EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-102 LHCb-PAPER-2015-001 Aug 20, 2015

Measurement of the forward $Z$ boson

production cross-section

in $pp$ collisions at $\sqrt{s}$ = 7 $\mathrm{\,Te\kern-2.07413ptV}$

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

A measurement of the production cross-section for $Z$ bosons that decay to
muons is presented. The data were recorded by the LHCb detector during $pp$
collisions at a centre-of-mass energy of 7 $\mathrm{\,Te\kern-1.00006ptV}$,
and correspond to an integrated luminosity of 1.0 fb-1. The cross-section is
measured for muons in the pseudorapidity range
$2.0\nolinebreak<\nolinebreak\eta\nolinebreak<\nolinebreak 4.5$ with
transverse momenta $\mbox{$p_{\rm T}$}\nolinebreak>\nolinebreak
20{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The dimuon mass is restricted to
$60\nolinebreak<\nolinebreak M_{\mu^{+}\mu^{-}}\nolinebreak<\nolinebreak
120{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The measured cross-section is

$\sigma_{Z\rightarrow\mu^{+}\mu^{-}}=(76.0\pm 0.3\pm 0.5\pm 1.0\pm
1.3)\,\text{pb}$

where the uncertainties are due to the sample size, systematic effects, the
beam energy and the luminosity. This result is in good agreement with
theoretical predictions at next-to-next-to-leading order in perturbative
quantum chromodynamics. The cross-section is also measured differentially as a
function of kinematic variables of the $Z$ boson. Ratios of the production
cross-sections of electroweak bosons are presented using updated LHCb
measurements of $W$ boson production. A precise test of the Standard Model is
provided by the measurement of the ratio

$\frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}}+\sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}}}{\sigma_{Z\rightarrow\mu^{+}\mu^{-}}}=20.63\pm
0.09\pm 0.12\pm 0.05,$

where the uncertainty due to luminosity cancels.

Published in JHEP 08 (2015) 039

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

##  1 Introduction

Measurements of the total and differential cross-sections for the production
of $Z$ bosons in $pp$ collisions test the Standard Model (SM) and provide
constraints on parton density functions (PDFs) of the proton.111Throughout
this article $Z$ represents both resonant production of $Z$ bosons and off-
mass-shell photons. Theoretical predictions for these cross-sections are
available at next-to-next-to-leading order (NNLO) in perturbative quantum
chromodynamics (pQCD) [1, 2, 3, 4, 5]. The dominant uncertainty on these
predictions reflects the uncertainties on the PDFs, which vary as functions of
the kinematic variables studied. 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.

LHCb has measured the $Z$ boson production cross-section at $\sqrt{s}$= 7
$\mathrm{\,Te\kern-1.00006ptV}$ using decays to muon pairs in a data set
corresponding to 37 pb-1 [7], and using electron [8] and tau lepton [9] pairs
in a data set of 1.0 fb-1. Production cross-sections of $W$ bosons and the
$W^{+}$/$W^{-}$ cross-section ratio have been measured in the muon channel
[10] with the $1.0\nolinebreak\text{ fb}^{-1}$ data set. Similar measurements
have also been performed by the ATLAS [11] and CMS [12] collaborations.

The analysis described here is an update of the one described in Ref. [7],
using a total integrated luminosity of about 1.0 fb-1. This increases
statistical precision and allows better control of systematic uncertainties,
with the result that the total uncertainties on the measurements are
significantly reduced. Measurements are performed 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 $Z$ 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
in this article are referred to as the fiducial requirements. Total cross-
sections are presented as well as differential cross-sections as functions of
the $Z$ boson rapidity $y_{Z}$, $p_{T,Z}$ and $\phi^{*}_{Z}$. Here
$\phi^{*}_{Z}$ is defined as [13]

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

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 $\Delta\eta$.

The $W$ boson cross-sections given in Ref. [10] are re-evaluated using a more
precise determination of the event trigger efficiency. The cross-sections are
presented as a function of the $\eta$ of the muon from the $W$ boson decay.
The values presented here supersede those of Ref. [10].

This paper is organised as follows: Section 2 describes the LHCb detector;
Sections 3 and 4 detail the selection of $Z$ boson candidates, the $Z$ boson
cross-section definition and relevant sources of systematic uncertainty;
Section 5 presents the results and Section 6 concludes the paper. Appendices A
and B provide tables of differential cross-sections and correlations between
these measurements.

##  2 Detector and data set

The LHCb detector [14, 15] 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 [16], 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 [17] 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, 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
[18]. 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 [19]. 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 as the global event cut (GEC) in this article.

The measurement presented here is based on $pp$ collision data collected at a
centre-of-mass energy of 7 $\mathrm{\,Te\kern-1.00006ptV}$. The integrated
luminosity amounts to 975 $\pm$ 17 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 similar results,
which are combined to give the final luminosity estimate with an uncertainty
of $1.7\%$ [23]. This analysis uses the same data set as in Ref. [10].

Several samples of simulated data are produced to estimate contributions from
background processes, to cross-check efficiencies and to unfold data for
detector-related effects. The Pythia generator [24, 25], configured as in Ref.
[26] with the CTEQ6L1 [27, 28] parameterisation for the PDFs, is used to
simulate $b\bar{b}$, $c\bar{c}$, $WW$, $t\bar{t}$ and $Z$ production. All
generated events are passed through a detector simulation based on Geant4
[29], followed by LHCb-specific trigger emulation and event reconstruction.

The results of the analysis are compared to theoretical predictions calculated
with the Fewz [30, 31] generator at NNLO for the PDF sets ABM12 [32], CT10
[33], HERA1.5 [34], JR09 [35], MSTW08 [36], and NNPDF3.0 [37]. Comparisons are
also made to the ResBos [38, 39, 40] and Powheg [41] generators configured
with the CT10 PDF set. ResBos includes an approximate NNLO calculation, plus a
next-to-next-to-leading logarithm approximation for the resummation of the
soft gluon radiation. Powheg provides a next-to-leading order (NLO)
calculation interfaced to a parton shower, in this case performed by Herwig
[42, 43]. The results are also compared to the predictions from MC@NLO [44,
45], which is interfaced with different generators to simulate the parton
shower. Parton showering is performed using Herwig [42, 43], with different
values for the root mean-square-deviation of the intrinsic $k_{T}$, and
Herwiri [46, 47, 48], which is based on infrared-improved [49] DGLAP-CS [50,
51, 52, 53, 54, 55] theory. 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 [56]. Total uncertainties correspond to the PDF and
$\alpha_{s}$ uncertainties at 68.3$\%$ confidence level and scale
uncertainties, added in quadrature.

##  3 Event selection

Events considered in this analysis are selected by the muon trigger. At the
hardware stage, this trigger requires a muon with $\mbox{$p_{\rm
T}$}>1.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and imposes an upper limit of
600 hits in the SPD sub-detector. At the software stage, a muon with
$\mbox{$p_{\rm T}$}>10{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ is required. The
muon track must also satisfy additional track quality criteria. Candidate
events are selected by requiring a pair of well-reconstructed particles of
opposite charge, identified as muons, that also pass the fiducial requirements
[7]. In total, 58 466 $Z$ boson candidates are selected and their invariant
mass distribution is shown in Fig. 1.

Figure 1: Invariant mass of dimuon candidates.

The background contamination in the candidate sample is low. Five background
sources are investigated: decays of heavy flavour hadrons, hadron
misidentification, $Z\nolinebreak\rightarrow\nolinebreak\tau^{+}\tau^{-}$
decays, $t\bar{t}$ and $W^{+}W^{-}$ production. Unlike muons from signal,
muons arising from decays of heavy flavour hadrons are neither directly
produced at the primary interaction vertex, nor are they isolated particles.
Using the techniques from Ref. [7], the contribution from this background is
estimated from the data to be $227\pm 32$ events, which amounts to 0.4$\%$ of
the candidate sample. The contribution from hadrons that decay in flight or
have sufficient energy to traverse the calorimeters and be detected in the
muon stations is studied in randomly triggered data, as described in Ref. [7],
and determined to be $116\pm 45$ events, which is 0.2$\%$ of the candidate
sample. Other electroweak and QCD backgrounds are estimated using Pythia
simulation [25] and normalised to the measured total cross-sections for
$Z\rightarrow\tau^{+}\tau^{-}$ decays [57, 58], $t\bar{t}$ [59, 60] and
$W^{+}W^{-}$ [61, 62] production. The estimate for these sources is $66\pm 6$
events, or 0.1$\%$ of the candidate sample. In total, the background is
estimated to be $409\pm 56$ events, or 0.7$\%$ of the candidate sample.

