 0.03 | 0.01 | $W^{+}$
0.04 | 0.14 | 0.19 | 0.18 | 0.18 | 0.18 | 0.18 | 0.17 | 0.16 | 0.15 | 0.12 | 0.11 | 0.09 | 0.07 | 0.05 | 0.04 | 0.03 | 0.00 | $W^{-}$
2.5–2.75 | 0.04 | 0.07 | 0.12 | 0.15 | 0.16 | 0.17 | 0.17 | 0.17 | 0.16 | 0.15 | 0.13 | 0.13 | 0.11 | 0.08 | 0.06 | 0.05 | 0.03 | 0.01 | $W^{+}$
0.04 | 0.07 | 0.11 | 0.14 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.14 | 0.12 | 0.12 | 0.10 | 0.08 | 0.06 | 0.04 | 0.03 | 0.01 | $W^{-}$
2.75–3 | 0.05 | 0.08 | 0.10 | 0.13 | 0.16 | 0.17 | 0.17 | 0.17 | 0.16 | 0.16 | 0.14 | 0.13 | 0.12 | 0.09 | 0.07 | 0.05 | 0.03 | 0.01 | $W^{+}$
0.05 | 0.07 | 0.09 | 0.12 | 0.14 | 0.15 | 0.15 | 0.16 | 0.15 | 0.14 | 0.12 | 0.12 | 0.11 | 0.08 | 0.06 | 0.04 | 0.03 | 0.01 | $W^{-}$
3–3.25 | 0.06 | 0.08 | 0.10 | 0.11 | 0.14 | 0.16 | 0.17 | 0.17 | 0.16 | 0.16 | 0.14 | 0.14 | 0.12 | 0.10 | 0.07 | 0.05 | 0.03 | 0.01 | $W^{+}$
0.05 | 0.08 | 0.09 | 0.10 | 0.13 | 0.15 | 0.15 | 0.16 | 0.15 | 0.15 | 0.13 | 0.13 | 0.11 | 0.09 | 0.07 | 0.05 | 0.03 | 0.01 | $W^{-}$
3.25–3.5 | 0.04 | 0.06 | 0.07 | 0.09 | 0.10 | 0.11 | 0.12 | 0.13 | 0.13 | 0.12 | 0.11 | 0.11 | 0.09 | 0.08 | 0.06 | 0.04 | 0.03 | 0.00 | $W^{+}$
0.04 | 0.06 | 0.08 | 0.09 | 0.10 | 0.12 | 0.13 | 0.13 | 0.13 | 0.13 | 0.11 | 0.11 | 0.10 | 0.08 | 0.06 | 0.04 | 0.03 | 0.00 | $W^{-}$
3.5–4 | 0.04 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 | 0.11 | 0.12 | 0.12 | 0.12 | 0.11 | 0.11 | 0.10 | 0.09 | 0.07 | 0.05 | 0.04 | 0.00 | $W^{+}$
0.04 | 0.06 | 0.08 | 0.09 | 0.10 | 0.11 | 0.12 | 0.13 | 0.14 | 0.14 | 0.12 | 0.12 | 0.11 | 0.10 | 0.08 | 0.06 | 0.04 | 0.01 | $W^{-}$
4–4.5 | 0.02 | 0.03 | 0.04 | 0.04 | 0.04 | 0.04 | 0.05 | 0.05 | 0.06 | 0.06 | 0.06 | 0.07 | 0.06 | 0.06 | 0.05 | 0.04 | 0.04 | 0.01 | $W^{+}$
0.03 | 0.04 | 0.04 | 0.05 | 0.05 | 0.06 | 0.06 | 0.06 | 0.07 | 0.07 | 0.07 | 0.08 | 0.08 | 0.07 | 0.06 | 0.05 | 0.04 | 0.01 | $W^{-}$

Table 20: Correlation coefficients between the differential $Z$ cross-sections
in bins of (top) $\eta^{\mu^{+}}$ and (bottom) $\eta^{\mu^{-}}$. The LHC beam
energy and luminosity uncertainties, which are fully correlated between cross-
section measurements, are excluded.

