EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-170 LHCb-PAPER-2016-021 September 7, 2016

Measurement of the forward $\mathrm{Z}$ boson production cross-section in pp
collisions at $\sqrt{s}=13$ $\mathrm{\,Te\kern-2.07413ptV}$

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

A measurement of the production cross-section of $\mathrm{Z}$ bosons in pp
collisions at $\sqrt{s}=13$ TeV is presented using dimuon and dielectron final
states in LHCb data. The cross-section is measured for leptons with
pseudorapidities in the range $2.0<\eta<4.5$, transverse momenta
$\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and dilepton invariant
mass in the range $60<m(\ell\ell)<120\mathrm{\,Ge\kern-1.00006ptV}$. The
integrated cross-section from averaging the two final states is

$\displaystyle\sigma_{\mathrm{Z}}^{\ell\ell}$ $\displaystyle=194.3\pm 0.9\pm
3.3\pm 7.6\rm\,pb,$

where the first uncertainty is statistical, the second is due to systematic
effects, and the third is due to the luminosity determination. In addition,
differential cross-sections are measured as functions of the $\mathrm{Z}$
boson rapidity, transverse momentum and the angular variable
$\phi^{*}_{\eta}$.

Published in JHEP 09 (2016) 136

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

##  1 Introduction

Measurements are reported of $\mathrm{Z}$ boson production111The label
$\mathrm{Z}$ boson is defined to include the effects of virtual photon
production and interference terms. The terms electron and muon are also used
to refer to both matter and anti-matter species of the particles. at the LHCb
experiment in proton-proton collisions at
$\sqrt{s}=13$$\mathrm{\,Te\kern-1.00006ptV}$. The analysis uses a dataset
corresponding to an integrated luminosity of $294\pm 11$$\mbox{\,pb}^{-1}$ and
considers events where the boson decays either to a dimuon or a dielectron
final state. The two final states offer statistically independent samples with
largely independent systematic uncertainties. The analysis is performed using
similar methods to previous LHCb measurements of electroweak boson production
at lower pp collision energies [1, 2, 3, 4, 5]. The LHCb detector measures
particle production in the forward region; the ATLAS and CMS collaborations
have reported similar measurements at
$\sqrt{s}=13$$\mathrm{\,Te\kern-1.00006ptV}$ [6, 7] in a different kinematic
region.

Measurements of electroweak gauge boson production are benchmark tests of
Standard Model processes at hadron colliders, and are of interest for
constraining the parton distribution functions (PDFs) that describe the
structure of the proton. Because of the longitudinal boost required for a
$\mathrm{Z}$ boson to be produced in the forward region, LHCb results are
particularly sensitive to effects at low and high values of Bjorken-$x$[8],
and have been used to constrain global PDF fits [9, 10, 11]. The $\sqrt{s}=13$
$\mathrm{\,Te\kern-1.00006ptV}$ pp collisions allow LHCb to access lower
values of $x$ than previous measurements at 7 and 8 TeV. In addition, the
boson transverse momentum ($p_{\rm T}$) and $\phi^{*}_{\eta}$ distributions
can be used to test Monte Carlo modelling of additional higher-order radiation
that arises from quantum chromodynamics (QCD). The $\phi^{*}_{\eta}$ variable
[12] is defined as
$\phi^{*}_{\eta}\equiv\tan(\phi_{\text{acop}}/2)/\cosh(\Delta\eta/2)$, where
the acoplanarity angle $\phi_{\text{acop}}\equiv\pi-\Delta\phi$ depends on the
difference in azimuthal angle of the two leptons, $\Delta\phi$, and
$\Delta\eta$ is the difference in pseudorapidity of the two leptons. This
variable probes similar physics to that probed by the boson transverse
momentum, but with better experimental resolution.

The fiducial region used for the results presented here is the same as in
previous measurements of $\mathrm{Z}$ boson production at LHCb [1, 13, 2, 3,
4, 5]. Both final-state leptons are required to have $\mbox{$p_{\rm
T}$}>20$$\mathrm{\,Ge\kern-1.00006ptV}$ and pseudorapidity
$2.0\nolinebreak<\nolinebreak\eta\nolinebreak<\nolinebreak 4.5$.222This
article uses natural units with $c=1$. The invariant mass of the dilepton
pair, $m(\ell\ell)$, is required to be in the range
$60\nolinebreak<\nolinebreak m(\ell\ell)\nolinebreak<\nolinebreak
120$$\mathrm{\,Ge\kern-1.00006ptV}$. The measurements are corrected for final-
state radiation to the Born level in quantum electrodynamics (QED), allowing
direct comparison of the results in the muon and electron final states, which
are reported separately in bins of the boson rapidity, $y_{\mathrm{Z}}$, of
$\phi^{*}_{\eta}$ and, using the dimuon events, as a function of the boson
$p_{\rm T}$. Cross-sections integrated over the fiducial region (fiducial
cross-sections) are also determined using both final states. These are then
averaged into a single measurement of the $\mathrm{Z}\rightarrow\ell\ell$
fiducial cross-section in $\sqrt{s}=13$ TeV pp collisions.

##  2 Detector and simulation

The LHCb detector [14, 15] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, primarily 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 $4{\mathrm{\,Tm}}$, 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$\mathrm{\,Ge\kern-1.00006ptV}$. 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 the $p_{\rm
T}$ is measured in $\mathrm{\,Ge\kern-1.00006ptV}$. 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 scintillating-pad (SPD) and preshower (PS) detectors, an
electromagnetic calorimeter (ECAL) and a hadronic calorimeter (HCAL). Muons
are identified by a system composed of alternating layers of iron and
multiwire proportional chambers.

The online event selection is performed by a trigger, 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. The
analysis described here uses triggers designed to select events containing at
least one muon or at least one electron. The hardware trigger used for these
studies requires that a candidate muon has $\mbox{$p_{\rm
T}$}>6$$\mathrm{\,Ge\kern-1.00006ptV}$ or that a candidate electron has
transverse energy $\mbox{$E_{\rm T}$}>2.28$$\mathrm{\,Ge\kern-1.00006ptV}$.
Global event cuts (GEC) are applied in the electron trigger in order to
prevent events with high occupancy from dominating the processing time: events
only pass the electron trigger if they contain fewer than 450 hits in the SPD
detector. No such requirement is made within the muon trigger. The software
trigger used here selects events containing a muon candidate with
$\mbox{$p_{\rm T}$}>12.5$$\mathrm{\,Ge\kern-1.00006ptV}$, or an electron
candidate with $\mbox{$p_{\rm T}$}>15$$\mathrm{\,Ge\kern-1.00006ptV}$.

The main challenge with electron reconstruction at LHCb is the energy
measurement. The calorimeters at LHCb are optimised for the study of low
$E_{\rm T}$ physics, and individual cells saturate for transverse energies
greater than approximately 10$\mathrm{\,Ge\kern-1.00006ptV}$. Electron
reconstruction at LHCb therefore relies on accurate tracking measurements to
determine the electron momentum. However, bremsstrahlung photons are often
emitted as an electron traverses the LHCb detector, so the measured momentum
does not directly correspond to the momentum of the electron produced in the
proton-proton collision. These photons are often collinear with the electron
and are detected in the same saturated calorimeter cell so that recovery of
this emitted photon energy is incomplete. Consequently LHCb accurately
determines the direction of electrons, but tends to underestimate their energy
by a variable amount, typically around 25%. Despite these challenges, the
excellent angular resolution of electrons provided by the LHCb detector means
that measurements using the dielectron final state can be used to complement
analyses of angular variables such as rapidity and $\phi^{*}_{\eta}$ in the
dimuon final state [2, 4].

Simulated pp collisions for the study of reconstruction effects are generated
using Pythia 8 [16, *Sjostrand:2006za] with a specific LHCb configuration
[18]. Decays of hadronic particles are described by EvtGen [19], in which
final-state radiation is modelled using Photos [20]. The interaction of the
generated particles with the detector, and its response, are implemented using
the Geant4 toolkit [21, *Agostinelli:2002hh] as described in Ref. [23].

The results reported in this article are compared to fixed-order predictions
calculated within perturbative quantum chromodynamics (pQCD) determined using
the FEWZ 3.1 generator [24] at $\mathcal{O}(\alpha_{s}^{2})$, where
${\alpha_{s}}$ is the coupling strength of the strong force. These predictions
do not include electroweak corrections. Predictions are made using MMHT14 [9],
NNPDF3.0 [10], and CT14 [11] PDF sets. In all cases, the factorisation and
renormalisation scales are set to the $\mathrm{Z}$ boson mass. Uncertainties
on the fixed-order predictions are evaluated by varying the factorisation and
renormalisation scales independently using the seven-point scale variation
prescription [25], and combining this effect in quadrature with the 68% CL
uncertainties associated with the PDF sets and the value of ${\alpha_{s}}$.
The results are also compared to predictions using the Monash 2013 tune of
Pythia 8 [16, *Sjostrand:2006za, 26] and an updated version of the LHCb-
specific Pythia 8 tune [18]. In addition, results are compared to predictions
from Powheg [27, 28] at $\mathcal{O}({\alpha_{s}})$ using the NNPDF3.0 PDF
set, with the showering implemented using Pythia 8\. These predictions are
calculated using the default Powheg settings and the Pythia 8 Monash 2013
tune. The $\mathrm{Z}$ differential cross-section results are also compared to
simulated datasets produced using MadGraph5_aMC@NLO[29]. Different schemes are
used to match and merge these samples. The MLM [30] sample has leading-order
accuracy for the emission of zero, one or two jets; the FxFx [31] sample has
next-to-leading-order (NLO) accuracy for zero- or one-jet emission; and the
UNLOPS [32] sample is accurate at NLO for zero- or one-jet emission and
accurate at LO for two-jet emission. Higher jet multiplicities are generated
by a parton shower, implemented here using the Monash 2013 tune for Pythia 8.

##  3 Dataset and event selection

This analysis uses a dataset corresponding to an integrated luminosity of
$294\pm 11$$\mbox{\,pb}^{-1}$ recorded by the LHCb experiment in pp collisions
at $\sqrt{s}=13$$\mathrm{\,Te\kern-1.00006ptV}$. This integrated luminosity is
determined using the beam-imaging techniques described in Ref. [33].
Candidates are selected by requiring two high $p_{\rm T}$ muons or electrons
of opposite charge. Additional requirements are then made to select pure
samples; these and the resulting purity are now discussed in turn for the
dimuon and dielectron final states.

###  3.1 Dimuon final state

The fiducial requirements outlined in Sect. 1 are applied as selection
criteria for the dimuon final state. In addition, the two tracks are required
to satisfy quality criteria and to be identified as muons. At least one of the
muons is required to be responsible for the event passing the hardware and
software stages of the trigger. The number of selected
$\mathrm{Z}\rightarrow\upmu\upmu$ candidates is $43\,643$.