The purity, defined to be the ratio of signal to total candidate events, is
$\rho$=0.993$\pm$0.002. It is assumed to be constant as a function of $y_{Z}$,
$p_{T,Z}$ and $\phi^{*}_{Z}$. A systematic uncertainty, discussed later, is
assigned to allow for possible inaccuracies in this assumption.

##  4 Cross-section measurement

Cross-sections are quoted in the kinematic range defined by the measurement
and are corrected for quantum electrodynamic (QED) final-state radiation (FSR)
in order to provide a consistent comparison with NLO and NNLO QCD predictions.
No corrections are applied for initial-state radiation, electroweak effects,
nor their interplay with QED effects. The cross-section in a given bin $i$ of
$y_{Z}$, $p_{T,Z}$ or $\phi^{*}_{Z}$, with both final-state muons inside the
fiducial region, is measured as

$\sigma_{Z\rightarrow\mu^{+}\mu^{-}}(i)=\frac{\rho}{\mathcal{L}}\ \frac{f_{\rm
FSR}(i)}{\varepsilon_{\rm
GEC}(i)}\sum_{j}U_{ij}\left(\sum_{k}\frac{1}{\varepsilon(\eta_{k}^{\mu^{+}},\eta_{k}^{\mu^{-}})}\right)_{j}.$
(2)

The indices $i$ and $j$ run over the bins of the variable under study. The
index $k$ runs over the candidates contributing to bin $j$. The total muon
reconstruction efficiency for an event is given by
$\varepsilon(\eta_{k}^{\mu^{+}},\eta_{k}^{\mu^{-}})$, which is dependent on
the pseudorapidity of the two muons. The matrix $U$ corrects the data for bin
migrations due to detector resolution effects. It is determined using an
unfolding procedure, which is described in Section 4.4. The efficiency of the
requirement on the number of SPD hits in the hardware trigger is denoted by
$\varepsilon_{\rm GEC}$. The correction factors for QED final-state radiation
are denoted by $f_{\rm FSR}(i)$ and are determined for each bin. The
integrated luminosity is denoted by $\mathcal{L}$. Though not entering the
expression for the cross-section, an uncertainty due to the beam energy is
assigned to all cross-sections. More detail on these individual components is
given below. Once the binned cross-sections are determined, they are summed to
give the total cross-section

$\sigma_{Z\rightarrow\mu^{+}\mu^{-}}=\sum_{i}\sigma_{Z\rightarrow\mu^{+}\mu^{-}}(i).$
(3)

The most precise estimate of the total cross-section is obtained by summing
the cross-sections as a function of rapidity, where uncertainties due to data
unfolding are negligible.

###  4.1 Muon reconstruction efficiencies

The data are corrected for efficiency losses due to track reconstruction, muon
identification, and trigger requirements. All efficiencies are determined from
data using the techniques detailed in Refs. [7, 8], where the track
reconstruction, muon identification, and muon trigger efficiencies are
obtained using tag-and-probe methods on the $Z$ resonance. The tag and 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 by the requirement for which the
efficiency is being measured. The efficiency is studied as a function of
several variables, which describe both the muon kinematics and the detector
occupancy. In this analysis the efficiency as a function of muon $\eta$ is
used. The efficiency in each bin of $\eta$ is defined as the fraction of tag-
and-probe candidate events where the probe satisfies a track reconstruction,
identification or trigger requirement.

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 efficiency depends on $\eta$ and varies between
89.5$\%$ and 98.5$\%$ with uncertainties between 0.4$\%$ and 1.9$\%$.

The muon identification efficiency is determined using probe tracks that are
reconstructed without using the muon system. The efficiency depends on $\eta$
and varies between 91.3$\%$ and 99.2$\%$ with uncertainties between 0.1$\%$
and 0.9$\%$.

The single-muon trigger efficiency is determined using reconstructed muons as
probes. The efficiency depends on $\eta$ and varies between 71.6$\%$ and
82.0$\%$ with uncertainties between 0.5$\%$ and 1.2$\%$. Since only one muon
candidate is required for the event to pass the trigger requirements, the
overall trigger efficiency for the analysis is about 95$\%$.

The efficiency to reconstruct any given event is taken to be the product of
the three individual efficiencies and determined on an event-by-event basis as
a function of muon $\eta$,

$\varepsilon(\mu^{+},\mu^{-})=\varepsilon_{\rm
trk}^{\mu^{+}}\cdot\varepsilon_{\rm trk}^{\mu^{-}}\cdot\varepsilon_{\rm
id}^{\mu^{+}}\cdot\varepsilon_{\rm id}^{\mu^{-}}\cdot\left(\varepsilon_{\rm
trg}^{\mu^{+}}+\varepsilon_{\rm trg}^{\mu^{-}}-\varepsilon_{\rm
trg}^{\mu^{+}}\cdot\varepsilon_{\rm trg}^{\mu^{-}}\right).$ (4)

In Equation 4, the efficiency $\varepsilon$ is written explicitly in terms of
the muon tracking ($\varepsilon_{\rm trk}$), identification ($\varepsilon_{\rm
id}$) and trigger ($\varepsilon_{\rm trg}$) efficiencies. The average
reconstruction efficiency for the analysis is about 85$\%$. Effects that
correlate the efficiency of the two muons are considered, but these are
negligible at the current level of precision.

###  4.2 GEC efficiency

The GEC efficiency is the efficiency of the SPD multiplicity limit at 600 hits
in the muon trigger. This efficiency is evaluated from data using two
independent methods. The first exploits the fact that the SPD multiplicities
of single $pp$ interactions are always below 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. [7]. 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.
[8]. Both methods give consistent results and $\varepsilon_{\rm
GEC}\nolinebreak=\nolinebreak(94.0\pm 0.2)\%$ is used in this analysis. The
central value is the estimate from the first method, while the difference
between the two estimates contributes to the uncertainty. This efficiency
depends linearly on $y_{Z}$ with about 2$\%$ variation across the full range.
A weaker dependence on both the $p_{T,Z}$ and $\phi^{*}_{Z}$ is also observed.
Corrections for these effects are made.

###  4.3 Final-state radiation

The FSR correction is taken to be the mean of the corrections calculated with
Herwig++ [63] and Pythia8 [25]. The corrections are tabulated in Appendix A
and are on average about 2.5$\%$.

###  4.4 Unfolding detector response

To correct for detector resolution effects, an unfolding is performed (matrix
$U$ of Equation 2) using LHCb simulation and the RooUnfold [64] software
package. The momentum resolution in the simulation is calibrated to the data.
The data are then unfolded using the iterative Bayesian approach proposed in
Ref. [65]. Other unfolding techniques [66, 67] give similar results.
Additionally, all unfolding methods are tested for model dependence using
underlying distributions from leading order Pythia [24, 25], leading order
Herwig++ [63], as well as NLO Powheg [41, 68, 69] showered with both Pythia
and Herwig using the Powheg matching scheme. The correction is on average
about 2$\%$ as a function of $p_{T,Z}$, while it is significantly less as a
function of $\phi^{*}_{Z}$. Only the $p_{T,Z}$ and $\phi^{*}_{Z}$
distributions are unfolded. Since $y_{Z}$ is well measured, no unfolding is
performed and $U$ is the identity matrix in this case.

###  4.5 Systematic uncertainties

Sources of systematic uncertainty and their effect on the total cross-section
measurement are summarised in Table 1.222Many of the systematic uncertainties
quoted here have a statistical component. The statistical uncertainty quoted
on the measurement is due to the number of observed $Z$ candidates. In the
case of unfolded measurements, the statistical uncertainty is provided by the
covariance matrix returned by RooUnfold. The measured cross-sections as a
function of $p_{T,Z}$ and $\phi^{*}_{Z}$ have additional systematic
uncertainties due to unfolding.

Table 1: Contributions to the relative uncertainty on the total $Z$ boson cross-section. Source | Uncertainty ($\%$)
---|---
Statistical | $0.39$
Trigger efficiency | $0.07$
Identification efficiency | $0.23$
Tracking efficiency | $0.53$
FSR | $0.11$
Purity | $0.22$
GEC efficiency | $0.26$
Systematic | $0.68$
Beam energy | $1.25$
Luminosity | $1.72$
Total | $2.27$

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
separately. The covariance matrices for each source are added and the diagonal
elements of the result determine the total systematic uncertainty due to
reconstruction efficiencies. These vary between 0.5 and 2.0$\%$ on the
differential cross-section measurements.

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 and
Herwig++ estimates and the second is half of the difference between their
central values. The latter dominates, with the uncertainties on the
differential cross-sections varying between 0.3 and 3$\%$.

The systematic uncertainty on the purity is determined from the number of
candidate and background events. In addition, an uncertainty based on 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 total uncertainties on the
differential cross-section measurements due to variations in purity are
typically less than 1$\%$.