$\eta^{\mu^{+}}$ | 2.00–2.25 | 2.25–2.50 | 2.50–2.75 | 2.75–3.00 | 3.00–3.25 | 3.25–3.50 | 3.50–4.00 | 4.00–4.50
---|---|---|---|---|---|---|---|---
2.00–2.25 | 1.00 |  |  |  |  |  |  |
2.25–2.50 | 0.31 | 1.00 |  |  |  |  |  |
2.50–2.75 | 0.30 | 0.27 | 1.00 |  |  |  |  |
2.75–3.00 | 0.31 | 0.28 | 0.26 | 1.00 |  |  |  |
3.00–3.25 | 0.32 | 0.28 | 0.26 | 0.27 | 1.00 |  |  |
3.25–3.50 | 0.27 | 0.25 | 0.23 | 0.23 | 0.23 | 1.00 |  |
3.50–4.00 | 0.33 | 0.30 | 0.28 | 0.28 | 0.28 | 0.25 | 1.00 |
4.00–4.50 | 0.28 | 0.25 | 0.23 | 0.24 | 0.23 | 0.20 | 0.23 | 1.00

$\eta^{\mu^{-}}$ | 2.00–2.25 | 2.25–2.50 | 2.50–2.75 | 2.75–3.00 | 3.00–3.25 | 3.25–3.50 | 3.50–4.00 | 4.00–4.50
---|---|---|---|---|---|---|---|---
2.00–2.25 | 1.00 |  |  |  |  |  |  |
2.25–2.50 | 0.29 | 1.00 |  |  |  |  |  |
2.50–2.75 | 0.30 | 0.29 | 1.00 |  |  |  |  |
2.75–3.00 | 0.30 | 0.28 | 0.28 | 1.00 |  |  |  |
3.00–3.25 | 0.30 | 0.27 | 0.27 | 0.27 | 1.00 |  |  |
3.25–3.50 | 0.27 | 0.25 | 0.25 | 0.24 | 0.24 | 1.00 |  |
3.50–4.00 | 0.31 | 0.29 | 0.29 | 0.28 | 0.28 | 0.25 | 1.00 |
4.00–4.50 | 0.28 | 0.25 | 0.25 | 0.24 | 0.24 | 0.21 | 0.24 | 1.00

Table 21: Correlation coefficients between the differential $W$ and $Z$ cross-
sections in bins of (top) $\eta^{\mu^{+}}$ and (bottom) $\eta^{\mu^{-}}$. The
LHC beam energy and luminosity uncertainties, which are fully correlated
between cross-section measurements, are excluded.

|  | $Z$
---|---|---
| $\eta^{\mu^{+}}$ | 2.00–2.25 | 2.25–2.50 | 2.50–2.75 | 2.75–3.00 | 3.00–3.25 | 3.25–3.50 | 3.50–4.00 | 4.00–4.50
$W$ | 2.00–2.25 | 0.48 | 0.19 | 0.19 | 0.20 | 0.20 | 0.18 | 0.22 | 0.18
2.25–2.50 | 0.15 | 0.38 | 0.16 | 0.16 | 0.16 | 0.14 | 0.17 | 0.14
2.50–2.75 | 0.14 | 0.14 | 0.26 | 0.14 | 0.14 | 0.13 | 0.16 | 0.12
2.75–3.00 | 0.14 | 0.14 | 0.14 | 0.26 | 0.15 | 0.13 | 0.16 | 0.12
3.00–3.25 | 0.15 | 0.14 | 0.14 | 0.15 | 0.25 | 0.13 | 0.15 | 0.12
3.25–3.50 | 0.11 | 0.11 | 0.11 | 0.11 | 0.11 | 0.17 | 0.12 | 0.09
3.50–4.00 | 0.10 | 0.10 | 0.11 | 0.11 | 0.11 | 0.10 | 0.18 | 0.08
4.00–4.50 | 0.06 | 0.06 | 0.06 | 0.06 | 0.06 | 0.05 | 0.06 | 0.11

|  | $Z$
---|---|---
| $\eta^{\mu^{-}}$ | 2.00–2.25 | 2.25–2.50 | 2.50–2.75 | 2.75–3.00 | 3.00–3.25 | 3.25–3.50 | 3.50–4.00 | 4.00–4.50
$W$ | 2.00–2.25 | 0.43 | 0.18 | 0.19 | 0.19 | 0.19 | 0.18 | 0.21 | 0.18
2.25–2.50 | 0.13 | 0.35 | 0.15 | 0.15 | 0.14 | 0.14 | 0.16 | 0.13
2.50–2.75 | 0.12 | 0.13 | 0.25 | 0.13 | 0.13 | 0.12 | 0.14 | 0.12
2.75–3.00 | 0.12 | 0.13 | 0.14 | 0.24 | 0.13 | 0.12 | 0.14 | 0.12
3.00–3.25 | 0.13 | 0.13 | 0.14 | 0.14 | 0.23 | 0.13 | 0.15 | 0.12
3.25–3.50 | 0.11 | 0.11 | 0.12 | 0.12 | 0.12 | 0.18 | 0.12 | 0.10
3.50–4.00 | 0.11 | 0.12 | 0.12 | 0.12 | 0.12 | 0.11 | 0.20 | 0.10
4.00–4.50 | 0.07 | 0.06 | 0.07 | 0.07 | 0.07 | 0.06 | 0.07 | 0.13

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LHCb collaboration