Five sources of background are investigated: heavy flavour hadron decays,
misidentified hadrons, $\mathrm{Z}\rightarrow\uptau\uptau$ decays,
${\mathrm{t}}{\overline{\mathrm{t}}}$ events, and WW events. Similar
techniques to those used in previous analyses are applied to quantify the
contribution of each source [3, 5]. The contribution where at least one muon
is produced by the decay of heavy flavour particles is studied by selecting
sub-samples where this contribution is enhanced, either by requiring that the
muons are not spatially isolated from other activity in the event, or by
requiring that the muons are not consistent with a common production point.
Studies on these two sub-samples are consistent, and the background
contribution is estimated to be $180\pm 50$ events. The contribution from
misidentified hadrons is evaluated from the probability with which hadrons are
incorrectly identified as muons, and is determined to be $100\pm 13$ events.
Following Refs. [1, 3, 5], this evaluation is made with randomly triggered
data. An alternative estimate of the contribution from these sources is found
by selecting events where both muons have the same charge, but pass all other
selection criteria. The assumption that the charges of the selected muons are
uncorrelated for these sources is validated by confirming that the same-sign
event yield is compatible with the opposite-sign event yield in background-
enriched regions. The overall number of same-sign events is 198, with the
numbers of $\upmu^{+}\upmu^{+}$ and $\upmu^{-}\upmu^{-}$ candidates
statistically compatible with each other. The difference between this number
and the sum of the hadron misidentification and heavy-flavour contributions is
assigned as an additional uncertainty on the purity estimate. The contribution
from $\mathrm{Z}\rightarrow\uptau\uptau$ decays where both $\uptau$ leptons
subsequently decay to muons is estimated from Pythia 8 simulation to be $30\pm
10$ events. The background from muons produced in top-quark decays is
determined from simulation normalised using the measurement of the cross-
section for top-pair production measured at the ATLAS experiment [34], and is
estimated to be $28\pm 10$ events. The background from WW decays is also
determined from the simulation and found to be negligible. Overall, the purity
of the dataset is estimated to be $\rho^{\upmu\upmu}=(99.2\pm 0.2)\%$,
consistent with purity estimates found in previous LHCb measurements at lower
centre-of-mass energies [3, 5]. As in these previous measurements, no
significant variation of the purity is found as a function of the kinematic
variables studied, and so the purity is treated as constant. A systematic
uncertainty associated with this assumption is discussed in Sect. 5.

###  3.2 Dielectron final state

The dielectron final state requires two opposite-sign electron candidates,
using the same selection criteria based on calorimeter energy deposits as
previous LHCb analyses [1, 4]. Electron candidates are required to have
$\mbox{$p_{\rm T}$}>20$$\mathrm{\,Ge\kern-1.00006ptV}$ and $2.0<\eta<4.5$. A
loose requirement is made on the dielectron invariant mass,
$m(\mathrm{e}\mathrm{e})>40$ $\mathrm{\,Ge\kern-1.00006ptV}$, since many
events where the dielectron system is produced with an invariant mass above 60
GeV may be reconstructed at lower mass due to bremsstrahlung. Effects arising
from the difference between the fiducial acceptance and the selection
requirements will be discussed in Sect. 4.4. At least one of the electrons is
required to be responsible for the event passing the hardware and software
stages of the LHCb trigger. In total $16\,395$ candidates are selected.

Backgrounds are determined using similar techniques as in previous analyses
[1, 4]. A sample of same-sign $\mathrm{e}^{\pm}\mathrm{e}^{\pm}$ combinations,
otherwise subject to the same selection criteria as the standard dataset, is
used to provide a data-based estimate of the largest backgrounds. Hadrons that
shower early in the ECAL and fake the signature of an electron are expected to
be the dominant background, and should contribute roughly equally to same-sign
and opposite-sign pairs. The contribution from heavy-flavour decays is also
expected to contribute approximately equally to same-sign and opposite-sign
datasets, and is much smaller than the background due to misidentified
hadrons. Overall, $1\,255$ candidate same-sign events are selected, with no
significant difference observed between the $\mathrm{e}^{+}\mathrm{e}^{+}$ and
$\mathrm{e}^{-}\mathrm{e}^{-}$ datasets. In order to ascertain the reliability
of this procedure, a hadron-enriched sample is selected by requiring that one
of the electron candidates is associated with a significant energy deposit in
the HCAL, suggesting that it is likely to be a misidentified hadron. The
numbers of same-sign and opposite-sign pairs satisfying these requirements are
found to agree within 6.2%. Consequently a 6.2% uncertainty is assigned to the
estimated yield of background events, which corresponds to a 0.5% uncertainty
on the signal yield. In addition, simulated background datasets of
$\mathrm{Z}\rightarrow\uptau\uptau$ decays,
${\mathrm{t}}{\overline{\mathrm{t}}}$ events and WW events are generated [16,
*Sjostrand:2006za] and studied similarly to the dimuon final state. These all
contribute at the level of 0.1% or less. The overall purity of the electron
dataset is found to be $\rho^{\mathrm{e}\mathrm{e}}=(92.2\pm 0.5)\%$.

##  4 Cross-section measurement

The $\mathrm{Z}$ boson production cross-section is measured in bins of
$y_{\mathrm{Z}}$, $\phi^{*}_{\eta}$, and, for the dimuon final state, in bins
of the boson $p_{\rm T}$. For the dimuon final state the efficiency is
obtained from per-event weights that depend on the kinematics of the muons,
whereas for the dielectron final state the reconstruction and detection
efficiencies are evaluated within each bin of the distribution. These
approaches are validated using simulation.

The cross-section for the dimuon final state in a particular bin $i$ is
determined as

$\displaystyle\sigma_{\mathrm{Z}}^{\upmu\upmu}(i)=$
$\displaystyle\frac{1}{L}\,\rho^{\upmu\upmu}f_{\textrm{\mbox{{FSR}}}}^{\upmu\upmu}(i)f_{\text{unf}}^{\upmu\upmu}(i)\sum\limits_{j=1}^{N_{\mathrm{Z}}^{\upmu\upmu}(i)}\frac{1}{\varepsilon(\upmu^{+}_{j},\upmu^{-}_{j})},$

where the index $j$ runs over the candidates contributing to the bin, with the
total number of candidates in the bin denoted by
$N_{\mathrm{Z}}^{\upmu\upmu}(i)$. The total reconstruction and detection
efficiency for a given event $j$, $\varepsilon(\upmu^{+}_{j},\upmu^{-}_{j})$,
depends on the kinematics of each muon. The correction factors for final-state
radiation (FSR) are denoted by $f_{\textrm{\mbox{{FSR}}}}^{\upmu\upmu}(i)$.
Corrections for resolution effects that cause bin-to-bin migrations, where
applicable, which do not change the fiducial cross-section, are denoted by
$f_{\text{unf}}^{\upmu\upmu}(i)$. Migration of events in and out of the
overall LHCb fiducial acceptance is negligible. The purity, introduced
earlier, is denoted $\rho^{\upmu\upmu}$. The integrated luminosity is denoted
by $L$.

For the dielectron final state the cross-section in a particular bin is
determined as

$\displaystyle\sigma_{\mathrm{Z}}^{\mathrm{e}\mathrm{e}}(i)=$
$\displaystyle\frac{1}{L}\,\rho^{ee}(i)f_{\textrm{\mbox{{FSR}}}}^{{\mathrm{e}\mathrm{e}}}(i)f^{\mathrm{e}\mathrm{e}}_{\text{MZ}}(i)\frac{N_{\mathrm{Z}}^{\mathrm{e}\mathrm{e}}(i)}{\varepsilon^{\mathrm{e}\mathrm{e}}(i)},$

where $N_{\mathrm{Z}}^{\mathrm{e}\mathrm{e}}(i)$ denotes the number of
candidates in bin $i$. The efficiency associated with reconstructing the
dielectron final state in bin $i$ is $\varepsilon^{\mathrm{e}\mathrm{e}}(i)$
and the purity is $\rho^{\mathrm{e}\mathrm{e}}$. The correction for FSR from
the electrons is denoted
$f_{\textrm{\mbox{{FSR}}}}^{\mathrm{e}\mathrm{e}}(i)$, while
$f_{\text{MZ}}^{\mathrm{e}\mathrm{e}}(i)$ corrects the measurement for
migrations in the dielectron invariant mass into and out of the fiducial
region.

For both final states the total cross-section is obtained by summing over $i$.
The various correction factors are discussed below.

###  4.1 Efficiency determination

For the measurement in the dimuon final state, candidates are assigned a
weight associated with the probability of reconstructing each muon, and the
correction for any inefficiency is applied on an event-by-event basis. Muon
reconstruction efficiencies are determined directly from data using the same
tag-and-probe techniques as applied in previous LHCb measurements of
high-$p_{\rm T}$ muons [1, 35, 3, 5]. Averaged over the muon kinematic
distributions, the track reconstruction efficiency is determined to be 95%,
the muon identification efficiency is determined to be 95% and the single muon
trigger efficiency is 80%. Since either muon can be responsible for the event
passing the trigger, the overall efficiency with which candidates pass the
trigger is higher, on average 95%. These efficiencies are determined as a
function of the muon pseudorapidity. Efficiency measurements as a function of
other variables, such as the muon $p_{\rm T}$ and the detector occupancy, are
studied as a cross-check, with no significant change in the final results.

For the measurement in the dielectron final state, electron reconstruction
efficiencies are determined from data and simulation for each bin of the
measurement, using the same techniques applied in previous LHCb measurements
of $\mathrm{Z}\rightarrow\mathrm{e}\mathrm{e}$ production [2, 4]. The use of
different techniques to determine efficiencies to those applied in the muon
channel provides uncorrelated systematic uncertainties between the two
measurements. The efficiency for electrons is factorised into similar
components to those applied in the dimuon analysis, though one extra effect is
considered. The GEC efficiency determines the probability that the dielectron
candidates pass the GEC present in the hardware trigger. There is no such
requirement in the dimuon trigger. The GEC efficiency for dielectron data is
determined from the dimuon data, correcting for small differences in the
detector response to muons and electrons. The average GEC efficiency is 79%
and exhibits a weak dependence on rapidity and $\phi^{*}_{\eta}$. The trigger
efficiency is determined directly from data using a tag-and-probe method, and
is typically 93%. The efficiency with which both electrons are identified by
the calorimetry is typically 78% and is determined from simulation that has
been calibrated with data. This efficiency exhibits a significant dependence
on the boson rapidity, since the LHCb calorimeter acceptance only extends as
far as $\eta\approx 4.25$. The track reconstruction and kinematic efficiency
describes the efficiency with which electrons that are in the fiducial region
are reconstructed with $\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$.
It corrects both for failure to reconstruct a track and for incomplete
bremsstrahlung recovery incorrectly reconstructing electrons with $p_{\rm T}$
below the 20 GeV threshold. This is also determined from simulation calibrated
to data, and is on average $48\%$.