The GEC efficiency is determined in each bin of $y_{Z}$, $p_{T,Z}$ and
$\phi^{*}_{Z}$. The systematic uncertainty is the sum in quadrature of a
component due to the available sample size in each bin and a component due to
the 0.2$\%$ uncertainty on the integrated number, as determined in Section
4.2. This varies between 0.4 and 4$\%$ across the differential measurements.

The systematic uncertainty due to unfolding is estimated by the differences
between the differential cross-sections using Bayesian and matrix inversion
unfolding techniques. The typical size is $1.5\%$.

The measurement is specified at centre-of-mass energy $\sqrt{s}$ = 7
$\mathrm{\,Te\kern-1.00006ptV}$. The beam energy, and consequently the centre-
of-mass energy, is known to 0.65$\%$ [70]. The sensitivity of the cross-
section to the centre-of-mass energy is studied using DYNNLO [71] and a
systematic uncertainty of 1.25$\%$ is assigned.

##  5 Results

###  5.1 _Z_ boson production cross-section

The measured rapidity distribution as shown in Fig. 2 is compared to the
prediction from Fewz [30, 31] with six different PDF sets. To compare the
shapes of the differential cross-sections, measurements and predictions are
normalised to the total fiducial cross-section. The normalised differential
cross-sections are shown in Figs. 2, 3 and 4. The measurements are compared to
the predictions from ResBos [38, 39, 40] and Powheg [41] where events are
interfaced with a parton shower that is simulated using Herwig [42, 43]. The
$p_{T,Z}$ and $\phi^{*}_{Z}$ distributions are well described by ResBos and
Powheg, with the central values overestimating the data slightly at low
$\phi^{*}_{Z}$ and underestimating slightly at high $\phi^{*}_{Z}$.
Comparisons to MC@NLO \+ Herwiri and MC@NLO \+ Herwig are shown in Figs. 5 and
6. Here Herwig is configured with the root mean-square-deviation of the
intrinsic $k_{T}$ distribution set to 0${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
in one instance and 2.2${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in another. The
predictions straddle the measurement at low $p_{T,Z}$ and $\phi^{*}_{Z}$. The
high $p_{T,Z}$ and $\phi^{*}_{Z}$ tails are underestimated.

The total inclusive cross-section for $Z\rightarrow\mu^{+}\mu^{-}$ production
for muons with $\mbox{$p_{\rm T}$}\nolinebreak>\nolinebreak
20\nolinebreak{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in the pseudorapidity
region $2.0<\eta<4.5$ and the dimuon invariant mass range
$60<M_{\mu^{+}\mu^{-}}<120{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ is
measured to be

$\sigma_{Z\rightarrow\mu^{+}\mu^{-}}=(76.0\pm 0.3\pm 0.5\pm 1.0\pm
1.3)\,\text{pb},$

where the first uncertainty is statistical, the second systematic, the third
is due to the beam energy and the fourth is due to the luminosity. The upper
plot of Fig. 7 shows agreement between this measurement and NNLO predictions
given by Fewz configured with various PDF sets. The measurement also agrees
with the measurements of the $Z$ boson production cross-section performed in
the electron [8] and tau lepton [9] channels but with a significantly smaller
uncertainty. All binned cross-sections are detailed in Tables 3, 4 and 5 of
Appendix A.

###  5.2 Ratios of electroweak boson production cross-sections

The cross-section ratios are defined for muons with $\mbox{$p_{\rm
T}$}>20{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $2.0<\eta<4.5$ and, in the case
of the $Z$ boson cross-section, a dimuon invariant mass between 60 and
120$\nolinebreak{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The ratio of $W$
boson to $Z$ boson production is defined as

$R_{\it
WZ}=\frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}}+\sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}}}{\sigma_{Z\rightarrow\mu^{+}\mu^{-}}}.$
(5)

The separate ratios of $W^{+}$ and $W^{-}$ to $Z$ boson production cross-
sections are defined as

$R_{\it
W^{\pm}Z}=\frac{\sigma_{W^{\pm}\rightarrow\mu^{\pm}\nu_{\mu}}}{\sigma_{Z\rightarrow\mu^{+}\mu^{-}}},$
(6)

while the $W$ boson cross-section ratio is defined as

$R_{\it
W}=\frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}}}{\sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}}}.$
(7)

Many sources of systematic uncertainty cancel or are reduced in the ratios. As
the data sets are identical, the largest single source of uncertainty on the
individual cross-sections, due to the luminosity determination, is removed.
The trigger used to select both samples is identical and most of the
uncertainty on the determination of the trigger efficiency cancels. In
particular, the GEC is common to both the $W$ and $Z$ boson analyses and it is
expected that the size of the efficiency correction is similar for $W$ and $Z$
events. Cross-checks in data and simulation support this assumption with a
precision of approximately 0.3$\%$, which is included as a systematic
uncertainty. The GEC efficiency was determined for the previous $W$ boson
measurement [10] to be $(95.9\pm 1.1)\%$, whereas an improved precision of
$(94.0\pm 0.2)\%$ is obtained in the current analysis. Consequently, the $W$
boson cross-section results are updated to benefit from the more precise
value. These results are listed in Tables 6, 7 and 8 of Appendix A, along with
the muon charge ratios and asymmetries, and supersede those in Ref. [10]. The
uncertainties on the tracking and muon identification partially cancel in the
ratios of $W$ and $Z$ bosons. The uncertainty on the $W^{+}(W^{-})$ cross-
section due to beam energy is 1.06(0.91)$\%$ and most of this uncertainty also
cancels in the ratios. The uncertainties on the purities of the $W$ and $Z$
boson selections are uncorrelated. The FSR uncertainties are taken to be
uncorrelated. The sources of uncertainty contributing to the determination of
the ratios are summarised in Table 2.

Table 2: Contributions to the relative uncertainty on the electroweak boson cross-section ratios. Source | Uncertainty ($\%$)
---|---
| $R_{\it WZ}$ | $R_{\it W^{+}Z}$ | $R_{\it W^{-}Z}$ | $R_{\it W}$
Statistical | $0.45$ | $0.48$ | $0.50$ | $0.38$
Trigger efficiency | $0.15$ | $0.16$ | $0.13$ | $0.07$
Identification efficiency | $0.12$ | $0.12$ | $0.12$ | $0.03$
Tracking efficiency | $0.24$ | $0.23$ | $0.26$ | $0.08$
FSR | $0.16$ | $0.21$ | $0.17$ | $0.21$
Purity | $0.41$ | $0.49$ | $0.55$ | $0.62$
GEC efficiency | $0.27$ | $0.28$ | $0.29$ | $0.18$
Systematic | $0.60$ | $0.67$ | $0.72$ | $0.69$
Beam energy | $0.26$ | $0.19$ | $0.34$ | $0.15$
Total | $0.79$ | $0.85$ | $0.94$ | $0.80$

The dominant uncertainties on the ratios are due to the purity and the size of
the sample. The correlation coefficients used in the uncertainty calculations
are tabulated in Appendix B.

The updated $W^{+}$ boson cross-section is

$\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}}=(878.0\pm 2.1\pm 6.7\pm 9.3\pm
15.0)\hskip 5.69046pt\text{pb},$

where the uncertainties are due to the sample size, systematic effects, the
beam energy and the luminosity determination. The updated $W^{-}$ boson cross-
section is

$\sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}}=(689.5\pm 2.0\pm 5.3\pm
6.3\pm 11.8)\hskip 5.69046pt\text{pb}.$

These measurements are in good agreement with the predictions of NNLO pQCD, as
shown in Fig. 7. Using the $Z$ boson cross-section from Section 5.1,
electroweak boson cross-section measurements and theoretical predictions, with
different parameterisations of the PDFs, are compared in Fig. 8, with contours
corresponding to the 68.3$\%$ confidence level.

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

$R_{\it WZ}=20.63\pm 0.09\pm 0.12\pm 0.05,$

where the first uncertainty is statistical, the second is systematic and the
third is due to the beam energy. The charged $W$ to $Z$ boson cross-section
ratios are measured as

$\displaystyle R_{\it W^{+}Z}$ $\displaystyle=11.56\pm 0.06\pm 0.08\pm 0.02,$
$\displaystyle R_{\it W^{-}Z}$ $\displaystyle=\phantom{0}9.07\pm 0.05\pm
0.07\pm 0.03,$

while the $W$ boson cross-section ratio is measured as

$R_{\it W}=1.274\pm 0.005\pm 0.009\pm 0.002.$

These measurements, as well as their predictions, are displayed in Fig. 9. For
$R_{\it WZ}$ and $R_{\it W^{+}Z}$, the data are well described by HERA1.5 and
JR09, while the values from CT10, MSTW08, NNPDF3.0 and ABM12 are larger than
those measured. All PDF sets show good agreement for $R_{\it W^{-}Z}$. As
previously reported [10], all PDF sets except ABM12 show good agreement for
$R_{\it W}$. The $R_{\it WZ}$ and $R_{\it W}$ ratios are measured with a
fractional uncertainty of $0.8\%$, which is similar both to the precision due
to the PDFs on the individual theoretical predictions and to the spread
between the predictions. Considering the spread in the different predictions,
the experimental measurements are in good agreement with SM predictions and
can be used to improve the determination of the PDFs.

(a)
(b)

Figure 2:  (a) Differential cross-section as a function of $y_{Z}$ compared
with the prediction of Fewz configured with various PDF sets. Different
predictions are displaced horizontally for visibility. (b) Normalised
differential cross-section as a function of $y_{Z}$ compared to the
predictions of ResBos and Powheg \+ Herwig. The shaded (yellow) bands indicate
the statistical and total uncertainties on the measurements, which are
symmetric about the central value.

(a)
(b)

Figure 3:  Normalised differential cross-section as a function of $p_{T,Z}$ on
(a) logarithmic and (b) linear scales. The shaded (yellow) bands indicate the
statistical and total uncertainties on the measurements, which are symmetric
about the central value. The measurements are compared to the predictions of
ResBos and Powheg \+ Herwig.

(a)
(b)

Figure 4:  Normalised differential cross-section as a function of
$\phi^{*}_{Z}$ on (a) logarithmic and (b) linear scales. The shaded (yellow)
bands indicate the statistical and total uncertainties on the measurements,
which are symmetric about the central value. The measurements are compared to
the predictions of ResBos and Powheg \+ Herwig.

(a)
(b)

Figure 5:  Normalised differential cross-section as a function of $p_{T,Z}$ on
(a) logarithmic and (b) linear scales. The shaded (yellow) bands indicate the
statistical and total uncertainties on the measurements, which are symmetric
about the central value. The measurements are compared to MC@NLO \+ Herwig
(HW) and MC@NLO \+ Herwiri (HERWIRI). Herwig is configured with two choices of
the root mean-square-deviation of the intrinsic $k_{T}$ distribution, 0 and
2.2 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

(a)
(b)

Figure 6:  Normalised differential cross-section as a function of
$\phi^{*}_{Z}$ on (a) logarithmic and (b) linear scales. The shaded (yellow)
bands indicate the statistical and total uncertainties on the measurements,
which are symmetric about the central value. The measurements are compared to
MC@NLO \+ Herwig (HW) and MC@NLO \+ Herwiri (HERWIRI). Herwig is configured
with two choices of the root mean-square-deviation of the intrinsic $k_{T}$
distribution, 0 and 2.2 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.  Figure 7:
LHCb measurements of electroweak boson production cross-sections compared to
NNLO pQCD as implemented by the Fewz generator using various PDF sets. The
shaded (yellow) bands indicate the statistical and total uncertainties on the
measurements, which are symmetric about the central value.  Figure 8:  Two
dimensional plots of electroweak boson cross-sections compared to NNLO
predictions for various parameterisations of the PDFs. The outer, shaded
(yellow) ellipse corresponds to the total uncertainty on the measurements. The
inner, shaded (purple) ellipse excludes the beam energy and luminosity
uncertainties. The uncertainty on the theoretical predictions corresponds to
the PDF uncertainty only. All ellipses correspond to uncertainties at 68.3$\%$
confidence level.  Figure 9: Ratios of electroweak boson production $R_{\it
W^{+}Z}$, $R_{\it W^{-}Z}$, $R_{\it WZ}$, $R_{\it W}$, compared to various
theoretical predictions. The shaded (yellow) bands indicate the statistical
and total uncertainties on the measurements, which are symmetric about the
central value.

##  6 Conclusions

A measurement of the forward $Z$ boson production cross-section at $\sqrt{s}$
= 7 $\mathrm{\,Te\kern-1.00006ptV}$ is presented, where the $Z$ bosons are
reconstructed in the decay $Z\rightarrow\mu^{+}\mu^{-}$. The total cross-
section in the fiducial range of the selection is in agreement with NNLO pQCD
calculations. Normalised differential cross-sections as a function of $y_{Z}$,
$\phi^{*}_{Z}$ and $p_{T,Z}$ are compared to the predictions of various
generators. The increased precision on the determination of the event trigger
efficiency motivates a re-evaluation of the recently measured $W$ boson
production cross-section. These are presented here and supersede the values
given in Ref. [10]. Combining the $Z$ boson cross-section with updated $W$
boson cross-sections measured in a similar fiducial volume allows for
precision measurements of electroweak boson cross-section ratios. In
particular, the $W$ to $Z$ boson ratio is determined with a relative precision
of $0.8\%$. The measured ratios are consistent with SM predictions but are
sensitive to the particular choice of PDF. Consequently, these results are
expected to provide significant constraints on PDFs.

## Acknowledgements

We thank B.F.L. Ward for providing MC@NLO \+ Herwig and MC@NLO \+ Herwiri
predictions. 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, HGF 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). The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). 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 EPLANET,
Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de
Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR
(Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for
the Exhibition of 1851 (United Kingdom).

Appendices

##  Appendix A Cross-sections

Table 3: Inclusive differential cross-sections for $Z$ boson production as a function of $y_{Z}$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. No candidates are observed in the 4.250 – 4.500 bin. $y_{Z}$ |  $\sigma_{Z}$ [pb] | $f_{\rm FSR}$
---|---|---
2.000 – 2.125 | 0.969 $\pm$ 0.039 $\pm$ 0.032 $\pm$ 0.012 $\pm$ 0.017 | 1.050$\pm$0.020
2.125 – 2.250 | 2.840 $\pm$ 0.063 $\pm$ 0.050 $\pm$ 0.036 $\pm$ 0.049 | 1.032$\pm$0.008
2.250 – 2.375 | 4.428 $\pm$ 0.077 $\pm$ 0.078 $\pm$ 0.055 $\pm$ 0.076 | 1.027$\pm$0.006
2.375 – 2.500 | 5.823 $\pm$ 0.088 $\pm$ 0.060 $\pm$ 0.073 $\pm$ 0.100 | 1.026$\pm$0.004
2.500 – 2.625 | 6.877 $\pm$ 0.095 $\pm$ 0.068 $\pm$ 0.086 $\pm$ 0.118 | 1.025$\pm$0.004
2.625 – 2.750 | 7.669 $\pm$ 0.100 $\pm$ 0.069 $\pm$ 0.096 $\pm$ 0.132 | 1.026$\pm$0.004
2.750 – 2.875 | 8.306 $\pm$ 0.104 $\pm$ 0.070 $\pm$ 0.104 $\pm$ 0.143 | 1.026$\pm$0.003
2.875 – 3.000 | 8.241 $\pm$ 0.103 $\pm$ 0.066 $\pm$ 0.103 $\pm$ 0.142 | 1.025$\pm$0.003
3.000 – 3.125 | 7.783 $\pm$ 0.099 $\pm$ 0.059 $\pm$ 0.097 $\pm$ 0.134 | 1.026$\pm$0.003
3.125 – 3.250 | 7.094 $\pm$ 0.096 $\pm$ 0.058 $\pm$ 0.089 $\pm$ 0.122 | 1.028$\pm$0.004
3.250 – 3.375 | 5.894 $\pm$ 0.087 $\pm$ 0.049 $\pm$ 0.074 $\pm$ 0.101 | 1.026$\pm$0.004
3.375 – 3.500 | 4.160 $\pm$ 0.073 $\pm$ 0.041 $\pm$ 0.052 $\pm$ 0.072 | 1.027$\pm$0.005
3.500 – 3.625 | 2.896 $\pm$ 0.061 $\pm$ 0.030 $\pm$ 0.036 $\pm$ 0.050 | 1.026$\pm$0.005
3.625 – 3.750 | 1.741 $\pm$ 0.047 $\pm$ 0.023 $\pm$ 0.022 $\pm$ 0.030 | 1.021$\pm$0.007
3.750 – 3.875 | 0.825 $\pm$ 0.032 $\pm$ 0.014 $\pm$ 0.010 $\pm$ 0.014 | 1.025$\pm$0.010
3.875 – 4.000 | 0.321 $\pm$ 0.020 $\pm$ 0.008 $\pm$ 0.004 $\pm$ 0.006 | 1.011$\pm$0.015
4.000 – 4.250 | 0.115 $\pm$ 0.013 $\pm$ 0.006 $\pm$ 0.001 $\pm$ 0.002 | 1.018$\pm$0.033
4.250 – 4.500 | $-$ | $-$
Table 4: Inclusive differential cross-sections for $Z$ boson production as a function of $p_{T,Z}$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. $p_{T,Z}[{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}]$ |  $\sigma_{Z}$ [pb] | $f_{\rm FSR}$
---|---|---
0.0 – 2.2 | 6.454 $\pm$ 0.105$\pm$ 0.129 $\pm$ 0.081 $\pm$ 0.111 | 1.090$\pm$0.006
2.2 – 3.4 | 6.520 $\pm$ 0.106$\pm$ 0.150 $\pm$ 0.081 $\pm$ 0.112 | 1.080$\pm$0.004
3.4 – 4.6 | 6.209 $\pm$ 0.102$\pm$ 0.221 $\pm$ 0.078 $\pm$ 0.107 | 1.063$\pm$0.004
4.6 – 5.8 | 5.868 $\pm$ 0.099$\pm$ 0.208 $\pm$ 0.073 $\pm$ 0.101 | 1.049$\pm$0.004
5.8 – 7.2 | 5.749 $\pm$ 0.098$\pm$ 0.154 $\pm$ 0.072 $\pm$ 0.099 | 1.034$\pm$0.004
7.2 – 8.7 | 5.607 $\pm$ 0.098$\pm$ 0.083 $\pm$ 0.070 $\pm$ 0.096 | 1.021$\pm$0.004
8.7 – 10.5 | 5.637 $\pm$ 0.098$\pm$ 0.054 $\pm$ 0.070 $\pm$ 0.097 | 1.002$\pm$0.004
10.5 – 12.8 | 5.524 $\pm$ 0.096$\pm$ 0.081 $\pm$ 0.069 $\pm$ 0.095 | 0.996$\pm$0.004
12.8 – 15.4 | 5.158 $\pm$ 0.092$\pm$ 0.067 $\pm$ 0.064 $\pm$ 0.089 | 0.984$\pm$0.005
15.4 – 19.0 | 4.963 $\pm$ 0.087$\pm$ 0.053 $\pm$ 0.062 $\pm$ 0.085 | 0.978$\pm$0.005
19.0 – 24.5 | 5.517 $\pm$ 0.088$\pm$ 0.055 $\pm$ 0.069 $\pm$ 0.095 | 0.985$\pm$0.004
24.5 – 34.0 | 5.465 $\pm$ 0.085$\pm$ 0.067 $\pm$ 0.068 $\pm$ 0.094 | 1.013$\pm$0.004
34.0 – 63.0 | 5.789 $\pm$ 0.085$\pm$ 0.076 $\pm$ 0.072 $\pm$ 0.100 | 1.038$\pm$0.004
63.0 – 270.0 | 1.516 $\pm$ 0.043$\pm$ 0.044 $\pm$ 0.019 $\pm$ 0.026 | 1.060$\pm$0.007
Table 5: Inclusive differential cross-sections for $Z$ boson production as a function of $\phi^{*}_{Z}$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. $\phi^{*}_{Z}$ |  $\sigma_{Z}$ [pb] | $f_{\rm FSR}$
---|---|---
0.00 – 0.01 |  8.549 $\pm$ 0.099 $\pm$ 0.088 $\pm$ 0.107 $\pm$ 0.147 | 1.034$\pm$0.004
0.01 – 0.02 |  7.805 $\pm$ 0.096 $\pm$ 0.106 $\pm$ 0.098 $\pm$ 0.134 | 1.035$\pm$0.003
0.02 – 0.03 |  7.051 $\pm$ 0.091 $\pm$ 0.083 $\pm$ 0.088 $\pm$ 0.121 | 1.034$\pm$0.004
0.03 – 0.05 | 11.362 $\pm$ 0.114 $\pm$ 0.108 $\pm$ 0.142 $\pm$ 0.195 | 1.029$\pm$0.003
0.05 – 0.07 |  8.124 $\pm$ 0.097 $\pm$ 0.120 $\pm$ 0.102 $\pm$ 0.140 | 1.026$\pm$0.003
0.07 – 0.10 |  8.436 $\pm$ 0.097 $\pm$ 0.074 $\pm$ 0.105 $\pm$ 0.145 | 1.021$\pm$0.003
0.10 – 0.15 |  8.611 $\pm$ 0.098 $\pm$ 0.131 $\pm$ 0.108 $\pm$ 0.148 | 1.020$\pm$0.003
0.15 – 0.20 |  4.819 $\pm$ 0.073 $\pm$ 0.092 $\pm$ 0.060 $\pm$ 0.083 | 1.018$\pm$0.004
0.20 – 0.30 |  5.206 $\pm$ 0.076 $\pm$ 0.058 $\pm$ 0.065 $\pm$ 0.090 | 1.019$\pm$0.004
0.30 – 0.40 |  2.541 $\pm$ 0.054 $\pm$ 0.051 $\pm$ 0.032 $\pm$ 0.044 | 1.022$\pm$0.006
0.40 – 0.60 |  2.018 $\pm$ 0.048 $\pm$ 0.060 $\pm$ 0.025 $\pm$ 0.035 | 1.024$\pm$0.007
0.60 – 0.80 |  0.755 $\pm$ 0.029 $\pm$ 0.035 $\pm$ 0.009 $\pm$ 0.013 | 1.029$\pm$0.011
0.80 – 1.20 |  0.457 $\pm$ 0.023 $\pm$ 0.018 $\pm$ 0.006 $\pm$ 0.008 | 1.025$\pm$0.014
1.20 – 2.00 |  0.166 $\pm$ 0.014 $\pm$ 0.011 $\pm$ 0.002 $\pm$ 0.003 | 1.030$\pm$0.023
2.00 – 4.00 |  0.045 $\pm$ 0.008 $\pm$ 0.017 $\pm$ 0.001 $\pm$ 0.001 | 1.031$\pm$0.041

Table 6: Inclusive differential cross-sections for $W^{+}$ (left) and $W^{-}$ (right) boson production as a function of muon $\eta$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. These supersede the results in Ref. [10]. $\eta^{\mu}$ |  $\sigma_{{W^{+}}}$ [pb] | $f_{\rm FSR}^{{W^{+}}}$ |  $\sigma_{{W^{-}}}$ [pb] | $f_{\rm FSR}^{{W^{-}}}$
---|---|---|---|---
2.00 – 2.25 | $192.2\pm 1.2\pm 3.5\pm 2.0\pm 3.3$ | $1.016\pm 0.004$ | $111.1\pm 0.9\pm 2.1\pm 1.0\pm 1.9$ | $1.019\pm 0.003$
2.25 – 2.50 | $178.8\pm 0.9\pm 3.1\pm 1.9\pm 3.1$ | $1.018\pm 0.004$ | $104.9\pm 0.7\pm 1.9\pm 1.0\pm 1.8$ | $1.015\pm 0.003$
2.50 – 2.75 | $154.3\pm 0.8\pm 2.1\pm 1.6\pm 2.6$ | $1.025\pm 0.005$ | $\phantom{0}96.1\pm 0.7\pm 1.3\pm 0.9\pm 1.6$ | $1.010\pm 0.003$
2.75 – 3.00 | $122.8\pm 0.7\pm 1.6\pm 1.3\pm 2.1$ | $1.015\pm 0.004$ | $\phantom{0}88.4\pm 0.7\pm 1.5\pm 0.8\pm 1.5$ | $1.007\pm 0.002$
3.00 – 3.25 | $\phantom{0}94.3\pm 0.6\pm 1.3\pm 1.0\pm 1.6$ | $1.021\pm 0.005$ | $\phantom{0}80.6\pm 0.6\pm 1.4\pm 0.7\pm 1.4$ | $1.009\pm 0.003$
3.25 – 3.50 | $\phantom{0}61.6\pm 0.5\pm 0.9\pm 0.7\pm 1.1$ | $1.015\pm 0.005$ | $\phantom{0}68.6\pm 0.6\pm 1.5\pm 0.6\pm 1.2$ | $1.017\pm 0.005$
3.50 – 4.00 | $\phantom{0}60.0\pm 0.5\pm 0.7\pm 0.6\pm 1.0$ | $1.024\pm 0.005$ | $\phantom{0}95.9\pm 0.7\pm 1.2\pm 0.9\pm 1.6$ | $1.012\pm 0.005$
4.00 – 4.50 | $\phantom{0}14.3\pm 0.4\pm 0.4\pm 0.2\pm 0.2$ | $1.021\pm 0.005$ | $\phantom{0}43.8\pm 0.8\pm 1.2\pm 0.4\pm 0.7$ | $1.000\pm 0.000$

Table 7: $W^{+}$ to $W^{-}$ boson production cross-section ratios as a function of muon $\eta$. Uncertainties are due to the sample size, systematic effects and the beam energy. These supersede the results in Ref. [10]. $\eta^{\mu}$ | $R_{W}$
---|---
2.00 – 2.25 | $1.730\pm 0.018\pm 0.030\pm 0.003$
2.25 – 2.50 | $1.706\pm 0.015\pm 0.040\pm 0.003$
2.50 – 2.75 | $1.606\pm 0.014\pm 0.021\pm 0.002$
2.75 – 3.00 | $1.388\pm 0.013\pm 0.024\pm 0.002$
3.00 – 3.25 | $1.169\pm 0.012\pm 0.021\pm 0.002$
3.25 – 3.50 | $0.898\pm 0.010\pm 0.025\pm 0.001$
3.50 – 4.00 | $0.626\pm 0.007\pm 0.006\pm 0.001$
4.00 – 4.50 | $0.328\pm 0.011\pm 0.011\pm 0.000$
Table 8: Lepton charge asymmetries as a function of muon $\eta$. Uncertainties are due to the sample size, systematic effects and the beam energy. These supersede the results in Ref. [10]. $\eta^{\mu}$ |  $A_{\mu}$ [%]
---|---
2.00 – 2.25 |  $-$$26.74\pm 0.48\pm 0.82\pm 0.07$
2.25 – 2.50 |  $-$$26.08\pm 0.41\pm 1.09\pm 0.07$
2.50 – 2.75 |  $-$$23.25\pm 0.42\pm 0.60\pm 0.07$
2.75 – 3.00 |  $-$$16.26\pm 0.46\pm 0.84\pm 0.07$
3.00 – 3.25 |  $-0$$7.81\pm 0.50\pm 0.90\pm 0.08$
3.25 – 3.50 |  $0$$-5.37\pm 0.57\pm 1.35\pm 0.08$
3.50 – 4.00 | $-23.04\pm 0.52\pm 0.49\pm 0.07$
4.00 – 4.50 | $-50.65\pm 1.22\pm 1.30\pm 0.06$

##  Appendix B Correlation Matrices

Table 9: Correlation coefficients of differential cross-section measurements
as a function of $y_{Z}$. The 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 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.125–2.25 | 0.18 | 1 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.25–2.375 | 0.14 | 0.19 | 1 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.375–2.5 | 0.14 | 0.19 | 0.18 | 1 |  |  |  |  |  |  |  |  |  |  |  |  |  |
2.5–2.625 | 0.13 | 0.18 | 0.16 | 0.19 | 1 |  |  |  |  |  |  |  |  |  |  |  |  |
2.625–2.75 | 0.12 | 0.16 | 0.15 | 0.18 | 0.18 | 1 |  |  |  |  |  |  |  |  |  |  |  |
2.75–2.875 | 0.11 | 0.15 | 0.14 | 0.17 | 0.17 | 0.18 | 1 |  |  |  |  |  |  |  |  |  |  |
2.875–3 | 0.10 | 0.13 | 0.13 | 0.16 | 0.16 | 0.17 | 0.17 | 1 |  |  |  |  |  |  |  |  |  |
3–3.125 | 0.09 | 0.12 | 0.12 | 0.14 | 0.15 | 0.15 | 0.16 | 0.16 | 1 |  |  |  |  |  |  |  |  |
3.125–3.25 | 0.08 | 0.1 | 0.10 | 0.12 | 0.13 | 0.14 | 0.14 | 0.14 | 0.14 | 1 |  |  |  |  |  |  |  |
3.25–3.375 | 0.06 | 0.08 | 0.08 | 0.11 | 0.11 | 0.12 | 0.12 | 0.13 | 0.13 | 0.13 | 1 |  |  |  |  |  |  |
3.375–3.5 | 0.05 | 0.06 | 0.06 | 0.08 | 0.09 | 0.09 | 0.10 | 0.10 | 0.11 | 0.11 | 0.11 | 1 |  |  |  |  |  |
3.5–3.625 | 0.04 | 0.05 | 0.05 | 0.06 | 0.07 | 0.08 | 0.08 | 0.09 | 0.09 | 0.10 | 0.10 | 0.10 | 1 |  |  |  |  |
3.625–3.75 | 0.03 | 0.04 | 0.03 | 0.04 | 0.05 | 0.06 | 0.06 | 0.07 | 0.07 | 0.08 | 0.09 | 0.08 | 0.08 | 1 |  |  |  |
3.75–3.875 | 0.02 | 0.03 | 0.02 | 0.03 | 0.03 | 0.04 | 0.04 | 0.05 | 0.05 | 0.06 | 0.06 | 0.06 | 0.06 | 0.06 | 1 |  |  |
3.875–4 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | 0.03 | 1 |  |
4–4.25 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.03 | 0.03 | 0.02 | 0.02 | 1 |
4.25–4.5 | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$

Table 10: Correlation coefficients of differential cross-section measurements
as a function of $p_{T,Z}$. The beam energy and luminosity uncertainties,
which are fully correlated between cross-section measurements, are excluded.

$p_{T,Z}$ [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 |  |  |  |  |  |  |  |  |  |  |  |  |
2.2–3.4 | -0.01 | 1 |  |  |  |  |  |  |  |  |  |  |  |
3.4–4.6 | 0.00 | 0.03 | 1 |  |  |  |  |  |  |  |  |  |  |
4.6–5.8 | 0.04 | 0.00 | 0.02 | 1 |  |  |  |  |  |  |  |  |  |
5.8–7.2 | 0.05 | 0.05 | 0.00 | 0.03 | 1 |  |  |  |  |  |  |  |  |
7.2–8.7 | 0.07 | 0.07 | 0.05 | 0.00 | 0.03 | 1 |  |  |  |  |  |  |  |
8.7–10.5 | 0.08 | 0.08 | 0.06 | 0.06 | 0.02 | 0.02 | 1 |  |  |  |  |  |  |
10.5–12.8 | 0.07 | 0.06 | 0.05 | 0.05 | 0.07 | 0.04 | 0.00 | 1 |  |  |  |  |  |
12.8–15.4 | 0.07 | 0.07 | 0.05 | 0.05 | 0.06 | 0.09 | 0.07 | -0.01 | 1 |  |  |  |  |
15.4–19 | 0.08 | 0.08 | 0.05 | 0.06 | 0.07 | 0.10 | 0.12 | 0.08 | -0.01 | 1 |  |  |  |
19–24.5 | 0.08 | 0.08 | 0.06 | 0.06 | 0.07 | 0.10 | 0.12 | 0.10 | 0.10 | 0.02 | 1 |  |  |
24.5–34 | 0.08 | 0.07 | 0.05 | 0.06 | 0.07 | 0.10 | 0.11 | 0.09 | 0.10 | 0.11 | 0.05 | 1 |  |
34–63 | 0.07 | 0.06 | 0.05 | 0.05 | 0.06 | 0.08 | 0.09 | 0.08 | 0.08 | 0.09 | 0.10 | 0.06 | 1 |
63–270 | 0.20 | 0.20 | 0.15 | 0.15 | 0.19 | 0.26 | 0.30 | 0.26 | 0.27 | 0.30 | 0.32 | 0.31 | 0.30 | 1

Table 11: Correlation coefficients of differential cross-section measurements
as a function of $\phi^{*}_{Z}$. The beam energy and luminosity uncertainties,
which are fully correlated between cross-section measurements, are excluded.

$\phi^{*}_{Z}$ | 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 |  |  |  |  |  |  |  |  |  |  |  |  |  |
0.01–0.02 | 0.14 | 1 |  |  |  |  |  |  |  |  |  |  |  |  |
0.02–0.03 | 0.16 | 0.12 | 1 |  |  |  |  |  |  |  |  |  |  |  |
0.03–0.05 | 0.20 | 0.17 | 0.17 | 1 |  |  |  |  |  |  |  |  |  |  |
0.05–0.07 | 0.15 | 0.12 | 0.13 | 0.16 | 1 |  |  |  |  |  |  |  |  |  |
0.07–0.10 | 0.19 | 0.16 | 0.17 | 0.21 | 0.15 | 1 |  |  |  |  |  |  |  |  |
0.10–0.15 | 0.14 | 0.12 | 0.13 | 0.16 | 0.12 | 0.15 | 1 |  |  |  |  |  |  |  |
0.15–0.20 | 0.11 | 0.10 | 0.10 | 0.13 | 0.10 | 0.12 | 0.09 | 1 |  |  |  |  |  |  |
0.20–0.30 | 0.15 | 0.13 | 0.13 | 0.17 | 0.13 | 0.16 | 0.13 | 0.10 | 1 |  |  |  |  |  |
0.30–0.40 | 0.10 | 0.08 | 0.09 | 0.11 | 0.08 | 0.10 | 0.08 | 0.06 | 0.08 | 1 |  |  |  |  |
0.40–0.60 | 0.07 | 0.06 | 0.07 | 0.08 | 0.06 | 0.08 | 0.06 | 0.05 | 0.07 | 0.04 | 1 |  |  |  |
0.60–0.80 | 0.05 | 0.04 | 0.04 | 0.05 | 0.04 | 0.05 | 0.04 | 0.03 | 0.04 | 0.03 | 0.02 | 1 |  |  |
0.80–1.20 | 0.05 | 0.04 | 0.04 | 0.05 | 0.04 | 0.05 | 0.04 | 0.03 | 0.04 | 0.03 | 0.02 | 0.01 | 1 |  |
1.20–2.00 | 0.02 | 0.02 | 0.02 | 0.03 | 0.02 | 0.03 | 0.02 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 | 0.00 | 1 |
2.00–4.00 | 0.005 | 0.004 | 0.005 | 0.006 | 0.004 | 0.005 | 0.004 | 0.004 | 0.004 | 0.002 | 0.002 | 0.002 | 0.002 | 0.001 | 1

Table 12: Correlation coefficients between differential cross-section
measurements as a function of $W$ boson muon $\eta$. The 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 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | $W^{+}$
| 0.46 | 1 |  |  |  |  |  |  |  |  |  |  |  |  |  |  | $W^{-}$
|  2.25–2.5 | -0.15 | 0.34 | 1 |  |  |  |  |  |  |  |  |  |  |  |  |  | $W^{+}$
| 0.30 | -0.24 | 0.09 | 1 |  |  |  |  |  |  |  |  |  |  |  |  | $W^{-}$
|  2.5–2.75 | -0.03 | 0.23 | 0.27 | -0.13 | 1 |  |  |  |  |  |  |  |  |  |  |  | $W^{+}$
| 0.24 | -0.14 | -0.21 | 0.35 | 0.41 | 1 |  |  |  |  |  |  |  |  |  |  | $W^{-}$
|  2.75–3 | 0.20 | -0.07 | -0.10 | 0.25 | -0.00 | 0.21 | 1 |  |  |  |  |  |  |  |  |  | $W^{+}$
| -0.19 | 0.39 | 0.46 | -0.37 | 0.27 | -0.24 | 0.28 | 1 |  |  |  |  |  |  |  |  | $W^{-}$
|  3–3.25 | -0.03 | 0.24 | 0.28 | -0.16 | 0.20 | -0.08 | -0.01 | 0.29 | 1 |  |  |  |  |  |  |  | $W^{+}$
| 0.31 | -0.23 | -0.32 | 0.46 | -0.13 | 0.35 | 0.25 | -0.37 | 0.27 | 1 |  |  |  |  |  |  | $W^{-}$
|  3.25–3.5 | -0.12 | 0.29 | 0.36 | -0.27 | 0.22 | -0.17 | -0.07 | 0.40 | 0.24 | -0.27 | 1 |  |  |  |  |  | $W^{+}$
| 0.33 | -0.32 | -0.41 | 0.52 | -0.19 | 0.40 | 0.28 | -0.47 | -0.21 | 0.53 | -0.07 | 1 |  |  |  |  | $W^{-}$
|  3.5–4 | 0.02 | 0.15 | 0.18 | -0.05 | 0.15 | -0.01 | 0.04 | 0.17 | 0.14 | -0.04 | 0.15 | -0.08 | 1 |  |  |  | $W^{+}$
| 0.21 | -0.09 | -0.14 | 0.30 | -0.02 | 0.25 | 0.19 | -0.17 | -0.04 | 0.30 | -0.12 | 0.33 | 0.45 | 1 |  |  | $W^{-}$
|  4–4.5 | -0.01 | 0.13 | 0.17 | -0.08 | 0.14 | -0.05 | -0.01 | 0.15 | 0.11 | -0.07 | 0.11 | -0.12 | 0.09 | 0.02 | 1 |  | $W^{+}$
| 0.08 | 0.01 | -0.01 | 0.09 | 0.03 | 0.08 | 0.07 | -0.02 | 0.02 | 0.10 | -0.02 | 0.09 | 0.03 | 0.10 | 0.11 | 1 | $W^{-}$
|  | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ |

Table 13: Correlation coefficients between differential cross-section
measurements as a function of $y_{Z}$ and $W$ boson muon $\eta$. 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 | 0.24 | 0.25 | 0.19 | 0.19 | 0.17 | 0.16 | 0.15 | 0.13 | 0.12 | 0.10 | 0.08 | 0.06 | 0.05 | 0.04 | 0.03 | 0.02 | 0.01 | $-$ | $W^{+}$
0.22 | 0.23 | 0.17 | 0.17 | 0.16 | 0.15 | 0.13 | 0.12 | 0.11 | 0.09 | 0.07 | 0.05 | 0.04 | 0.04 | 0.03 | 0.02 | 0.01 | $-$ | $W^{-}$
2.25–2.5 | 0.03 | 0.11 | 0.13 | 0.14 | 0.12 | 0.11 | 0.10 | 0.10 | 0.09 | 0.07 | 0.06 | 0.04 | 0.03 | 0.02 | 0.01 | 0.01 | 0.01 | $-$ | $W^{+}$
0.03 | 0.10 | 0.12 | 0.13 | 0.11 | 0.10 | 0.10 | 0.09 | 0.08 | 0.07 | 0.06 | 0.04 | 0.03 | 0.02 | 0.01 | 0.01 | 0.00 | $-$ | $W^{-}$
2.5–2.75 | 0.03 | 0.04 | 0.06 | 0.10 | 0.10 | 0.10 | 0.09 | 0.09 | 0.08 | 0.07 | 0.07 | 0.05 | 0.04 | 0.03 | 0.02 | 0.01 | 0.01 | $-$ | $W^{+}$
0.03 | 0.03 | 0.06 | 0.10 | 0.09 | 0.09 | 0.08 | 0.08 | 0.08 | 0.07 | 0.06 | 0.05 | 0.04 | 0.02 | 0.02 | 0.01 | 0.01 | $-$ | $W^{-}$
2.75–3 | 0.03 | 0.04 | 0.04 | 0.07 | 0.09 | 0.10 | 0.09 | 0.09 | 0.09 | 0.08 | 0.07 | 0.06 | 0.05 | 0.04 | 0.02 | 0.01 | 0.01 | $-$ | $W^{+}$
0.02 | 0.03 | 0.03 | 0.05 | 0.07 | 0.07 | 0.07 | 0.07 | 0.06 | 0.06 | 0.05 | 0.04 | 0.04 | 0.03 | 0.01 | 0.01 | 0.01 | $-$ | $W^{-}$
3–3.25 | 0.04 | 0.04 | 0.04 | 0.06 | 0.08 | 0.10 | 0.10 | 0.10 | 0.09 | 0.09 | 0.08 | 0.07 | 0.06 | 0.05 | 0.03 | 0.01 | 0.01 | $-$ | $W^{+}$
0.03 | 0.04 | 0.03 | 0.05 | 0.06 | 0.08 | 0.08 | 0.08 | 0.08 | 0.07 | 0.07 | 0.06 | 0.05 | 0.04 | 0.02 | 0.01 | 0.01 | $-$ | $W^{-}$
3.25–3.5 | 0.02 | 0.03 | 0.03 | 0.04 | 0.04 | 0.05 | 0.06 | 0.06 | 0.06 | 0.06 | 0.05 | 0.05 | 0.04 | 0.03 | 0.02 | 0.01 | 0.01 | $-$ | $W^{+}$
0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.04 | 0.05 | 0.05 | 0.05 | 0.04 | 0.04 | 0.03 | 0.03 | 0.02 | 0.02 | 0.01 | 0.00 | $-$ | $W^{-}$
3.5–4 | 0.03 | 0.03 | 0.03 | 0.04 | 0.04 | 0.05 | 0.06 | 0.08 | 0.09 | 0.08 | 0.08 | 0.07 | 0.07 | 0.05 | 0.04 | 0.03 | 0.02 | $-$ | $W^{+}$
0.03 | 0.03 | 0.03 | 0.04 | 0.04 | 0.05 | 0.06 | 0.08 | 0.09 | 0.09 | 0.08 | 0.07 | 0.07 | 0.05 | 0.04 | 0.03 | 0.02 | $-$ | $W^{-}$
4–4.5 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.03 | 0.04 | 0.05 | 0.05 | 0.06 | 0.06 | 0.04 | 0.03 | 0.03 | $-$ | $W^{+}$
0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.03 | 0.03 | 0.03 | 0.04 | 0.05 | 0.07 | 0.07 | 0.07 | 0.07 | 0.05 | 0.04 | 0.03 | $-$ | $W^{-}$

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LHCb collaboration

R. Aaij38, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
Alvarez Cartelle53, A.A. Alves Jr57, S. Amato2, S. Amerio22, Y. Amhis7, L.
An3, L. Anderlini17,g, J. Anderson40, M. Andreotti16,f, J.E. Andrews58, R.B.
Appleby54, O. Aquines Gutierrez10, F. Archilli38, P. d’Argent11, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, C. Baesso60, W. Baldini16,38, R.J.
Barlow54, C. Barschel38, S. Barsuk7, W. Barter38, V. Batozskaya28, V.
Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1,
L.J. Bel41, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson38, J.
Benton46, A. Berezhnoy32, R. Bernet40, A. Bertolin22, M.-O. Bettler38, M. van
Beuzekom41, A. Bien11, S. Bifani45, T. Bird54, A. Birnkraut9, A. Bizzeti17,i,
T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N.
Bondar30,38, W. Bonivento15, S. Borghi54, A. Borgia59, M. Borsato7, T.J.V.
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Cardini15, P. Carniti20, L. Carson50, K. Carvalho Akiba2,38, R. Casanova
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X. Cid Vidal38, G. Ciezarek41, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47,
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Cruz Torres60, S. Cunliffe53, R. Currie53, C. D’Ambrosio38, J. Dalseno46,
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Durante38, R. Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49,38, U.
Egede53, V. Egorychev31, S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R.
Ekelhof9, L. Eklund51, I. El Rifai5, Ch. Elsasser40, S. Ely59, S. Esen11, H.M.
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S. Farry52, R. Fay52, D. Ferguson50, V. Fernandez Albor37, F. Ferrari14, F.
Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M. Fiore16,38,f, M.
Fiorini16,f, M. Firlej27, C. Fitzpatrick39, T. Fiutowski27, P. Fol53, M.
Fontana10, F. Fontanelli19,j, R. Forty38, O. Francisco2, M. Frank38, C.
Frei38, M. Frosini17, J. Fu21,38, E. Furfaro24,l, A. Gallas Torreira37, D.
Galli14,d, S. Gallorini22,38, S. Gambetta19,j, M. Gandelman2, P. Gandini59, Y.
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Geraci21,v, D. Gerick11, E. Gersabeck11, M. Gersabeck54, T. Gershon48, Ph.
Ghez4, A. Gianelle22, S. Gianì39, V. Gibson47, L. Giubega29, V.V. Gligorov38,
C. Göbel60, D. Golubkov31, A. Golutvin53,31,38, A. Gomes1,a, C. Gotti20,k, M.
Grabalosa Gándara5, R. Graciani Diaz36, L.A. Granado Cardoso38, E. Graugés36,
E. Graverini40, G. Graziani17, A. Grecu29, E. Greening55, S. Gregson47, P.
Griffith45, L. Grillo11, O. Grünberg63, B. Gui59, E. Gushchin33, Yu. Guz35,38,
T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S.
Hall53, B. Hamilton58, T. Hampson46, X. Han11, S. Hansmann-Menzemer11, N.
Harnew55, S.T. Harnew46, J. Harrison54, J. He38, T. Head39, V. Heijne41, K.
Hennessy52, P. Henrard5, L. Henry8, J.A. Hernando Morata37, E. van
Herwijnen38, M. Heß63, A. Hicheur2, D. Hill55, M. Hoballah5, C. Hombach54, W.
Hulsbergen41, T. Humair53, N. Hussain55, D. Hutchcroft52, D. Hynds51, M.
Idzik27, P. Ilten56, R. Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41, A.
Jawahery58, F. Jing3, M. John55, D. Johnson38, C.R. Jones47, C. Joram38, B.
Jost38, N. Jurik59, S. Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38,†,
S. Karodia51, M. Kelsey59, I.R. Kenyon45, M. Kenzie38, T. Ketel42, B.
Khanji20,38,k, C. Khurewathanakul39, S. Klaver54, K. Klimaszewski28, O.
Kochebina7, M. Kolpin11, I. Komarov39, R.F. Koopman42, P. Koppenburg41,38, M.
Korolev32, L. Kravchuk33, K. Kreplin11, M. Kreps48, G. Krocker11, P.
Krokovny34, F. Kruse9, W. Kucewicz26,o, M. Kucharczyk26, V. Kudryavtsev34, K.
Kurek28, T. Kvaratskheliya31, V.N. La Thi39, D. Lacarrere38, G. Lafferty54, A.
Lai15, D. Lambert50, R.W. Lambert42, G. Lanfranchi18, C. Langenbruch48, B.
Langhans38, T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van Leerdam41, J.-P.
Lees4, R. Lefèvre5, A. Leflat32, J. Lefrançois7, O. Leroy6, T. Lesiak26, B.
Leverington11, Y. Li7, T. Likhomanenko64, M. Liles52, R. Lindner38, C. Linn38,
F. Lionetto40, B. Liu15, S. Lohn38, I. Longstaff51, J.H. Lopes2, P. Lowdon40,
D. Lucchesi22,r, H. Luo50, A. Lupato22, E. Luppi16,f, O. Lupton55, F.
Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O. Maev30, S. Malde55, A.
Malinin64, G. Manca15,e, G. Mancinelli6, P. Manning59, A. Mapelli38, J.
Maratas5, J.F. Marchand4, U. Marconi14, C. Marin Benito36, P. Marino23,38,t,
R. Märki39, J. Marks11, G. Martellotti25, M. Martinelli39, D. Martinez
Santos42, F. Martinez Vidal66, D. Martins Tostes2, A. Massafferri1, R.
Matev38, Z. Mathe38, C. Matteuzzi20, A. Mauri40, B. Maurin39, A. Mazurov45, M.
McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B. McSkelly52, B.
Meadows57, F. Meier9, M. Meissner11, M. Merk41, D.A. Milanes62, M.-N. Minard4,
D.S. Mitzel11, J. Molina Rodriguez60, S. Monteil5, M. Morandin22, P.
Morawski27, A. Mordà6, M.J. Morello23,t, J. Moron27, A.B. Morris50, R.
Mountain59, F. Muheim50, J. Müller9, K. Müller40, V. Müller9, M. Mussini14, B.
Muster39, P. Naik46, T. Nakada39, R. Nandakumar49, I. Nasteva2, M. Needham50,
N. Neri21, S. Neubert11, N. Neufeld38, M. Neuner11, A.D. Nguyen39, T.D.
Nguyen39, C. Nguyen-Mau39,q, V. Niess5, R. Niet9, N. Nikitin32, T. Nikodem11,
A. Novoselov35, D.P. O’Hanlon48, A. Oblakowska-Mucha27, V. Obraztsov35, S.
Ogilvy51, O. Okhrimenko44, R. Oldeman15,e, C.J.G. Onderwater67, B. Osorio
Rodrigues1, J.M. Otalora Goicochea2, A. Otto38, P. Owen53, A. Oyanguren66, A.
Palano13,c, F. Palombo21,u, M. Palutan18, J. Panman38, A. Papanestis49, M.
Pappagallo51, L.L. Pappalardo16,f, C. Parkes54, G. Passaleva17, G.D. Patel52,
M. Patel53, C. Patrignani19,j, A. Pearce54,49, A. Pellegrino41, G. Penso25,m,
M. Pepe Altarelli38, S. Perazzini14,d, P. Perret5, L. Pescatore45, K.
Petridis46, A. Petrolini19,j, M. Petruzzo21, E. Picatoste Olloqui36, B.
Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, S. Playfer50, M. Plo
Casasus37, T. Poikela38, F. Polci8, A. Poluektov48,34, I. Polyakov31, E.
Polycarpo2, A. Popov35, D. Popov10, B. Popovici29, C. Potterat2, E. Price46,
J.D. Price52, J. Prisciandaro39, A. Pritchard52, C. Prouve46, V. Pugatch44, A.
Puig Navarro39, G. Punzi23,s, W. Qian4, R. Quagliani7,46, B. Rachwal26, J.H.
Rademacker46, B. Rakotomiaramanana39, M. Rama23, M.S. Rangel2, I. Raniuk43, N.
Rauschmayr38, G. Raven42, F. Redi53, S. Reichert54, M.M. Reid48, A.C. dos
Reis1, S. Ricciardi49, S. Richards46, M. Rihl38, K. Rinnert52, V. Rives
Molina36, P. Robbe7,38, A.B. Rodrigues1, E. Rodrigues54, P. Rodriguez Perez54,
S. Roiser38, V. Romanovsky35, A. Romero Vidal37, M. Rotondo22, J. Rouvinet39,
T. Ruf38, H. Ruiz36, P. Ruiz Valls66, J.J. Saborido Silva37, N. Sagidova30, P.
Sail51, B. Saitta15,e, V. Salustino Guimaraes2, C. Sanchez Mayordomo66, B.
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F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M. Witek26, G.
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Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3.

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

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, 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
vPolitecnico di Milano, Milano, Italy
†Deceased