R. Aaij39, C. Abellán Beteta41, B. Adeva38, M. Adinolfi47, A. Affolder53, Z.
Ajaltouni5, S. Akar6, J. Albrecht10, F. Alessio39, M. Alexander52, S. Ali42,
G. Alkhazov31, P. Alvarez Cartelle54, A.A. Alves Jr58, S. Amato2, S. Amerio23,
Y. Amhis7, L. An3,40, L. Anderlini18, G. Andreassi40, M. Andreotti17,g, J.E.
Andrews59, R.B. Appleby55, O. Aquines Gutierrez11, F. Archilli39, P.
d’Argent12, A. Artamonov36, M. Artuso60, E. Aslanides6, G. Auriemma26,n, M.
Baalouch5, S. Bachmann12, J.J. Back49, A. Badalov37, C. Baesso61, W.
Baldini17,39, R.J. Barlow55, C. Barschel39, S. Barsuk7, W. Barter39, V.
Batozskaya29, V. Battista40, A. Bay40, L. Beaucourt4, J. Beddow52, F.
Bedeschi24, I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,k, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson39, J. Benton47, A.
Berezhnoy33, R. Bernet41, A. Bertolin23, M.-O. Bettler39, M. van Beuzekom42,
S. Bifani46, P. Billoir8, T. Bird55, A. Birnkraut10, A. Bizzeti18,i, T.
Blake49, F. Blanc40, J. Blouw11, S. Blusk60, V. Bocci26, A. Bondar35, N.
Bondar31,39, W. Bonivento16, S. Borghi55, M. Borisyak66, M. Borsato38, T.J.V.
Bowcock53, E. Bowen41, C. Bozzi17,39, S. Braun12, M. Britsch12, T. Britton60,
J. Brodzicka55, N.H. Brook47, E. Buchanan47, C. Burr55, A. Bursche41, J.
Buytaert39, S. Cadeddu16, R. Calabrese17,g, M. Calvi21,k, M. Calvo Gomez37,p,
P. Campana19, D. Campora Perez39, L. Capriotti55, A. Carbone15,e, G.
Carboni25,l, R. Cardinale20,j, A. Cardini16, P. Carniti21,k, L. Carson51, K.
Carvalho Akiba2, G. Casse53, L. Cassina21,k, L. Castillo Garcia40, M.
Cattaneo39, Ch. Cauet10, G. Cavallero20, R. Cenci24,t, M. Charles8, Ph.
Charpentier39, M. Chefdeville4, S. Chen55, S.-F. Cheung56, N. Chiapolini41, M.
Chrzaszcz41,27, X. Cid Vidal39, G. Ciezarek42, P.E.L. Clarke51, M.
Clemencic39, H.V. Cliff48, J. Closier39, V. Coco39, J. Cogan6, E. Cogneras5,
V. Cogoni16,f, L. Cojocariu30, G. Collazuol23,r, P. Collins39, A. Comerma-
Montells12, A. Contu39, A. Cook47, M. Coombes47, S. Coquereau8, G. Corti39, M.