###  4.2 Resolution effects

The excellent angular resolution of the LHCb detector in comparison to the bin
widths means that no significant bin-to-bin migrations occur in the
$\phi^{*}_{\eta}$ or $y_{\mathrm{Z}}$ distributions for either the dimuon or
dielectron final states. In addition, net migration in and out of the overall
LHCb angular acceptance is negligible. However, small migrations in the boson
$p_{\rm T}$ distribution measured using the dimuon final state are expected at
low transverse momenta. These effects are typically of similar size to the
statistical uncertainty in each bin. This distribution is therefore unfolded
to correct for the impact of these migrations using multiplicative correction
factors (defined above as $f_{\text{unf}}^{\upmu\upmu}$) determined for each
bin from simulation.

###  4.3 Final-state radiation corrections

The data are corrected for the effect of FSR from the leptons, allowing
comparison of electron and muon final states. The correction in each bin of
the measured differential distributions is taken as the average of the values
determined using Herwig++ [36] and Pythia 8 [16, *Sjostrand:2006za]. The two
generators typically agree at the per-mille level; the mean correction is
about 2% for muons and 5% for electrons, but dependence is seen as functions
of the different kinematic variables studied. The strongest variation is seen
as a function of the boson $p_{\rm T}$, where the correction varies over the
distribution by about 10%. The corrections applied are tabulated in the
appendix.

###  4.4 Acceptance corrections

The acceptance correction $f_{\text{MZ}}^{\text{ee}}$ is applied for electrons
to correct for events which pass the selection but are not in the fiducial
acceptance in dilepton mass. This correction factor, typically 0.97, is
determined from simulation as in previous analyses [2, 4] and cross-checked
using data. No correction is applied for muons, where the fiducial acceptance
is identical to the kinematic requirement in the acceptance, and where the
experimental resolution is sufficient such that net migrations in and out of
the acceptance due to experimental resolution are negligible.

###  4.5 Measuring fiducial cross-sections

The fiducial cross-sections are determined by integrating over the
$y_{{}_{\mathrm{Z}}}$ distributions. Since no candidates in the bin
$4.25<y_{{}_{\mathrm{Z}}}<4.50$ are observed for electrons, a correction for
this bin is evaluated using FEWZ [24]. This correction is found to be 0.7 pb.
The fraction of the fiducial cross-section expected in the bin determined
using Pythia 8 simulation [16, *Sjostrand:2006za] is consistent with this
estimate to within 0.1 pb. This is assigned as the uncertainty associated with
the contribution from this bin to the fiducial cross-section measured in the
dielectron final state. Consistent results are obtained when integrating over
$\phi^{*}_{\eta}$ or $p_{\rm T}$.

##  5 Systematic uncertainties

The systematic uncertainties associated with the measurement are estimated
using the same techniques as in previous analyses [1, 3, 4, 5]. The
contributions from different sources are combined in quadrature. The
uncertainties on the fiducial cross-section measurement are summarised in
Table 1.

For both muons and electrons, the statistical precisions of the efficiencies
are assigned as systematic uncertainties. For muons, the accuracy of the tag-
and-probe methods used to determine efficiencies is tested in simulation, and
efficiencies calculated using the tag-and-probe method are generally found to
match simulated efficiencies at the per-mille level, with the largest
difference arising from the determination of the track reconstruction
efficiency. An uncertainty of 1% is assigned to this efficiency for each muon.
The method of treating each muon independently and applying the efficiencies
as a function of the muon pseudorapidity is also studied in simulation, and is
found to be accurate to better than 0.6%. This is also assigned as a
systematic uncertainty. For electrons, the accuracy of the method used to
determine the trigger efficiency is studied by applying it to the simulated
dataset and comparing the resulting efficiencies to those directly determined
in the same dataset: no bias is observed, and no additional uncertainty is
assigned. For the electron track reconstruction efficiency the relative
performance in data and simulation is studied using a tag-and-probe method and
an uncertainty of 1.6% is assigned. The uncertainty associated with potential
mismodelling of the electron identification efficiency is determined by
comparing between data and simulation the distributions of calorimeter energy
deposits used to identify electrons. The impact of any mismodelling is
propagated through the measurement, and an uncertainty of 1.3% is assigned.
Apart from the uncertainties arising from the statistical precision of the
efficiency evaluation, these uncertainties are treated as fully correlated
between bins. Since the efficiencies are determined using different methods
for muons and electrons these uncertainties are taken as uncorrelated between
the dimuon and dielectron final states.

The uncertainties on the purity estimates described in Sect. 3 introduce
uncertainties on the overall cross-sections of $0.2\%$ for muons and $0.5\%$
uncertainty for electrons, treated as correlated between all bins. For the
muon analysis, the purity is assumed to be uniform across all bins. To
evaluate the uncertainty associated with this assumption, the purity is
allowed to vary in each bin, with the change from the nominal result providing
an additional uncertainty at the per-mille level for the differential
measurement.

The statistical uncertainty on the FSR corrections is treated as a systematic
uncertainty on the corrections. This is combined in quadrature with the
difference between the corrections derived using the Herwig++ [36] and Pythia
8 [16, *Sjostrand:2006za] simulated datasets. The uncertainties on the FSR
corrections are taken as uncorrelated between all bins.

The dimuon analysis is repeated using a momentum scale calibration and
detector alignment determined from $\mathrm{Z}\rightarrow\upmu\upmu$ events,
in a similar approach to that documented in Ref. [37]. The impact on the
measured total cross-section and the differential $y_{\mathrm{Z}}$ and
$\phi^{*}_{\eta}$ measurements is negligible. The mean effect in any bin of
transverse momentum is typically 1% and is not statistically significant.
However this is assigned as an additional uncertainty on the differential
cross-section in each bin of transverse momentum. While the $\mathrm{Z}$ boson
transverse momentum distribution is not measured in the dielectron final
state, the momentum scale plays a larger role in the analysis of the
dielectron final state due to the significant effect of bremsstrahlung and
migrations in electron $p_{\rm T}$ across the 20
$\mathrm{\,Ge\kern-1.00006ptV}$ threshold. The impact of the scale around this
threshold is evaluated in the same way as in previous
$\mathrm{Z}\rightarrow\mathrm{e}\mathrm{e}$ analyses at LHCb [1, 4]. A fit to
the $\min[\mbox{$p_{\rm T}$}(\mathrm{e}^{+}),\mbox{$p_{\rm
T}$}(\mathrm{e}^{-})]$ spectrum returns a momentum scale correction factor of
$1.000\pm 0.005$ for simulation. Propagating this uncertainty on the electron
momentum scale onto the cross-section measurement yields an uncertainty of
about $0.6\%$, which is treated as correlated between all bins.

Table 1: Summary of the relative uncertainties on the $\mathrm{Z}$ boson total cross-section. Source |  $\Delta\sigma_{\mathrm{Z}}^{\upmu\upmu}$ [%] | $\Delta\sigma_{\mathrm{Z}}^{\mathrm{e}\mathrm{e}}[\%]$
---|---|---
Statistical | 0.5 | 0.9
Reconstruction efficiencies | 2.4 | 2.4
Purity | 0.2 | 0.5
FSR | 0.1 | 0.2
Total systematic (excl. lumi.) | 2.4 | 2.5
Luminosity | 3.9 | 3.9

The transverse momentum distribution is unfolded to account for potential
migration of events between bins arising from the experimental resolution
using correction factors in each bin. A systematic uncertainty on this
approach is set by considering the Bayesian method [38, 39] with two
iterations as an alternative. The difference between the two approaches is at
the per-mille level in each bin and is assigned as the uncertainty. As in
previous analyses [3, 5], the unfolding is studied using different models of
the underlying distribution, and no significant additional variation is
observed.

The only uncertainty treated as correlated between the muon and electron final
states is the one associated with the luminosity determination. This
uncertainty is determined to be 3.9% following the procedures used in Ref.
[33]. The uncertainty on the FSR correction may also be correlated, but is
sufficiently small for the effects of such correlation to be negligible. The
measurement is performed for the nominal centre-of-mass energy of the
colliding beams. This energy was determined to an accuracy of 0.65% for the
4$\mathrm{\,Te\kern-1.00006ptV}$ proton beams used in earlier LHC operations
[40]. No studies have yet been published for the 6.5
$\mathrm{\,Te\kern-1.00006ptV}$ proton beams used here, but for calculations
performed using the FEWZ generator [24] at NNLO in pQCD, a 0.65% shift in the
beam and collision energy would correspond to a shift in the fiducial cross-
section of 0.9%. This is not assigned as an additional uncertainty. The
correlation matrices for the measurements of the differential cross-section as
a function of the $\mathrm{Z}$ boson rapidity are given in the appendix.

##  6 Results

The inclusive $\mathrm{Z}$ boson cross-section for decays to a dilepton final
state with the dilepton invariant mass in the range $60<m(\ell\ell)<120$
$\mathrm{\,Ge\kern-1.00006ptV}$, and where the leptons have
$p_{\text{T}}\nolinebreak>\nolinebreak 20$$\mathrm{\,Ge\kern-1.00006ptV}$ and
$2.0<\eta<4.5$, is measured in $\sqrt{s}=13\mathrm{\,Te\kern-1.00006ptV}$ pp
collisions to be

$\displaystyle\sigma_{\mathrm{Z}}^{\upmu\upmu}$ $\displaystyle=198.0\pm 0.9\pm
4.7\pm 7.7\rm\,pb,$ $\displaystyle\sigma_{\mathrm{Z}}^{\mathrm{e}\mathrm{e}}$
$\displaystyle=190.2\pm 1.7\pm 4.7\pm 7.4\rm\,pb.$

The first uncertainties quoted are statistical, the second arise from
systematic effects, and the third are due to the accuracy of the luminosity
determination. This cross-section is determined at the Born level in QED.
Taking the luminosity uncertainty to be fully correlated, the two measurements
are consistent at the level of $1.1\,\sigma$, and are linearly combined to
give

$\displaystyle\sigma_{\mathrm{Z}}^{\ell\ell}$ $\displaystyle=194.3\pm 0.9\pm
3.3\pm 7.6\rm\,pb,$

where the combination minimises the sum of the statistical and systematic
uncertaintes in quadrature. The integrated cross-section in the fiducial
acceptance and the differential measurement as a function of the $\mathrm{Z}$
boson rapidity are compared in Figs. 1 and 2 to the fixed-order predictions
for both dimuon and dielectron final states. The measured differential cross-
sections are tabulated in the appendix. Fixed-order predictions describe the
LHCb data well for a range of PDF sets. The measured differential cross-
section is slightly larger than the next-to-next-to-leading order pQCD
predictions at lower rapidities, in line with observations in Ref. [7]. The
differences between the PDF sets, and the PDF uncertainties, are larger than
those at lower values of $\sqrt{s}$. Larger LHCb datasets with the uncertainty
on the luminosity determination reduced to the level of previous studies
(1.2%) should significantly constrain the PDFs. The differential cross-
sections as a function of $p_{\rm T}$ and $\phi^{*}_{\eta}$, normalised to the
total cross-section, are shown in Figs. 3, 4 and 5. Since the largest
systematic effects are independent of these variables, systematic
uncertainties largely cancel when these distributions are normalised, and the
uncertainties on the normalised distributions are dominated by the statistical
components. The LHCb data agree better with Pythia 8 predictions than with
Powheg \+ Pythia 8 predictions, as seen also in previous analyses [3, 2]. The
LHCb specific tune of Pythia 8 does not describe the data significantly better
than the Monash 2013 tune. In addition, the data do not favour a particular
matching and merging scheme generated using MadGraph5_aMC@NLO.

##  7 Conclusions

The $\mathrm{Z}$ production cross-section measured in pp collisions at
$\sqrt{s}=13$$\mathrm{\,Te\kern-1.00006ptV}$ is presented using LHCb events
where the $\mathrm{Z}$ boson decays to two muons or two electrons. The cross-
section is measured in a fiducial acceptance defined by lepton pseudorapidity
in the range $2.0<\eta<4.5$, transverse momentum $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$, and dilepton invariant mass in the
range $60<m(\ell\ell)<120\mathrm{\,Ge\kern-1.00006ptV}$. The cross-section is
measured to be

$\displaystyle\sigma_{\mathrm{Z}}^{\ell\ell}$ $\displaystyle=194.3\pm 0.9\pm
3.3\pm 7.6\rm\,pb,$

where the uncertainties are due to the size of the dataset, systematic
effects, and the luminosity determination respectively. In addition, the
measurement is performed in bins of the $\mathrm{Z}$ boson rapidity,
transverse momentum and $\phi^{*}_{\eta}$. The measurement is compared to
theoretical predictions calculated at $\mathcal{O}(\alpha_{s}^{2})$ in pQCD as
a function of the boson rapidity. The results do not favour any specific
parton distribution function, but the differences between the PDF sets suggest
that, with more data and a reduction in the uncertainty associated with the
luminosity determination, LHCb results will significantly constrain the PDFs.
The $\phi^{*}_{\eta}$ and boson transverse momentum distributions are compared
to theoretical predictions that model higher orders in pQCD in different ways.
No significant deviations are seen between the data and the Standard Model.

Figure 1: The fiducial cross-section compared between theory and data. The
bands correspond to the average of the dimuon and dielectron final states,
with the inner band corresponding to the statistical uncertainty and the outer
band corresponding to the total uncertainty. The top three points correspond
to $\mathcal{O}(\alpha_{s}^{2})$ predictions with different PDF sets. The
inner error bars on these points are due to the PDF uncertainty, with the
outer error bars giving the contribution of all uncertainties. The bottom
points correspond to the LHCb measurements in the dielectron and dimuon final
states and their average, with the inner error bar showing the statistical
uncertainty and the outer error bar the total uncertainty.

Figure 2: The differential cross-section as a function of the $\mathrm{Z}$
boson rapidity, compared between theory and data. The bands correspond to the
data, with the inner band corresponding to the statistical uncertainty and the
outer band corresponding to the total uncertainty. The points correspond to
$\mathcal{O}(\alpha_{s}^{2})$ predictions with different PDF sets. The inner
error bars on these points are due to the PDF uncertainty, with the outer
error bars giving the contribution of all uncertainties. The different
predictions are displaced horizontally within bins to enable ease of
comparison. The upper plot shows the differential cross-section, and the lower
plot shows the same information as ratios to the central values of the
NNPDF3.0 predictions.

Figure 3: The normalised differential cross-section as a function of the
$\mathrm{Z}$ boson $\phi^{*}_{\eta}$, compared between theory and data. The
bands correspond to the data, with the inner band corresponding to the
statistical uncertainty and the outer band corresponding to the total
uncertainty. The points correspond to the theoretical predictions from the
different generators and tunes. The different predictions are displaced
horizontally within bins to enable ease of comparison. The upper plot shows
the normalised differential cross-section, and the lower plot shows the same
information as ratios to the central values of the predictions produced using
the Monash 2013 tune of Pythia 8\. The uncertainties on the theoretical
predictions, visible at high $\phi^{*}_{\eta}$, are statistical.

Figure 4: The normalised differential cross-section as a function of the
$\mathrm{Z}$ boson transverse momentum, compared between theory and data. The
bands correspond to the data, with the inner band corresponding to the
statistical uncertainty and the outer band corresponding to the total
uncertainty. The points correspond to the theoretical predictions from the
different generators and tunes. The different predictions are displaced
horizontally within bins to enable ease of comparison. The upper plot shows
the normalised differential cross-section, and the lower plot shows the same
information as ratios to the central values of the predictions produced using
the Monash 2013 tune of Pythia 8.

Figure 5: The ratio of the normalised differential cross-sections to the
predictions evaluated using the FxFx scheme. The bands correspond to the data,
with the inner band corresponding to the statistical uncertainty and the outer
band corresponding to the total uncertainty. The different predictions are
displaced horizontally within bins to enable ease of comparison. Alternative
schemes give different predictions, shown as points.All predictions are
generated using MadGraph5_aMC@NLO. The uncertainties on the theoretical
predictions are statistical. The upper plot shows the $\phi^{*}_{\eta}$
distribution, and the lower plot shows the $p_{\rm T}$ distribution.

## 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 FASO (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 and Yandex
LLC (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. 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 and Yandex
LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal
Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust
(United Kingdom).

Appendix

## Tabulated results and correlation matrices

The FSR corrections used in this analysis are given in Tables 2, 3, and 4. The
bins are indexed in increasing rapidity, $\phi^{*}_{\eta}$ and transverse
momentum, and the same binning schemes as in Refs. [3, 4, 5] are used. The bin
index scheme defined in Tables 2, 3, and 4 is used throughout the appendix.
The differential cross-section results are tabulated in Tables 5, 6 and 7. The
correlation matrices are given in Tables 8, 9, 10, 11, and 12.

Table 2: The FSR correction applied as a function of the boson rapidity. Bin index | Bin range | $f_{\text{FSR}}^{\upmu\upmu}$ | $f_{\text{FSR}}^{\mathrm{e}\mathrm{e}}$
---|---|---|---
1 | 2.000-2.125 | 1.016$\pm$0.005 | 1.034$\pm$0.003
2 | 2.125-2.250 | 1.017$\pm$0.004 | 1.037$\pm$0.005
3 | 2.250-2.375 | 1.021$\pm$0.002 | 1.040$\pm$0.002
4 | 2.375-2.500 | 1.018$\pm$0.002 | 1.041$\pm$0.002
5 | 2.500-2.625 | 1.023$\pm$0.003 | 1.043$\pm$0.002
6 | 2.625-2.750 | 1.022$\pm$0.003 | 1.044$\pm$0.004
7 | 2.750-2.875 | 1.022$\pm$0.002 | 1.047$\pm$0.004
8 | 2.875-3.000 | 1.023$\pm$0.003 | 1.048$\pm$0.002
9 | 3.000-3.125 | 1.026$\pm$0.002 | 1.051$\pm$0.002
10 | 3.125-3.250 | 1.026$\pm$0.002 | 1.051$\pm$0.002
11 | 3.250-3.375 | 1.025$\pm$0.004 | 1.055$\pm$0.001
12 | 3.375-3.500 | 1.026$\pm$0.005 | 1.053$\pm$0.003
13 | 3.500-3.625 | 1.027$\pm$0.002 | 1.049$\pm$0.005
14 | 3.625-3.750 | 1.024$\pm$0.002 | 1.051$\pm$0.007
15 | 3.750-3.875 | 1.021$\pm$0.003 | 1.045$\pm$0.004
16 | 3.875-4.000 | 1.019$\pm$0.019 | 1.038$\pm$0.011
17 | 4.000-4.250 | 1.034$\pm$0.014 | 1.061$\pm$0.013
18 | 4.250-4.500 | 1.046$\pm$0.119 |
Table 3: The FSR correction applied as a function of $\phi^{*}_{\eta}$. Bin index | Bin range | $f_{\text{FSR}}^{\upmu\upmu}$ | $f_{\text{FSR}}^{\mathrm{e}\mathrm{e}}$
---|---|---|---
1 | 0.00-0.01 | 1.034$\pm$0.002 | 1.057$\pm$0.002
2 | 0.01-0.02 | 1.035$\pm$0.002 | 1.057$\pm$0.001
3 | 0.02-0.03 | 1.028$\pm$0.001 | 1.054$\pm$0.001
4 | 0.03-0.05 | 1.027$\pm$0.002 | 1.050$\pm$0.002
5 | 0.05-0.07 | 1.022$\pm$0.002 | 1.048$\pm$0.001
6 | 0.07-0.10 | 1.018$\pm$0.003 | 1.041$\pm$0.002
7 | 0.10-0.15 | 1.015$\pm$0.004 | 1.040$\pm$0.004
8 | 0.15-0.20 | 1.016$\pm$0.001 | 1.038$\pm$0.003
9 | 0.20-0.30 | 1.012$\pm$0.003 | 1.039$\pm$0.002
10 | 0.30-0.40 | 1.014$\pm$0.003 | 1.042$\pm$0.003
11 | 0.40-0.60 | 1.017$\pm$0.005 | 1.042$\pm$0.002
12 | 0.60-0.80 | 1.021$\pm$0.004 | 1.044$\pm$0.007
13 | 0.80-1.20 | 1.027$\pm$0.010 | 1.044$\pm$0.004
14 | 1.20-2.00 | 1.028$\pm$0.008 | 1.048$\pm$0.007
15 | 2.00-4.00 | 1.002$\pm$0.041 | 1.080$\pm$0.023
Table 4: The FSR correction applied as a function of the boson transverse momentum. Bin index | Bin range [GeV] | $f_{\text{FSR}}^{\upmu\upmu}$
---|---|---
1 | 0.0-2.2 | 1.090$\pm$0.004
2 | 2.2-3.4 | 1.075$\pm$0.002
3 | 3.4-4.6 | 1.062$\pm$0.003
4 | 4.6-5.8 | 1.045$\pm$0.003
5 | 5.8-7.2 | 1.029$\pm$0.001
6 | 7.2-8.7 | 1.014$\pm$0.005
7 | 8.7-10.5 | 1.002$\pm$0.007
8 | 10.5-12.8 | 0.990$\pm$0.008
9 | 12.8-15.4 | 0.984$\pm$0.005
10 | 15.4-19.0 | 0.976$\pm$0.008
11 | 19.0-24.5 | 0.980$\pm$0.005
12 | 24.5-34.0 | 1.007$\pm$0.002
13 | 34.0-63.0 | 1.035$\pm$0.001
14 | 63.0-270.0 | 1.064$\pm$0.004