Corvo17,g, B. Couturier39, G.A. Cowan51, D.C. Craik51, A. Crocombe49, M. Cruz
Torres61, S. Cunliffe54, R. Currie54, C. D’Ambrosio39, E. Dall’Occo42, J.
Dalseno47, P.N.Y. David42, A. Davis58, O. De Aguiar Francisco2, K. De Bruyn6,
S. De Capua55, M. De Cian12, J.M. De Miranda1, L. De Paula2, P. De Simone19,
C.-T. Dean52, D. Decamp4, M. Deckenhoff10, L. Del Buono8, N. Déléage4, M.
Demmer10, D. Derkach66, O. Deschamps5, F. Dettori39, B. Dey22, A. Di Canto39,
F. Di Ruscio25, H. Dijkstra39, S. Donleavy53, F. Dordei39, M. Dorigo40, A.
Dosil Suárez38, A. Dovbnya44, K. Dreimanis53, L. Dufour42, G. Dujany55, K.
Dungs39, P. Durante39, R. Dzhelyadin36, A. Dziurda27, A. Dzyuba31, S.
Easo50,39, U. Egede54, V. Egorychev32, S. Eidelman35, S. Eisenhardt51, U.
Eitschberger10, R. Ekelhof10, L. Eklund52, I. El Rifai5, Ch. Elsasser41, S.
Ely60, S. Esen12, H.M. Evans48, T. Evans56, M. Fabianska27, A. Falabella15, C.
Färber39, N. Farley46, S. Farry53, R. Fay53, D. Ferguson51, V. Fernandez
Albor38, F. Ferrari15, F. Ferreira Rodrigues1, M. Ferro-Luzzi39, S.
Filippov34, M. Fiore17,39,g, M. Fiorini17,g, M. Firlej28, C. Fitzpatrick40, T.
Fiutowski28, F. Fleuret7,b, K. Fohl39, P. Fol54, M. Fontana16, F.
Fontanelli20,j, D. C. Forshaw60, R. Forty39, M. Frank39, C. Frei39, M.
Frosini18, J. Fu22, E. Furfaro25,l, A. Gallas Torreira38, D. Galli15,e, S.
Gallorini23, S. Gambetta51, M. Gandelman2, P. Gandini56, Y. Gao3, J. García
Pardiñas38, J. Garra Tico48, L. Garrido37, D. Gascon37, C. Gaspar39, R.
Gauld56, L. Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck12, M.
Gersabeck55, T. Gershon49, Ph. Ghez4, S. Gianì40, V. Gibson48, O.G. Girard40,
L. Giubega30, V.V. Gligorov39, C. Göbel61, D. Golubkov32, A. Golutvin54,39, A.
Gomes1,a, C. Gotti21,k, M. Grabalosa Gándara5, R. Graciani Diaz37, L.A.
Granado Cardoso39, E. Graugés37, E. Graverini41, G. Graziani18, A. Grecu30, E.
Greening56, P. Griffith46, L. Grillo12, O. Grünberg64, B. Gui60, E.
Gushchin34, Yu. Guz36,39, T. Gys39, T. Hadavizadeh56, C. Hadjivasiliou60, G.
Haefeli40, C. Haen39, S.C. Haines48, S. Hall54, B. Hamilton59, X. Han12, S.
Hansmann-Menzemer12, N. Harnew56, S.T. Harnew47, J. Harrison55, J. He39, T.
Head40, V. Heijne42, A. Heister9, K. Hennessy53, P. Henrard5, L. Henry8, J.A.
Hernando Morata38, E. van Herwijnen39, M. Heß64, A. Hicheur2, D. Hill56, M.
Hoballah5, C. Hombach55, W. Hulsbergen42, T. Humair54, M. Hushchyn66, N.
Hussain56, D. Hutchcroft53, D. Hynds52, M. Idzik28, P. Ilten57, R.
Jacobsson39, A. Jaeger12, J. Jalocha56, E. Jans42, A. Jawahery59, M. John56,
D. Johnson39, C.R. Jones48, C. Joram39, B. Jost39, N. Jurik60, S. Kandybei44,
W. Kanso6, M. Karacson39, T.M. Karbach39,†, S. Karodia52, M. Kecke12, M.
Kelsey60, I.R. Kenyon46, M. Kenzie39, T. Ketel43, E. Khairullin66, B.