Table 5: The measured differential cross-sections as a function of the boson rapidity. The first uncertainty is due to the size of the dataset, the second is due to experimental systematic uncertainties, and the third is due to the luminosity. Bin index |  $\rm{d}\sigma_{\mathrm{Z}}^{\upmu\upmu}/\rm{d}y_{\mathrm{Z}}$ [pb] |  $\rm{d}\sigma_{\mathrm{Z}}^{\rm{ee}}/\rm{d}y_{\mathrm{Z}}$ [pb]
---|---|---
1 | 14.2 | $\pm$ | 0.7 | $\pm$ | 0.5 | $\pm$ | 0.6 | 11.8 | $\pm$ | 1.3 | $\pm$ | 0.7 | $\pm$ | 0.5
2 | 41.9 | $\pm$ | 1.2 | $\pm$ | 1.2 | $\pm$ | 1.6 | 42.1 | $\pm$ | 2.2 | $\pm$ | 1.6 | $\pm$ | 1.6
3 | 65.2 | $\pm$ | 1.5 | $\pm$ | 1.8 | $\pm$ | 2.5 | 66.1 | $\pm$ | 2.5 | $\pm$ | 2.1 | $\pm$ | 2.6
4 | 91.3 | $\pm$ | 1.8 | $\pm$ | 2.3 | $\pm$ | 3.6 | 87.9 | $\pm$ | 2.9 | $\pm$ | 2.6 | $\pm$ | 3.4
5 | 108.0 | $\pm$ | 2.0 | $\pm$ | 2.7 | $\pm$ | 4.2 | 95.8 | $\pm$ | 3.0 | $\pm$ | 2.8 | $\pm$ | 3.7
6 | 121.4 | $\pm$ | 2.1 | $\pm$ | 3.0 | $\pm$ | 4.7 | 118.5 | $\pm$ | 3.3 | $\pm$ | 3.4 | $\pm$ | 4.6
7 | 136.0 | $\pm$ | 2.2 | $\pm$ | 3.3 | $\pm$ | 5.3 | 133.3 | $\pm$ | 3.6 | $\pm$ | 3.7 | $\pm$ | 5.2
8 | 140.8 | $\pm$ | 2.2 | $\pm$ | 3.4 | $\pm$ | 5.5 | 141.3 | $\pm$ | 3.7 | $\pm$ | 3.9 | $\pm$ | 5.5
9 | 145.5 | $\pm$ | 2.3 | $\pm$ | 3.5 | $\pm$ | 5.7 | 151.2 | $\pm$ | 4.0 | $\pm$ | 4.2 | $\pm$ | 5.9
10 | 144.0 | $\pm$ | 2.3 | $\pm$ | 3.4 | $\pm$ | 5.6 | 133.6 | $\pm$ | 3.9 | $\pm$ | 3.7 | $\pm$ | 5.2
11 | 137.1 | $\pm$ | 2.2 | $\pm$ | 3.3 | $\pm$ | 5.3 | 129.6 | $\pm$ | 4.1 | $\pm$ | 3.7 | $\pm$ | 5.1
12 | 121.8 | $\pm$ | 2.1 | $\pm$ | 3.0 | $\pm$ | 4.8 | 116.5 | $\pm$ | 4.0 | $\pm$ | 3.4 | $\pm$ | 4.5
13 | 100.4 | $\pm$ | 1.9 | $\pm$ | 2.4 | $\pm$ | 3.9 | 93.5 | $\pm$ | 3.8 | $\pm$ | 2.9 | $\pm$ | 3.6
14 | 75.2 | $\pm$ | 1.7 | $\pm$ | 1.8 | $\pm$ | 2.9 | 63.8 | $\pm$ | 3.7 | $\pm$ | 2.2 | $\pm$ | 2.5
15 | 57.9 | $\pm$ | 1.5 | $\pm$ | 1.5 | $\pm$ | 2.3 | 58.6 | $\pm$ | 3.7 | $\pm$ | 2.4 | $\pm$ | 2.3
16 | 41.1 | $\pm$ | 1.2 | $\pm$ | 1.3 | $\pm$ | 1.6 | 34.7 | $\pm$ | 4.0 | $\pm$ | 1.9 | $\pm$ | 1.4
17 | 18.4 | $\pm$ | 0.6 | $\pm$ | 0.6 | $\pm$ | 0.7 | 18.8 | $\pm$ | 3.2 | $\pm$ | 1.6 | $\pm$ | 0.7
18 | 2.6 | $\pm$ | 0.2 | $\pm$ | 0.3 | $\pm$ | 0.1 |  |  |  |  |  |  |

Table 6: The measured differential cross-sections as a function of $\phi^{*}_{\eta}$. The first uncertainty is due to the size of the dataset, the second is due to experimental systematic uncertainties, and the third is due to the luminosity. Bin index |  $\rm{d}\sigma_{\mathrm{Z}}^{\upmu\upmu}/\rm{d}\phi^{*}_{\eta}$ [pb] |  $\rm{d}\sigma_{\mathrm{Z}}^{\rm{ee}}/\rm{d}\phi^{*}_{\eta}$ [pb]
---|---|---
1 | 1873 | $\pm$ | 29 | $\pm$ | 45 | $\pm$ | 73 | 1725 | $\pm$ | 49 | $\pm$ | 48 | $\pm$ | 67
2 | 1741 | $\pm$ | 28 | $\pm$ | 42 | $\pm$ | 68 | 1696 | $\pm$ | 49 | $\pm$ | 48 | $\pm$ | 66
3 | 1635 | $\pm$ | 27 | $\pm$ | 39 | $\pm$ | 64 | 1549 | $\pm$ | 47 | $\pm$ | 44 | $\pm$ | 60
4 | 1330 | $\pm$ | 17 | $\pm$ | 32 | $\pm$ | 52 | 1296 | $\pm$ | 30 | $\pm$ | 35 | $\pm$ | 51
5 | 983 | $\pm$ | 15 | $\pm$ | 24 | $\pm$ | 38 | 955 | $\pm$ | 26 | $\pm$ | 27 | $\pm$ | 37
6 | 722 | $\pm$ | 10 | $\pm$ | 17 | $\pm$ | 28 | 730 | $\pm$ | 19 | $\pm$ | 20 | $\pm$ | 28
7 | 471 | $\pm$ | 7 | $\pm$ | 11 | $\pm$ | 18 | 432 | $\pm$ | 11 | $\pm$ | 12 | $\pm$ | 17
8 | 300 | $\pm$ | 5 | $\pm$ | 7 | $\pm$ | 12 | 300 | $\pm$ | 10 | $\pm$ | 9 | $\pm$ | 12
9 | 160.4 | $\pm$ | 2.7 | $\pm$ | 3.8 | $\pm$ | 6.3 | 152.4 | $\pm$ | 4.7 | $\pm$ | 4.4 | $\pm$ | 5.9
10 | 81.2 | $\pm$ | 1.9 | $\pm$ | 1.9 | $\pm$ | 3.2 | 82.6 | $\pm$ | 3.6 | $\pm$ | 2.7 | $\pm$ | 3.2
11 | 38.0 | $\pm$ | 0.9 | $\pm$ | 0.9 | $\pm$ | 1.5 | 34.0 | $\pm$ | 1.7 | $\pm$ | 1.1 | $\pm$ | 1.3
12 | 14.72 | $\pm$ | 0.58 | $\pm$ | 0.36 | $\pm$ | 0.57 | 14.71 | $\pm$ | 1.01 | $\pm$ | 0.63 | $\pm$ | 0.57
13 | 6.21 | $\pm$ | 0.27 | $\pm$ | 0.16 | $\pm$ | 0.24 | 4.94 | $\pm$ | 0.43 | $\pm$ | 0.23 | $\pm$ | 0.19
14 | 1.289 | $\pm$ | 0.086 | $\pm$ | 0.043 | $\pm$ | 0.050 | 1.213 | $\pm$ | 0.148 | $\pm$ | 0.080 | $\pm$ | 0.047
15 | 0.190 | $\pm$ | 0.021 | $\pm$ | 0.009 | $\pm$ | 0.007 | 0.201 | $\pm$ | 0.042 | $\pm$ | 0.021 | $\pm$ | 0.008

Table 7: The measured differential cross-sections as a function of $p_{\rm T}$. The first uncertainty is due to the size of the dataset, the second is due to experimental systematic uncertainties, and the third is due to the luminosity. Bin index |  $\rm{d}\sigma_{\mathrm{Z}}^{\upmu\upmu}/\rm{d}{p_{\text{T, Z}}}$ [pb / GeV]
---|---
1 | 5.55 | $\pm$ | 0.11 | $\pm$ | 0.15 | $\pm$ | 0.22
2 | 11.01 | $\pm$ | 0.21 | $\pm$ | 0.29 | $\pm$ | 0.43
3 | 11.36 | $\pm$ | 0.21 | $\pm$ | 0.30 | $\pm$ | 0.44
4 | 11.06 | $\pm$ | 0.21 | $\pm$ | 0.29 | $\pm$ | 0.43
5 | 9.93 | $\pm$ | 0.18 | $\pm$ | 0.26 | $\pm$ | 0.39
6 | 8.86 | $\pm$ | 0.16 | $\pm$ | 0.23 | $\pm$ | 0.35
7 | 7.22 | $\pm$ | 0.13 | $\pm$ | 0.19 | $\pm$ | 0.28
8 | 6.48 | $\pm$ | 0.11 | $\pm$ | 0.18 | $\pm$ | 0.25
9 | 5.28 | $\pm$ | 0.09 | $\pm$ | 0.14 | $\pm$ | 0.21
10 | 4.29 | $\pm$ | 0.07 | $\pm$ | 0.12 | $\pm$ | 0.17
11 | 2.88 | $\pm$ | 0.05 | $\pm$ | 0.08 | $\pm$ | 0.11
12 | 1.760 | $\pm$ | 0.029 | $\pm$ | 0.046 | $\pm$ | 0.069
13 | 0.709 | $\pm$ | 0.011 | $\pm$ | 0.018 | $\pm$ | 0.028
14 | 0.0376 | $\pm$ | 0.0009 | $\pm$ | 0.0010 | $\pm$ | 0.0015

Table 8: The correlation matrix for the differential cross-section measurement as a function of $\mathrm{Z}$ boson rapidity, for the dimuon final state, excluding the luminosity uncertainty, which is fully correlated between bins. Bin index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2 | 0.37 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
3 | 0.35 | 0.50 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
4 | 0.35 | 0.51 | 0.57 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
5 | 0.35 | 0.50 | 0.57 | 0.62 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
6 | 0.34 | 0.50 | 0.57 | 0.62 | 0.64 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
7 | 0.34 | 0.50 | 0.57 | 0.63 | 0.65 | 0.67 | 1.00 |  |  |  |  |  |  |  |  |  |  |
8 | 0.33 | 0.49 | 0.57 | 0.62 | 0.64 | 0.67 | 0.68 | 1.00 |  |  |  |  |  |  |  |  |  |
9 | 0.33 | 0.48 | 0.57 | 0.61 | 0.63 | 0.66 | 0.67 | 0.69 | 1.00 |  |  |  |  |  |  |  |  |
10 | 0.32 | 0.47 | 0.55 | 0.61 | 0.64 | 0.66 | 0.68 | 0.68 | 0.67 | 1.00 |  |  |  |  |  |  |  |
11 | 0.31 | 0.45 | 0.53 | 0.59 | 0.62 | 0.64 | 0.66 | 0.67 | 0.67 | 0.68 | 1.00 |  |  |  |  |  |  |
12 | 0.28 | 0.42 | 0.48 | 0.57 | 0.59 | 0.61 | 0.63 | 0.62 | 0.61 | 0.65 | 0.64 | 1.00 |  |  |  |  |  |
13 | 0.28 | 0.41 | 0.47 | 0.54 | 0.57 | 0.59 | 0.61 | 0.61 | 0.60 | 0.64 | 0.63 | 0.63 | 1.00 |  |  |  |  |
14 | 0.26 | 0.38 | 0.43 | 0.50 | 0.53 | 0.54 | 0.57 | 0.56 | 0.56 | 0.59 | 0.59 | 0.59 | 0.58 | 1.00 |  |  |  |
15 | 0.23 | 0.34 | 0.39 | 0.46 | 0.48 | 0.49 | 0.51 | 0.51 | 0.50 | 0.55 | 0.54 | 0.55 | 0.54 | 0.51 | 1.00 |  |  |
16 | 0.19 | 0.28 | 0.31 | 0.37 | 0.39 | 0.39 | 0.41 | 0.41 | 0.39 | 0.44 | 0.44 | 0.46 | 0.45 | 0.43 | 0.42 | 1.00 |  |
17 | 0.19 | 0.27 | 0.31 | 0.36 | 0.38 | 0.39 | 0.40 | 0.40 | 0.40 | 0.44 | 0.44 | 0.45 | 0.44 | 0.42 | 0.41 | 0.35 | 1.00 |
18 | 0.05 | 0.08 | 0.09 | 0.11 | 0.11 | 0.11 | 0.12 | 0.12 | 0.11 | 0.13 | 0.13 | 0.14 | 0.14 | 0.14 | 0.14 | 0.12 | 0.14 | 1.00

Table 9: The correlation matrix for the differential cross-section measurements as a function of the $\mathrm{Z}$ boson rapidity, for the dielectron final state, excluding the luminosity uncertainty, which is fully correlated between bins. Bin index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2 | 0.07 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
3 | 0.09 | 0.19 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
4 | 0.09 | 0.17 | 0.22 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
5 | 0.11 | 0.22 | 0.28 | 0.26 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
6 | 0.12 | 0.24 | 0.30 | 0.28 | 0.35 | 1.00 |  |  |  |  |  |  |  |  |  |  |
7 | 0.12 | 0.24 | 0.31 | 0.29 | 0.36 | 0.39 | 1.00 |  |  |  |  |  |  |  |  |  |
8 | 0.12 | 0.24 | 0.31 | 0.29 | 0.37 | 0.39 | 0.40 | 1.00 |  |  |  |  |  |  |  |  |
9 | 0.12 | 0.24 | 0.31 | 0.28 | 0.36 | 0.39 | 0.40 | 0.40 | 1.00 |  |  |  |  |  |  |  |
10 | 0.11 | 0.23 | 0.29 | 0.27 | 0.34 | 0.37 | 0.38 | 0.38 | 0.38 | 1.00 |  |  |  |  |  |  |
11 | 0.11 | 0.22 | 0.28 | 0.26 | 0.33 | 0.35 | 0.36 | 0.36 | 0.36 | 0.34 | 1.00 |  |  |  |  |  |
12 | 0.10 | 0.21 | 0.26 | 0.24 | 0.31 | 0.33 | 0.34 | 0.34 | 0.34 | 0.32 | 0.31 | 1.00 |  |  |  |  |
13 | 0.09 | 0.18 | 0.23 | 0.22 | 0.27 | 0.29 | 0.30 | 0.30 | 0.30 | 0.29 | 0.27 | 0.26 | 1.00 |  |  |  |
14 | 0.07 | 0.14 | 0.18 | 0.17 | 0.21 | 0.23 | 0.23 | 0.24 | 0.23 | 0.22 | 0.21 | 0.20 | 0.18 | 1.00 |  |  |
15 | 0.07 | 0.14 | 0.17 | 0.16 | 0.20 | 0.22 | 0.22 | 0.23 | 0.22 | 0.21 | 0.20 | 0.19 | 0.17 | 0.13 | 1.00 |  |
16 | 0.04 | 0.08 | 0.11 | 0.10 | 0.13 | 0.13 | 0.14 | 0.14 | 0.14 | 0.13 | 0.13 | 0.12 | 0.10 | 0.08 | 0.08 | 1.00 |
17 | 0.03 | 0.06 | 0.07 | 0.07 | 0.09 | 0.09 | 0.10 | 0.10 | 0.10 | 0.09 | 0.09 | 0.08 | 0.07 | 0.06 | 0.05 | 0.03 | 1.00

Table 10: The correlation matrix for the differential cross-section measurement as a function of $\phi^{*}_{\eta}$, for the dimuon final state, excluding the luminosity uncertainty, which is fully correlated between bins. Bin index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
2 | 0.69 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
3 | 0.68 | 0.66 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
4 | 0.73 | 0.72 | 0.71 | 1.00 |  |  |  |  |  |  |  |  |  |  |
5 | 0.70 | 0.69 | 0.67 | 0.73 | 1.00 |  |  |  |  |  |  |  |  |  |
6 | 0.71 | 0.70 | 0.69 | 0.74 | 0.71 | 1.00 |  |  |  |  |  |  |  |  |
7 | 0.70 | 0.69 | 0.70 | 0.74 | 0.70 | 0.72 | 1.00 |  |  |  |  |  |  |  |
8 | 0.67 | 0.65 | 0.66 | 0.70 | 0.66 | 0.68 | 0.69 | 1.00 |  |  |  |  |  |  |
9 | 0.68 | 0.67 | 0.66 | 0.71 | 0.68 | 0.69 | 0.69 | 0.65 | 1.00 |  |  |  |  |  |
10 | 0.59 | 0.58 | 0.57 | 0.62 | 0.59 | 0.60 | 0.60 | 0.57 | 0.58 | 1.00 |  |  |  |  |
11 | 0.56 | 0.54 | 0.56 | 0.60 | 0.55 | 0.57 | 0.59 | 0.56 | 0.55 | 0.48 | 1.00 |  |  |  |
12 | 0.43 | 0.42 | 0.42 | 0.45 | 0.42 | 0.44 | 0.44 | 0.42 | 0.42 | 0.36 | 0.36 | 1.00 |  |  |
13 | 0.40 | 0.40 | 0.38 | 0.41 | 0.41 | 0.41 | 0.40 | 0.38 | 0.39 | 0.34 | 0.31 | 0.24 | 1.00 |  |
14 | 0.25 | 0.23 | 0.27 | 0.28 | 0.23 | 0.26 | 0.30 | 0.28 | 0.26 | 0.21 | 0.26 | 0.18 | 0.12 | 1.00 |
15 | 0.16 | 0.15 | 0.17 | 0.18 | 0.15 | 0.17 | 0.18 | 0.17 | 0.16 | 0.14 | 0.15 | 0.11 | 0.09 | 0.10 | 1.00

Table 11: The correlation matrix for the differential cross-section measurements as a function of $\phi^{*}_{\eta}$, for the dielectron final state, excluding the luminosity uncertainty, which is fully correlated between bins. Bin index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
2 | 0.36 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
3 | 0.35 | 0.35 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
4 | 0.45 | 0.45 | 0.43 | 1.00 |  |  |  |  |  |  |  |  |  |  |
5 | 0.37 | 0.37 | 0.36 | 0.46 | 1.00 |  |  |  |  |  |  |  |  |  |
6 | 0.39 | 0.38 | 0.37 | 0.48 | 0.39 | 1.00 |  |  |  |  |  |  |  |  |
7 | 0.39 | 0.38 | 0.37 | 0.48 | 0.39 | 0.41 | 1.00 |  |  |  |  |  |  |  |
8 | 0.34 | 0.34 | 0.33 | 0.42 | 0.35 | 0.36 | 0.36 | 1.00 |  |  |  |  |  |  |
9 | 0.35 | 0.34 | 0.33 | 0.43 | 0.35 | 0.37 | 0.37 | 0.33 | 1.00 |  |  |  |  |  |
10 | 0.27 | 0.27 | 0.26 | 0.34 | 0.28 | 0.29 | 0.29 | 0.25 | 0.26 | 1.00 |  |  |  |  |
11 | 0.25 | 0.25 | 0.24 | 0.31 | 0.26 | 0.26 | 0.27 | 0.23 | 0.24 | 0.19 | 1.00 |  |  |  |
12 | 0.19 | 0.19 | 0.18 | 0.23 | 0.19 | 0.20 | 0.20 | 0.18 | 0.18 | 0.14 | 0.13 | 1.00 |  |  |
13 | 0.15 | 0.15 | 0.15 | 0.19 | 0.15 | 0.16 | 0.16 | 0.14 | 0.14 | 0.11 | 0.10 | 0.08 | 1.00 |  |
14 | 0.11 | 0.11 | 0.11 | 0.14 | 0.11 | 0.12 | 0.12 | 0.10 | 0.11 | 0.08 | 0.08 | 0.06 | 0.05 | 1.00 |
15 | 0.08 | 0.08 | 0.08 | 0.10 | 0.08 | 0.09 | 0.09 | 0.08 | 0.08 | 0.06 | 0.06 | 0.04 | 0.03 | 0.02 | 1.00

Table 12: The correlation matrix for the differential cross-section measurements as a function of boson $p_{\rm T}$, for the dimuon final state, excluding the luminosity uncertainty, which is fully correlated between bins.  Bin index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
2 | 0.54 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
3 | 0.54 | 0.55 | 1.00 |  |  |  |  |  |  |  |  |  |  |
4 | 0.53 | 0.54 | 0.55 | 1.00 |  |  |  |  |  |  |  |  |  |
5 | 0.55 | 0.55 | 0.55 | 0.56 | 1.00 |  |  |  |  |  |  |  |  |
6 | 0.54 | 0.56 | 0.56 | 0.55 | 0.56 | 1.00 |  |  |  |  |  |  |  |
7 | 0.53 | 0.53 | 0.54 | 0.55 | 0.56 | 0.54 | 1.00 |  |  |  |  |  |  |
8 | 0.52 | 0.54 | 0.55 | 0.55 | 0.55 | 0.55 | 0.54 | 1.00 |  |  |  |  |  |
9 | 0.51 | 0.52 | 0.54 | 0.55 | 0.55 | 0.53 | 0.55 | 0.55 | 1.00 |  |  |  |  |
10 | 0.53 | 0.54 | 0.55 | 0.55 | 0.57 | 0.54 | 0.55 | 0.55 | 0.56 | 1.00 |  |  |  |
11 | 0.53 | 0.55 | 0.57 | 0.56 | 0.56 | 0.56 | 0.55 | 0.57 | 0.57 | 0.56 | 1.00 |  |  |
12 | 0.53 | 0.56 | 0.57 | 0.56 | 0.56 | 0.56 | 0.55 | 0.58 | 0.57 | 0.57 | 0.60 | 1.00 |  |
13 | 0.54 | 0.55 | 0.57 | 0.58 | 0.58 | 0.56 | 0.58 | 0.58 | 0.60 | 0.59 | 0.60 | 0.61 | 1.00 |
14 | 0.42 | 0.44 | 0.45 | 0.47 | 0.47 | 0.44 | 0.47 | 0.48 | 0.50 | 0.49 | 0.50 | 0.51 | 0.54 | 1.00