Khanji21,39,k, C. Khurewathanakul40, T. Kirn9, S. Klaver55, K. Klimaszewski29,
O. Kochebina7, M. Kolpin12, I. Komarov40, R.F. Koopman43, P. Koppenburg42,39,
M. Kozeiha5, L. Kravchuk34, K. Kreplin12, M. Kreps49, P. Krokovny35, F.
Kruse10, W. Krzemien29, W. Kucewicz27,o, M. Kucharczyk27, V. Kudryavtsev35, A.
K. Kuonen40, K. Kurek29, T. Kvaratskheliya32, D. Lacarrere39, G.
Lafferty55,39, A. Lai16, D. Lambert51, G. Lanfranchi19, C. Langenbruch49, B.
Langhans39, T. Latham49, C. Lazzeroni46, R. Le Gac6, J. van Leerdam42, J.-P.
Lees4, R. Lefèvre5, A. Leflat33,39, J. Lefrançois7, E. Lemos Cid38, O. Leroy6,
T. Lesiak27, B. Leverington12, Y. Li7, T. Likhomanenko66,65, M. Liles53, R.
Lindner39, C. Linn39, F. Lionetto41, B. Liu16, X. Liu3, D. Loh49, I.
Longstaff52, J.H. Lopes2, D. Lucchesi23,r, M. Lucio Martinez38, H. Luo51, A.
Lupato23, E. Luppi17,g, O. Lupton56, A. Lusiani24, F. Machefert7, F. Maciuc30,
O. Maev31, K. Maguire55, S. Malde56, A. Malinin65, G. Manca7, G. Mancinelli6,
P. Manning60, A. Mapelli39, J. Maratas5, J.F. Marchand4, U. Marconi15, C.
Marin Benito37, P. Marino24,39,t, J. Marks12, G. Martellotti26, M. Martin6, M.
Martinelli40, D. Martinez Santos38, F. Martinez Vidal67, D. Martins Tostes2,
L.M. Massacrier7, A. Massafferri1, R. Matev39, A. Mathad49, Z. Mathe39, C.
Matteuzzi21, A. Mauri41, B. Maurin40, A. Mazurov46, M. McCann54, J.
McCarthy46, A. McNab55, R. McNulty13, B. Meadows58, F. Meier10, M. Meissner12,
D. Melnychuk29, M. Merk42, E Michielin23, D.A. Milanes63, M.-N. Minard4, D.S.
Mitzel12, J. Molina Rodriguez61, I.A. Monroy63, S. Monteil5, M. Morandin23, P.
Morawski28, A. Mordà6, M.J. Morello24,t, J. Moron28, A.B. Morris51, R.
Mountain60, F. Muheim51, D. Müller55, J. Müller10, K. Müller41, V. Müller10,
M. Mussini15, B. Muster40, P. Naik47, T. Nakada40, R. Nandakumar50, A.
Nandi56, I. Nasteva2, M. Needham51, N. Neri22, S. Neubert12, N. Neufeld39, M.
Neuner12, A.D. Nguyen40, T.D. Nguyen40, C. Nguyen-Mau40,q, V. Niess5, R.
Niet10, N. Nikitin33, T. Nikodem12, A. Novoselov36, D.P. O’Hanlon49, A.
Oblakowska-Mucha28, V. Obraztsov36, S. Ogilvy52, O. Okhrimenko45, R.
Oldeman16,f, C.J.G. Onderwater68, B. Osorio Rodrigues1, J.M. Otalora
Goicochea2, A. Otto39, P. Owen54, A. Oyanguren67, A. Palano14,d, F.
Palombo22,u, M. Palutan19, J. Panman39, A. Papanestis50, M. Pappagallo52, L.L.
Pappalardo17,g, C. Pappenheimer58, W. Parker59, C. Parkes55, G. Passaleva18,
G.D. Patel53, M. Patel54, C. Patrignani20,j, A. Pearce55,50, A. Pellegrino42,
G. Penso26,m, M. Pepe Altarelli39, S. Perazzini15,e, P. Perret5, L.
Pescatore46, K. Petridis47, A. Petrolini20,j, M. Petruzzo22, E. Picatoste
Olloqui37, B. Pietrzyk4, M. Pikies27, D. Pinci26, A. Pistone20, A. Piucci12,
S. Playfer51, M. Plo Casasus38, T. Poikela39, F. Polci8, A. Poluektov49,35, I.
Polyakov32, E. Polycarpo2, A. Popov36, D. Popov11,39, B. Popovici30, C.
Potterat2, E. Price47, J.D. Price53, J. Prisciandaro38, A. Pritchard53, C.
Prouve47, V. Pugatch45, A. Puig Navarro40, G. Punzi24,s, W. Qian4, R.
Quagliani7,47, B. Rachwal27, J.H. Rademacker47, M. Rama24, M. Ramos Pernas38,
M.S. Rangel2, I. Raniuk44, N. Rauschmayr39, G. Raven43, F. Redi54, S.
Reichert55, A.C. dos Reis1, V. Renaudin7, S. Ricciardi50, S. Richards47, M.
Rihl39, K. Rinnert53,39, V. Rives Molina37, P. Robbe7,39, A.B. Rodrigues1, E.
Rodrigues55, J.A. Rodriguez Lopez63, P. Rodriguez Perez55, S. Roiser39, V.
Romanovsky36, A. Romero Vidal38, J. W. Ronayne13, M. Rotondo23, T. Ruf39, P.
Ruiz Valls67, J.J. Saborido Silva38, N. Sagidova31, B. Saitta16,f, V.
Salustino Guimaraes2, C. Sanchez Mayordomo67, B. Sanmartin Sedes38, R.
Santacesaria26, C. Santamarina Rios38, M. Santimaria19, E. Santovetti25,l, A.
Sarti19,m, C. Satriano26,n, A. Satta25, D.M. Saunders47, D. Savrina32,33, S.
Schael9, M. Schiller39, H. Schindler39, M. Schlupp10, M. Schmelling11, T.
Schmelzer10, B. Schmidt39, O. Schneider40, A. Schopper39, M. Schubiger40,
M.-H. Schune7, R. Schwemmer39, B. Sciascia19, A. Sciubba26,m, A. Semennikov32,
A. Sergi46, N. Serra41, J. Serrano6, L. Sestini23, P. Seyfert21, M. Shapkin36,
I. Shapoval17,44,g, Y. Shcheglov31, T. Shears53, L. Shekhtman35, V.
Shevchenko65, A. Shires10, B.G. Siddi17, R. Silva Coutinho41, L. Silva de
Oliveira2, G. Simi23,s, M. Sirendi48, N. Skidmore47, T. Skwarnicki60, E.
Smith56,50, E. Smith54, I.T. Smith51, J. Smith48, M. Smith55, H. Snoek42, M.D.
Sokoloff58,39, F.J.P. Soler52, F. Soomro40, D. Souza47, B. Souza De Paula2, B.
Spaan10, P. Spradlin52, S. Sridharan39, F. Stagni39, M. Stahl12, S. Stahl39,
S. Stefkova54, O. Steinkamp41, O. Stenyakin36, S. Stevenson56, S. Stoica30, S.
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S. Topp-Joergensen56, N. Torr56, E. Tournefier4, S. Tourneur40, K. Trabelsi40,
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Zhokhov32, L. Zhong3, V. Zhukov9, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
36Institute for High Energy Physics (IHEP), Protvino, Russia
37Universitat de Barcelona, Barcelona, Spain
38Universidad de Santiago de Compostela, Santiago de Compostela, Spain
39European Organization for Nuclear Research (CERN), Geneva, Switzerland
40Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
41Physik-Institut, Universität Zürich, Zürich, Switzerland
42Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
43Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
44NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
45Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
46University of Birmingham, Birmingham, United Kingdom
47H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
48Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
49Department of Physics, University of Warwick, Coventry, United Kingdom
50STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
51School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
52School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
53Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
54Imperial College London, London, United Kingdom
55School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
56Department of Physics, University of Oxford, Oxford, United Kingdom
57Massachusetts Institute of Technology, Cambridge, MA, United States
58University of Cincinnati, Cincinnati, OH, United States
59University of Maryland, College Park, MD, United States
60Syracuse University, Syracuse, NY, United States
61Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
62Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
63Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
64Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
65National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
66Yandex School of Data Analysis, Moscow, Russia, associated to 32
67Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
68Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 42

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
†Deceased