## References

  * [1] LHCb collaboration, R. Aaij et al., _Inclusive $W$ and $Z$ production in the forward region at $\sqrt{s}=7$ TeV_, JHEP 06 (2012) 058, arXiv:1204.1620
  * [2] LHCb collaboration, R. Aaij et al., _Measurement of the cross-section for $Z\rightarrow e^{+}e^{-}$ production in $pp$ collisions at $\sqrt{s}=7$ TeV_, JHEP 02 (2013) 106, arXiv:1212.4620
  * [3] LHCb collaboration, R. Aaij et al., _Measurement of the forward $Z$ boson cross-section in $pp$ collisions at $\sqrt{s}=7$ TeV_, JHEP 08 (2015) 039, arXiv:1505.07024
  * [4] LHCb collaboration, R. Aaij et al., _Measurement of $Z\rightarrow e^{+}e^{-}$ production at $\sqrt{s}=8$ TeV_, JHEP 05 (2015) 109, arXiv:1503.00963
  * [5] LHCb collaboration, R. Aaij et al., _Measurement of forward $W$ and $Z$ boson production in $pp$ collisions at $\sqrt{s}=8$ TeV _, JHEP 01 (2015) 155, arXiv:1511.08039
  * [6] ATLAS collaboration, G. Aad et al., _Measurement of $W^{\pm}$ and $Z$-boson production cross sections in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector_, arXiv:1603.09222
  * [7] CMS Collaboration, _Measurements of inclusive and differential Z boson production cross sections in pp collisions at $\sqrt{s}=13$ TeV_, CMS-PAS-SMP-15-011, CERN, Geneva, 2016
  * [8] R. S. Thorne, A. D. Martin, W. J. Stirling, and G. Watt, _Parton distributions and QCD at LHCb_ , in Proceedings, 16th International Workshop on Deep Inelastic Scattering and Related Subjects (DIS 2008) (R. Devenish and J. Ferrando, eds.), Science Wise Publ., 2008.  arXiv:0808.1847
  * [9] L. A. Harland-Lang, A. D. Martin, P. Motylinski, and R. S. Thorne, _Parton distributions in the LHC era: MMHT 2014 PDFs_ , Eur. Phys. J. C75 (2015) 204, arXiv:1412.3989
  * [10] NNPDF collaboration, R. D. Ball et al., _Parton distributions for the LHC Run II_ , JHEP 04 (2015) 040, arXiv:1410.8849
  * [11] S. Dulat et al., _New parton distribution functions from a global analysis of quantum chromodynamics_ , Phys. Rev. D93 (2016) 033006, arXiv:1506.07443
  * [12] A. Banfi et al., _Optimisation of variables for studying dilepton transverse momentum distributions at hadron colliders_ , Eur. Phys. J. C71 (2011) 1600, arXiv:1009.1580
  * [13] LHCb collaboration, R. Aaij et al., _A study of the $Z$ production cross-section in $pp$ collisions at $\sqrt{s}=7$ TeV using tau final states_, JHEP 01 (2013) 111, arXiv:1210.6289
  * [14] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [15] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [16] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [17] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [18] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [19] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [20] P. Golonka and Z. Was, _PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays_, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [21] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [22] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [23] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [24] Y. Li and F. Petriello, _Combining QCD and electroweak corrections to dilepton production in the framework of the FEWZ simulation code_ , Phys. Rev. D86 (2012) 094034, arXiv:1208.5967
  * [25] K. Hamilton, P. Nason, E. Re, and G. Zanderighi, _NNLOPS simulation of Higgs boson production_ , JHEP 10 (2013) 222, arXiv:1309.0017
  * [26] P. Skands, S. Carrazza, and J. Rojo, _Tuning PYTHIA 8.1: The Monash 2013 Tune_ , Eur. Phys. J. C74 (2014) 3024, arXiv:1404.5630
  * [27] P. Nason, _A new method for combining NLO QCD with shower Monte Carlo algorithms_ , JHEP 11 (2004) 040, arXiv:hep-ph/0409146
  * [28] S. Alioli, P. Nason, C. Oleari, and E. Re, _NLO vector-boson production matched with shower in POWHEG_ , JHEP 07 (2008) 060, arXiv:0805.4802
  * [29] J. Alwall et al., _The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations_ , JHEP 07 (2014) 079, arXiv:1405.0301
  * [30] M. Mangano, _The so-called MLM prescription for ME/PS matching_ , talk presented at the Fermilab ME/MC Tuning Workshop, Batavia U.S.A., October 4, 2002
  * [31] R. Frederix and S. Frixione, _Merging meets matching in MC@NLO_ , JHEP 12 (2012) 061, arXiv:1209.6215
  * [32] L. Lönnblad and S. Prestel, _Merging multi-leg NLO matrix elements with parton showers_ , JHEP 03 (2013) 166, arXiv:1211.7278
  * [33] LHCb collaboration, R. Aaij et al., _Precision luminosity measurements at LHCb_ , JINST 9 (2014) P12005, arXiv:1410.0149
  * [34] ATLAS collaboration, M. Aaboud et al., _Measurement of the $t\bar{t}$ production cross-section using $e\mu$ events with b-tagged jets in pp collisions at $\sqrt{s}$=13 TeV with the ATLAS detector_, arXiv:1606.02699
  * [35] LHCb collaboration, R. Aaij et al., _Measurement of the forward $W$ boson production cross-section in $pp$ collisions at $\sqrt{s}=7$ TeV_, JHEP 12 (2014) 079, arXiv:1408.4354
  * [36] M. Bahr et al., _Herwig++ physics and manual_ , Eur. Phys. J. C58 (2008) 639, arXiv:0803.0883
  * [37] LHCb collaboration, R. Aaij et al., _Measurement of the forward-backward asymmetry in $Z/\gamma^{\ast}\rightarrow\mu^{+}\mu^{-}$ decays and determination of the effective weak mixing angle_, JHEP 11 (2015) 190, arXiv:1509.07645
  * [38] G. D’Agostini, _A multidimensional unfolding method based on Bayes’ theorem_ , Nucl. Instrum. Meth. A362 (1995) 487
  * [39] T. Adye, _Unfolding algorithms and tests using RooUnfold_ , arXiv:1105.1160
  * [40] J. Wenninger, _Energy calibration of the LHC beams at $4\,$TeV_, CERN-ATS-2013-040

LHCb collaboration

R. Aaij39, B. Adeva38, M. Adinolfi47, 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. An40, L. Anderlini18,
G. Andreassi40, M. Andreotti17,g, J.E. Andrews59, R.B. Appleby55, O. Aquines
Gutierrez11, F. Archilli1, P. d’Argent12, J. Arnau Romeu6, A. Artamonov36, M.
Artuso60, E. Aslanides6, G. Auriemma26, M. Baalouch5, I. Babuschkin55, S.
Bachmann12, J.J. Back49, A. Badalov37, C. Baesso61, W. Baldini17, R.J.
Barlow55, C. Barschel39, S. Barsuk7, W. Barter39, V. Batozskaya29, B.
Batsukh60, V. Battista40, A. Bay40, L. Beaucourt4, J. Beddow52, F. Bedeschi24,
I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,i, K. Belous36, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson39, J. Benton47, A.
Berezhnoy33, R. Bernet41, A. Bertolin23, F. Betti15, M.-O. Bettler39, M. van
Beuzekom42, I. Bezshyiko41, S. Bifani46, P. Billoir8, T. Bird55, A.
Birnkraut10, A. Bitadze55, A. Bizzeti18,u, T. Blake49, F. Blanc40, J. Blouw11,
S. Blusk60, V. Bocci26, T. Boettcher57, A. Bondar35, N. Bondar31,39, W.
Bonivento16, A. Borgheresi21,i, S. Borghi55, M. Borisyak67, M. Borsato38, F.
Bossu7, M. Boubdir9, T.J.V. Bowcock53, E. Bowen41, C. Bozzi17,39, S. Braun12,
M. Britsch12, T. Britton60, J. Brodzicka55, E. Buchanan47, C. Burr55, A.
Bursche2, J. Buytaert39, S. Cadeddu16, R. Calabrese17,g, M. Calvi21,i, M.
Calvo Gomez37,m, A. Camboni37, P. Campana19, D. Campora Perez39, D.H. Campora
Perez39, L. Capriotti55, A. Carbone15,e, G. Carboni25,j, R. Cardinale20,h, A.
Cardini16, P. Carniti21,i, L. Carson51, K. Carvalho Akiba2, G. Casse53, L.
Cassina21,i, L. Castillo Garcia40, M. Cattaneo39, Ch. Cauet10, G. Cavallero20,
R. Cenci24,t, M. Charles8, Ph. Charpentier39, G. Chatzikonstantinidis46, M.
Chefdeville4, S. Chen55, S.-F. Cheung56, V. Chobanova38, M. Chrzaszcz41,27, X.
Cid Vidal38, G. Ciezarek42, P.E.L. Clarke51, M. Clemencic39, H.V. Cliff48, J.
Closier39, V. Coco58, J. Cogan6, E. Cogneras5, V. Cogoni16,39,f, L.
Cojocariu30, G. Collazuol23,o, P. Collins39, A. Comerma-Montells12, A.
Contu39, A. Cook47, S. Coquereau8, G. Corti39, M. Corvo17,g, C.M. Costa
Sobral49, 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, M. De Serio14,d,
P. De Simone19, C.-T. Dean52, D. Decamp4, M. Deckenhoff10, L. Del Buono8, M.
Demmer10, D. Derkach67, O. Deschamps5, F. Dettori39, B. Dey22, A. Di Canto39,
H. Dijkstra39, F. Dordei39, M. Dorigo40, A. Dosil Suárez38, A. Dovbnya44, K.
Dreimanis53, L. Dufour42, G. Dujany55, K. Dungs39, P. Durante39, R.
Dzhelyadin36, A. Dziurda39, A. Dzyuba31, N. Déléage4, S. Easo50, M. Ebert51,
U. Egede54, V. Egorychev32, S. Eidelman35, S. Eisenhardt51, U. Eitschberger10,
R. Ekelhof10, L. Eklund52, Ch. Elsasser41, S. Ely60, S. Esen12, H.M. Evans48,
T. Evans56, A. Falabella15, N. Farley46, S. Farry53, R. Fay53, D. Fazzini21,i,
D. Ferguson51, V. Fernandez Albor38, A. Fernandez Prieto38, F. Ferrari15,39,
F. Ferreira Rodrigues1, M. Ferro-Luzzi39, S. Filippov34, R.A. Fini14, M.
Fiore17,g, M. Fiorini17,g, M. Firlej28, C. Fitzpatrick40, T. Fiutowski28, F.
Fleuret7,b, K. Fohl39, M. Fontana16, F. Fontanelli20,h, D.C. Forshaw60, R.
Forty39, V. Franco Lima53, M. Frank39, C. Frei39, J. Fu22,q, E. Furfaro25,j,
C. Färber39, A. Gallas Torreira38, D. Galli15,e, S. Gallorini23, S.
Gambetta51, M. Gandelman2, P. Gandini56, Y. Gao3, L.M. Garcia Martin68, J.
García Pardiñas38, J. Garra Tico48, L. Garrido37, P.J. Garsed48, D. Gascon37,
C. Gaspar39, L. Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck12, M.
Gersabeck55, T. Gershon49, Ph. Ghez4, S. Gianì40, V. Gibson48, O.G. Girard40,
L. Giubega30, K. Gizdov51, V.V. Gligorov8, D. Golubkov32, A. Golutvin54,39, A.
Gomes1,a, I.V. Gorelov33, C. Gotti21,i, M. Grabalosa Gándara5, R. Graciani
Diaz37, L.A. Granado Cardoso39, E. Graugés37, E. Graverini41, G. Graziani18,
A. Grecu30, P. Griffith46, L. Grillo21, B.R. Gruberg Cazon56, O. Grünberg65,
E. Gushchin34, Yu. Guz36, T. Gys39, C. Göbel61, T. Hadavizadeh56, C.
Hadjivasiliou5, G. Haefeli40, C. Haen39, S.C. Haines48, S. Hall54, B.
Hamilton59, X. Han12, S. Hansmann-Menzemer12, N. Harnew56, S.T. Harnew47, J.
Harrison55, M. Hatch39, J. He62, T. Head40, A. Heister9, K. Hennessy53, P.
Henrard5, L. Henry8, J.A. Hernando Morata38, E. van Herwijnen39, M. Heß65, A.
Hicheur2, D. Hill56, C. Hombach55, W. Hulsbergen42, T. Humair54, M.
Hushchyn67, N. Hussain56, D. Hutchcroft53, 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, J.M. Kariuki47, S. Karodia52, M. Kecke12, M.
Kelsey60, I.R. Kenyon46, M. Kenzie39, T. Ketel43, E. Khairullin67, B.
Khanji21,39,i, C. Khurewathanakul40, T. Kirn9, S. Klaver55, K. Klimaszewski29,
S. Koliiev45, M. Kolpin12, I. Komarov40, R.F. Koopman43, P. Koppenburg42, A.
Kozachuk33, M. Kozeiha5, L. Kravchuk34, K. Kreplin12, M. Kreps49, P.
Krokovny35, F. Kruse10, W. Krzemien29, W. Kucewicz27,l, M. Kucharczyk27, V.
Kudryavtsev35, A.K. Kuonen40, K. Kurek29, T. Kvaratskheliya32,39, D.
Lacarrere39, G. Lafferty55,39, A. Lai16, D. Lambert51, G. Lanfranchi19, C.
Langenbruch9, B. Langhans39, T. Latham49, C. Lazzeroni46, R. Le Gac6, J. van
Leerdam42, J.-P. Lees4, A. Leflat33,39, J. Lefrançois7, R. Lefèvre5, F.
Lemaitre39, E. Lemos Cid38, O. Leroy6, T. Lesiak27, B. Leverington12, Y. Li7,
T. Likhomanenko67,66, R. Lindner39, C. Linn39, F. Lionetto41, B. Liu16, X.
Liu3, D. Loh49, I. Longstaff52, J.H. Lopes2, D. Lucchesi23,o, M. Lucio
Martinez38, H. Luo51, A. Lupato23, E. Luppi17,g, O. Lupton56, A. Lusiani24, X.
Lyu62, F. Machefert7, F. Maciuc30, O. Maev31, K. Maguire55, S. Malde56, A.
Malinin66, T. Maltsev35, G. Manca7, G. Mancinelli6, P. Manning60, J.
Maratas5,v, J.F. Marchand4, U. Marconi15, C. Marin Benito37, P. Marino24,t, J.
Marks12, G. Martellotti26, M. Martin6, M. Martinelli40, D. Martinez Santos38,
F. Martinez Vidal68, 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, A. Merli22,q, E.
Michielin23, D.A. Milanes64, M.-N. Minard4, D.S. Mitzel12, J. Molina
Rodriguez61, I.A. Monroy64, S. Monteil5, M. Morandin23, P. Morawski28, A.
Mordà6, M.J. Morello24,t, J. Moron28, A.B. Morris51, R. Mountain60, F.
Muheim51, M. Mulder42, M. Mussini15, D. Müller55, J. Müller10, K. Müller41, V.
Müller10, P. Naik47, T. Nakada40, R. Nandakumar50, A. Nandi56, I. Nasteva2, M.
Needham51, N. Neri22, S. Neubert12, N. Neufeld39, M. Neuner12, A.D. Nguyen40,
C. Nguyen-Mau40,n, S. Nieswand9, R. Niet10, N. Nikitin33, T. Nikodem12, A.
Novoselov36, D.P. O’Hanlon49, A. Oblakowska-Mucha28, V. Obraztsov36, S.
Ogilvy19, R. Oldeman48, C.J.G. Onderwater69, J.M. Otalora Goicochea2, A.
Otto39, P. Owen41, A. Oyanguren68, P.R. Pais40, A. Palano14,d, F. Palombo22,q,
M. Palutan19, J. Panman39, A. Papanestis50, M. Pappagallo14,d, L.L.
Pappalardo17,g, C. Pappenheimer58, W. Parker59, C. Parkes55, G. Passaleva18,
A. Pastore14,d, G.D. Patel53, M. Patel54, C. Patrignani15,e, A. Pearce55,50,
A. Pellegrino42, G. Penso26,k, M. Pepe Altarelli39, S. Perazzini39, P.
Perret5, L. Pescatore46, K. Petridis47, A. Petrolini20,h, A. Petrov66, M.
Petruzzo22,q, 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. Polyakov60, E. Polycarpo2, G.J. Pomery47, 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,p, W. Qian56, R. Quagliani7,47, B. Rachwal27, J.H.
Rademacker47, M. Rama24, M. Ramos Pernas38, M.S. Rangel2, I. Raniuk44, G.
Raven43, F. Redi54, S. Reichert10, A.C. dos Reis1, C. Remon Alepuz68, V.
Renaudin7, S. Ricciardi50, S. Richards47, M. Rihl39, K. Rinnert53,39, V. Rives
Molina37, P. Robbe7,39, A.B. Rodrigues1, E. Rodrigues58, J.A. Rodriguez
Lopez64, P. Rodriguez Perez55, A. Rogozhnikov67, S. Roiser39, V.
Romanovskiy36, A. Romero Vidal38, J.W. Ronayne13, M. Rotondo23, M.S.
Rudolph60, T. Ruf39, P. Ruiz Valls68, J.J. Saborido Silva38, E. Sadykhov32, N.
Sagidova31, B. Saitta16,f, V. Salustino Guimaraes2, C. Sanchez Mayordomo68, B.
Sanmartin Sedes38, R. Santacesaria26, C. Santamarina Rios38, M. Santimaria19,
E. Santovetti25,j, A. Sarti19,k, C. Satriano26,s, A. Satta25, D.M. Saunders47,
D. Savrina32,33, S. Schael9, M. Schellenberg10, M. Schiller39, H. Schindler39,
M. Schlupp10, M. Schmelling11, T. Schmelzer10, B. Schmidt39, O. Schneider40,
A. Schopper39, K. Schubert10, M. Schubiger40, M.-H. Schune7, R. Schwemmer39,
B. Sciascia19, A. Sciubba26,k, 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. Shevchenko66, A. Shires10, B.G.
Siddi17, R. Silva Coutinho41, L. Silva de Oliveira2, G. Simi23,o, S.
Simone14,d, M. Sirendi48, N. Skidmore47, T. Skwarnicki60, E. Smith54, I.T.
Smith51, J. Smith48, M. Smith55, H. Snoek42, M.D. Sokoloff58, F.J.P. Soler52,
D. Souza47, B. Souza De Paula2, B. Spaan10, P. Spradlin52, S. Sridharan39, F.
Stagni39, M. Stahl12, S. Stahl39, P. Stefko40, S. Stefkova54, O. Steinkamp41,
O. Stenyakin36, S. Stevenson56, S. Stoica30, S. Stone60, B. Storaci41, S.
Stracka24,t, M. Straticiuc30, U. Straumann41, L. Sun58, W. Sutcliffe54, K.
Swientek28, V. Syropoulos43, M. Szczekowski29, T. Szumlak28, S. T’Jampens4, A.
Tayduganov6, T. Tekampe10, G. Tellarini17,g, F. Teubert39, C. Thomas56, E.
Thomas39, J. van Tilburg42, V. Tisserand4, M. Tobin40, S. Tolk48, L.
Tomassetti17,g, D. Tonelli39, S. Topp-Joergensen56, F. Toriello60, E.
Tournefier4, S. Tourneur40, K. Trabelsi40, M. Traill52, M.T. Tran40, M.
Tresch41, A. Trisovic39, A. Tsaregorodtsev6, P. Tsopelas42, A. Tully48, N.
Tuning42, A. Ukleja29, A. Ustyuzhanin67,66, U. Uwer12, C. Vacca16,39,f, V.
Vagnoni15,39, S. Valat39, G. Valenti15, A. Vallier7, R. Vazquez Gomez19, P.
Vazquez Regueiro38, S. Vecchi17, M. van Veghel42, J.J. Velthuis47, M.
Veltri18,r, G. Veneziano40, A. Venkateswaran60, M. Vernet5, M. Vesterinen12,
B. Viaud7, D. Vieira1, M. Vieites Diaz38, X. Vilasis-Cardona37,m, V. Volkov33,
A. Vollhardt41, B. Voneki39, D. Voong47, A. Vorobyev31, V. Vorobyev35, C.
Voß65, J.A. de Vries42, C. Vázquez Sierra38, R. Waldi65, C. Wallace49, R.
Wallace13, J. Walsh24, J. Wang60, D.R. Ward48, H.M. Wark53, N.K. Watson46, D.
Websdale54, A. Weiden41, M. Whitehead39, J. Wicht49, G. Wilkinson56,39, M.
Wilkinson60, M. Williams39, M.P. Williams46, M. Williams57, T. Williams46,
F.F. Wilson50, J. Wimberley59, J. Wishahi10, W. Wislicki29, M. Witek27, G.
Wormser7, S.A. Wotton48, K. Wraight52, S. Wright48, K. Wyllie39, Y. Xie63, Z.
Xing60, Z. Xu40, Z. Yang3, H. Yin63, J. Yu63, X. Yuan35, O. Yushchenko36, M.
Zangoli15, K.A. Zarebski46, M. Zavertyaev11,c, L. Zhang3, Y. Zhang7, Y.
Zhang62, A. Zhelezov12, Y. Zheng62, A. Zhokhov32, X. Zhu3, 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
37ICCUB, Universitat 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
62University of Chinese Academy of Sciences, Beijing, China, associated to 3
63Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
64Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
65Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
66National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
67Yandex School of Data Analysis, Moscow, Russia, associated to 32
68Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
69Van 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 Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines