EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-045 LHCb-PAPER-2015-003 3 March 2015

Measurement of forward ${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$
production at $\sqrt{s}=8$$\mathrm{\,Te\kern-2.07413ptV}$

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

A measurement of the cross-section for ${\mathrm{Z}}$-boson production in the
forward region of $\mathrm{p}$ $\mathrm{p}$ collisions at
8$\mathrm{\,Te\kern-1.00006ptV}$ centre-of-mass energy is presented. The
measurement is based on a sample of
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ decays reconstructed
using the LHCb detector, corresponding to an integrated luminosity of
2.0$\mbox{\,fb}^{-1}$. The acceptance is defined by the requirements
$2.0<\eta<4.5$ and $\mbox{$p_{\rm T}$}>20$$\mathrm{\,Ge\kern-1.00006ptV}$ for
the pseudorapidities and transverse momenta of the leptons. Their invariant
mass is required to lie in the range 60–120$\mathrm{\,Ge\kern-1.00006ptV}$.
The cross-section is determined to be

$\sigma({\mathrm{p}}{\mathrm{p}}\rightarrow{\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}})=93.81\pm
0.41({\rm stat})\pm 1.48({\rm syst})\pm 1.14({\rm lumi})\;{\rm pb}\,,$

where the first uncertainty is statistical and the second reflects all
systematic effects apart from that arising from the luminosity, which is given
as the third uncertainty. Differential cross-sections are presented as
functions of the Z-boson rapidity and of the angular variable $\phi^{*}$,
which is related to the ${\mathrm{Z}}$-boson transverse momentum.

Submitted to JHEP

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

##  1 Introduction

Measurements of vector boson production in hadron collisions permit tests of
electroweak physics and of QCD. The effective kinematic range of the LHCb
detector[1], approximately $2.0<\eta<4.5$ where $\eta$ is the pseudorapidity,
complements that of the general purpose LHC detectors whose acceptance for
precise measurements extends to $|\eta|\approx 2.5$. Measurements at LHCb are
sensitive to the knowledge of the proton structure functions at very low
Bjorken $x$ values, where the parton distribution functions (PDFs) are not
well constrained by previous data, or by other LHC experiments [2].

The most straightforward decay mode in which LHCb can study the production of
the $\mathrm{Z}$ boson is the channel
${\mathrm{Z}}\rightarrow{\upmu^{+}\upmu^{-}}$[3], since the experiment has a
highly efficient trigger and precise reconstruction capabilities for high-
momentum muons. However, it is also desirable to examine the channel
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$,111Throughout this
note we use ${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ to imply
the formation of $\mathrm{e}^{+}\mathrm{e}^{-}$ through either a $\mathrm{Z}$
or a virtual photon $\gamma^{*}$, including the effect of their interference.
which offers a statistically independent sample, with substantially different
sources of systematic uncertainties. The main difficulty with electron
reconstruction in LHCb is the energy measurement. A significant amount of
material is traversed by the particles before they reach the magnet, and their
measured momenta are therefore frequently reduced by bremsstrahlung, which
cannot be recovered fully using the calorimeters because of saturation at an
energy corresponding to a transverse momentum of around
10$\mathrm{\,Ge\kern-1.00006ptV}$ per channel. Consequently the initial
electron directions are well determined, but their measured momenta are low by
a variable amount, $\sim 25\%$ on average. Therefore the rapidity of the
$\mathrm{Z}$ boson, $y_{{\mathrm{Z}}}$, is well determined while its
transverse momentum, $p_{\rm T}$, is poorly measured and biased. Thus, as in
Ref. [4], the distribution of the angular variable $\phi^{*}$, which is
correlated with $p_{\rm T}$ but less affected by bremsstrahlung, is studied.
The $\phi^{*}$ variable [5] is defined in terms of the directions of the
particle momenta

$\phi^{*}\equiv\frac{\tan(\phi_{\mathrm{acop}}/2)}{\cosh(\Delta\eta/2)}\approx\frac{\mbox{$p_{\rm
T}$}}{M}\,,$

where $\Delta\eta$ is the difference in pseudorapidity between the leptons,
the acoplanarity angle $\phi_{\mathrm{acop}}=\pi-|\Delta\phi|$ depends on the
difference between the azimuthal directions of the lepton momenta,
$\Delta\phi$, and $M$ and $p_{\rm T}$ are the invariant mass and transverse
momentum of the lepton pair.222Natural units with $\hbar=c=1$ are used
throughout, so that mass and momentum are measured in units of energy.

In this paper, we present a measurement of the cross-section for
${\mathrm{p}}{\mathrm{p}}\rightarrow{\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$
using the data recorded by LHCb in 2012 at
$\sqrt{s}=8$$\mathrm{\,Te\kern-1.00006ptV}$, corresponding to an integrated
luminosity of 2.0$\mbox{\,fb}^{-1}$. The approach is essentially the same as
that used in a previous study of the same channel at
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ [4]. The current measurement, as
well as being at a higher centre-of-mass energy, benefits from a significantly
higher and more precisely determined integrated luminosity, and from stable
trigger conditions. Futhermore, an improved Monte Carlo simulation of the
detector and an improved modelling of electron bremsstrahlung are available.
The determination is performed in the same kinematic region as the LHCb
measurement of ${\mathrm{Z}}\rightarrow{\upmu^{+}\upmu^{-}}$ [3], namely
$60<M({\mathrm{Z}})<120$$\mathrm{\,Ge\kern-1.00006ptV}$ and $2.0<\eta<4.5$ and
$\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ for the leptons.

Section 2 gives a brief description of the detector, triggers and software,
after which Sect. 3 describes the event selection and the analysis procedure,
and Sect. 4 explains the techniques used for determining the main
uncertainties in the measurement. The results are presented in Sect. 5
followed by a brief summary in Sect. 6.

##  2 Detector and simulation

The LHCb detector [1, 6] is a single-arm forward spectrometer designed for the
study of particles containing $\mathrm{b}$ or $\mathrm{c}$ quarks. The
detector includes a high-precision tracking system consisting of a silicon-
strip vertex detector surrounding the pp interaction region, a large-area
silicon-strip detector located upstream of a dipole magnet with a bending
power of about $4{\rm\,Tm}$, and three stations of silicon-strip detectors and
straw drift tubes, placed downstream of the magnet. The tracking system
provides a measurement of momentum, $p$, 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 $p_{\rm T}$ is in
$\mathrm{\,Ge\kern-1.00006ptV}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photon, electron and hadron candidates are identified by a calorimeter system
consisting of scintillating-pad (SPD) and preshower (PRS) detectors, an
electromagnetic calorimeter (ECAL) and a hadronic calorimeter (HCAL). Muons
are identified by a system composed of alternating layers of iron and
multiwire proportional chambers.

The trigger consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage, which applies a
full event reconstruction. Events are first required to pass the hardware
trigger for electrons, which selects events having an electromagnetic cluster
of high transverse energy geometrically associated with signals in the PRS and
SPD detectors. This high-$p_{\rm T}$ single-electron trigger is then refined
by the software trigger. Global event cuts on the numbers of hits in several
detectors, such as the SPD, are applied in order to prevent high-multiplicity
events from dominating the processing time.

Simulated event samples of
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ with
$M({\mathrm{e}^{+}\mathrm{e}^{-}})>40$$\mathrm{\,Ge\kern-1.00006ptV}$ are used
in the analysis. Simulated samples of
${\mathrm{Z}}\rightarrow{\uptau^{+}\uptau^{-}}$,
${{\mathrm{t}}{\overline{\mathrm{t}}}}$, ${\mathrm{W}^{+}}{\mathrm{W}^{-}}$
and ${\mathrm{W}^{\pm}}{\mathrm{Z}}$ are used to assess possible background
contributions. In the simulation, pp collisions are generated using Pythia 8.1
[7, *Sjostrand:2007gs] with a specific LHCb configuration [9]. The interaction
of the generated particles with the detector and its response are implemented
using the Geant4 toolkit [10, *Agostinelli:2002hh] as described in Ref. [12].

##  3 Data analysis

The reconstructed particles used as the basis of the analysis satisfy basic
track quality requirements. The following criteria are applied in order to
refine the sample of candidates for analysis:

  * •

either the electron or the positron candidate should satisfy a single-electron
trigger at all stages of the trigger;

  * •

the reconstructed electron and positron candidates should have pseudorapidity
and transverse momentum satisfying $2.0<\eta<4.5$ and $\mbox{$p_{\rm
T}$}>20$$\mathrm{\,Ge\kern-1.00006ptV}$ respectively. The reconstructed
$\mathrm{e}^{+}\mathrm{e}^{-}$ invariant mass should be greater than
40$\mathrm{\,Ge\kern-1.00006ptV}$;

  * •

to ensure good track quality, the electron and positron candidates should have
momenta measured with estimated fractional uncertainty smaller than $10\%$;

  * •

in order to identify the particles as electron candidates, both are required
to show associated energy deposition in the calorimeters characteristic of
high-energy electrons, namely $E_{\rm ECAL}/p>0.1$, $E_{\rm HCAL}/p<0.05$ and
$E_{\rm PRS}>50$$\mathrm{\,Me\kern-1.00006ptV}$ where $E_{\rm ECAL}$, $E_{\rm
HCAL}$ and $E_{\rm PRS}$ denote the energies recorded in the electromagnetic
calorimeter, hadronic calorimeter and preshower detector respectively;

  * •

if more than one ${\mathrm{e}^{+}\mathrm{e}^{-}}$ pair satisfies the above
criteria in an event (which occurs in approximately 0.7% of cases), one is
selected at random.

Applying these selection requirements on data, 65 552
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ candidates are
obtained. Most backgrounds are removed by subtracting a sample of same-sign
${\mathrm{e}^{\pm}}{\mathrm{e}^{\pm}}$ candidates. The validity of this
procedure is assessed in Sect. 4. Applying identical selection criteria, 4595
same-sign candidates are found.

The cross-section is determined using the following expression:

$\sigma=\frac{N({\mathrm{e}^{+}\mathrm{e}^{-}})-N({\mathrm{e}^{\pm}}{\mathrm{e}^{\pm}})-N_{\rm
bg}}{\epsilon\cdot\int\mathcal{L}\mathrm{d}t}\cdot f_{\mathrm{MZ}}\,,$ (1)

where $N({\mathrm{e}^{+}\mathrm{e}^{-}})$ is the number of signal candidates
selected in data, $N({\mathrm{e}^{\pm}}{\mathrm{e}^{\pm}})$ is the number of
same-sign candidates, $N_{\rm bg}$ is the expected background not covered by
same-sign candidates (predominantly
${\mathrm{Z}}\rightarrow{\uptau^{+}\uptau^{-}}$) taken from simulation and
$\int\mathcal{L}\mathrm{d}t$ is the integrated luminosity. The event detection
efficiency, $\epsilon$, is evaluated using a combination of data and
simulation as explained below, and refers to events for which the true
electrons satisfy $2.0<\eta<4.5$, $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and
$60<M({\mathrm{e}^{+}\mathrm{e}^{-}})<120$$\mathrm{\,Ge\kern-1.00006ptV}$. The
factor $f_{\mathrm{MZ}}$ (determined from simulation) corrects for the
inclusion in the data sample of
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ candidates that pass
the event selection even though their true mass lies outside the range
$60<M({\mathrm{e}^{+}\mathrm{e}^{-}})<120$$\mathrm{\,Ge\kern-1.00006ptV}$. The
correction procedure is applied for 17 bins in $\mathrm{Z}$ rapidity in the
range $2.00<y_{{\mathrm{Z}}}<4.25$.333Although tracks can be reconstructed at
larger rapidities, the efficiency for electron identification vanishes just
above $y_{{\mathrm{Z}}}=4.25$ because of the inner edge of the calorimeter
acceptance, so that no candidate event at higher rapidity survives in either
data or simulation. The analysis is also performed for 15 bins in $\phi^{*}$.
The choice of binning takes account of the available sample size and the
resolutions achieved on $y_{{\mathrm{Z}}}$ and $\phi^{*}$. The luminosity is
obtained with an overall uncertainty of $1.2\%$[13].

The efficiency of the event selection is factorised into several components,

$\epsilon=\epsilon_{\mathrm{track}}\cdot\epsilon_{\mathrm{kin}}\cdot\epsilon_{\mathrm{PID}}\cdot\epsilon_{\mathrm{GEC}}\cdot\epsilon_{\mathrm{trig}}\,.$
(2)

The efficiencies are determined such that the efficiency for each stage of the
analysis is estimated for events that pass the preceding stages. Thus,
$\epsilon_{\mathrm{track}}$ is the efficiency associated with the
reconstruction of both electrons as tracks satisfying the quality requirements
and $\epsilon_{\mathrm{kin}}$ gives the efficiency that both these
reconstructed electron tracks satisfy the kinematic acceptance requirements on
$p_{\rm T}$ and $\eta$. Similarly, $\epsilon_{\mathrm{PID}}$ is the efficiency
for identification of the tracks as electrons, $\epsilon_{\mathrm{GEC}}$ is
the estimated efficiency of the global event cuts for these events and
$\epsilon_{\mathrm{trig}}$ is the trigger efficiency. The determination of
these contributions to the efficiency is performed separately in each bin of
$y_{{\mathrm{Z}}}$ or of $\phi^{*}$. The contributions that the terms in the
efficiency make to the systematic uncertainty on the measurement are
summarised in Sect. 4.

The tracking efficiency, $\epsilon_{\rm track}$, gives the probability that,
in events in which the electrons satisfy $2.0<\eta<4.5$, $\mbox{$p_{\rm
T}$}>20$$\mathrm{\,Ge\kern-1.00006ptV}$ and
$60<M({\mathrm{e}^{+}\mathrm{e}^{-}})<120$$\mathrm{\,Ge\kern-1.00006ptV}$ at
the particle level (i.e. based on their true momenta, as known in simulated
events), both of them correspond to reconstructed tracks satisfying the track
quality requirements. In order to characterise accurately the dependence of
the efficiency on $y_{{\mathrm{Z}}}$ and $\phi^{*}$, the efficiency is taken
from simulation. A consistency check using data allows a systematic
uncertainty to be assigned as described in Sect. 4. The efficiency shows a
significant dependence on $y_{\rm Z}$, but almost no variation with
$\phi^{*}$.

The kinematic efficiency, $\epsilon_{\rm kin}$, accounts for the possibility
that a ${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ decay in which
the electron momenta at particle level satisfy the kinematic requirements on
$p_{\rm T}$ and $\eta$ may not do so for the reconstructed momenta, even
though the tracks are reconstructed and satisfy the track quality
requirements. This is a sizeable correction because of bremsstrahlung. The
efficiency is determined using simulated events, with data used to assess the
systematic uncertainty as described in Sect. 4. In contrast to the earlier
analysis [4], the particle-level electron momentum used here is the momentum
before final-state radiation (FSR), so that the kinematic efficiency also
includes the effect of FSR as implemented in Pythia 8.1, and an additional
correction is no longer applied.

The particle identification efficiency, $\epsilon_{\rm PID}$, accounts for the
possibility that a signal event passing all track finding and kinematic
requirements fails the electron identification requirements, either because
the track falls outside the calorimeter acceptance, or because the
requirements on calorimeter energies are not satisfied. The overall efficiency
is taken from simulation in order to model accurately a significant dependence
on $y_{{\mathrm{Z}}}$. This dependence is a consequence of the geometrical
acceptance and is assumed to be modelled reliably. The efficiency of the
calorimeter energy requirements is validated using data as described in Sect.
4, leading to a systematic uncertainty.

The only global event cut that has any significant effect on the
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ channel is a
requirement in the electron triggers that the number of hits in the SPD be
less than 600. In order to assess the consequent loss of events, use is made
of ${\mathrm{Z}}\rightarrow{\upmu^{+}\upmu^{-}}$ events that satisfy the
dimuon trigger, for which the number of SPD hits, $N_{\rm SPD}$, is required
to be less than 900. The distribution of $N_{\rm SPD}$ in dielectron events
should be the same as that in dimuon events apart from the contribution from
the leptons. In the region $N_{\rm SPD}<600$ it is observed that the
distribution for ${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ is
consistent with that for ${\mathrm{Z}}\rightarrow{\upmu^{+}\upmu^{-}}$ with an
upward shift of $10\pm 5$ hits associated with showering of the electron and
positron. This shift is confirmed in simulation. Accordingly, we use the
fraction of ${\mathrm{Z}}\rightarrow{\upmu^{+}\upmu^{-}}$ dimuon triggers in
the range $590\leq N_{\rm SPD}<900$ to estimate the loss of dielectron events
in the range $600\leq N_{\rm SPD}<910$. The small fraction of dimuon events
having $N_{\rm SPD}\geq 900$ is estimated to be 0.7% by extrapolation using an
empirical fit to the distribution. The efficiency shows a weak dependence on
$\mathrm{Z}$ rapidity and $\phi^{*}$.

The trigger efficiencies for events passing the selection cuts are determined
from data using a “tag-and-probe” method. The principle is to use events in
which the electron satisfies the trigger to determine the efficiency for the
positron to satisfy the trigger and vice versa.

The values of the various correction factors, averaged over all values of
$y_{{\mathrm{Z}}}$, are summarised in Table 1. The uncorrelated components of
the uncertainties are generally related to the statistical uncertainty
associated with each efficiency. These can be sizeable in individual bins, but
become small when their effect on the integrated cross-section is considered.
The correlated components are taken to be fully correlated between bins, and
therefore have roughly the same effect on individual bins and on the
integrated cross-section. The principal systematic uncertainties are discussed
in greater detail in Sect. 4. The overall efficiency is shown as a function of
$y_{{\mathrm{Z}}}$ and $\phi^{*}$ in Fig. 1.

Figure 1: Overall detection efficiency, $\epsilon$, determined from a combination of data and simulation as described in the text, shown as a function of (left) $y_{{\mathrm{Z}}}$ and (right) $\phi^{*}$. Table 1: Efficiencies and other factors used for the cross-section determination (see Eq. (1)) averaged over the experimental acceptance by integrating over $y_{{\mathrm{Z}}}$. The fractional uncertainties on the overall factors are also given, separated into components that are assumed to be correlated and uncorrelated between bins of the differential distributions. |  | Fractional uncertainty
---|---|---
| Average value | Uncorrelated | Correlated
$\epsilon_{\mathrm{track}}$ | 0.912 | 0.001 | 0.010
$\epsilon_{\mathrm{kin}}$ | 0.507 | 0.002 | 0.006
$\epsilon_{\mathrm{PID}}$ | 0.838 | 0.001 | 0.007
$\epsilon_{\mathrm{GEC}}$ | 0.916 | — | 0.006
$\epsilon_{\mathrm{trig}}$ | 0.892 | 0.001 | —
$\epsilon$ | 0.319 | 0.002 | 0.016
$f_{\mathrm{MZ}}$ | 0.969 | 0.001 | —
Background estimation | — | — | 0.004
$\int\mathcal{L}{\rm d}t$ /$\mbox{\,pb}^{-1}$ | 1976 | — | 0.012

##  4 Systematic uncertainties

The tracking efficiency is evaluated using simulation and checked using data.
The principle is to search for events where a track appears to be missing, so
that the signature of a $\mathrm{Z}$ becomes a high-$p_{\rm T}$ electron track
accompanied by a high-energy ECAL cluster with no associated track. An
efficiency is determined by comparison with the corresponding number of events
in which two tracks are reconstructed. To reduce background, more stringent
particle identification requirements are imposed on the tag electron, and
isolation requirements are imposed on both the electron and the ECAL cluster.
This cannot be regarded as a direct measurement of the efficiency of the main
analysis selection because more stringent requirements are employed. Instead,
the same procedure is applied to the simulated event sample. The ratio between
the two, $0.990\pm 0.004$, is taken as a correction to $\epsilon_{\rm track}$
obtained from simulation, with the full size of the correction taken as a
systematic uncertainty, $\pm 0.010$, which is assumed to be fully correlated
between bins of the differential distributions.

The kinematic efficiency is also evaluated from simulation. Accurate
simulation of the detector material is necessary in order to model correctly
energy losses through bremsstrahlung, and any inaccuracy would lead to a
scaling of the measured momenta. This is tested by examining the modelling of
the $p_{\rm T}$ distributions by simulation, particularly in the neighbourhood
of the 20$\mathrm{\,Ge\kern-1.00006ptV}$ threshold. Figure 2 shows the
distribution of $\min(\mbox{$p_{\rm T}$}({\mathrm{e}^{+}}),\mbox{$p_{\rm
T}$}({\mathrm{e}^{-}}))$ for data compared with simulation. In order to
quantify the uncertainty in $\epsilon_{\rm kin}$, the $p_{\rm T}$ values in
data are scaled by a global factor $\alpha$ to represent the effect of an
uncertainty in the detector material. The $\chi^{2}$ between data and
simulation is examined as $\alpha$ is varied. The resulting uncertainty in
$\alpha$ translates into a relative uncertainty in $\epsilon_{\rm kin}$ of
0.6% (or 1.2% for $y_{{\mathrm{Z}}}>3.75$), which is taken to be a systematic
uncertainty fully correlated between bins.

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

The contribution to $\epsilon_{\rm PID}$ resulting from the calorimeter
acceptance is purely geometrical and is assumed to be modelled reliably in
simulation. To assess the reliability of simulation for the calorimeter energy
requirements, events are selected in which one electron is tagged using the
standard criteria, while a second probe track is found that satisfies all the
requirements apart from that on the energy recorded in one of the
calorimeters. By examining the distributions of calorimeter energy in the
neighbourhood of the threshold applied, an estimate of any correction needed
and its uncertainty is made. The test is repeated for each part of the
calorimeter in turn. As a result of these studies, a systematic uncertainty of
0.7% on $\epsilon_{\rm PID}$ is assigned, independent of $y_{{\mathrm{Z}}}$
and $\phi^{*}$, and treated as fully correlated between bins.

The statistical uncertainty in the determination of $\epsilon_{\rm GEC}$ is
taken as part of the systematic uncertainties. The uncertainty in the $10\pm
5$ $N_{\rm SPD}$ offset leads to an additional systematic uncertainty of 0.4%
overall, while an uncertainty of 0.2% is assigned based on comparing various
extrapolation techniques. The value of $\epsilon_{\mathrm{GEC}}$ is determined
as a function of $y_{{\mathrm{Z}}}$ and $\phi^{*}$. The statistical
uncertainty on the determination of $\epsilon_{\mathrm{trig}}$ is treated as a
systematic uncertainty.

The principal background to the selected
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ sample is expected to
arise from failures of particle identification, typically where one or two
high-$p_{\rm T}$ hadrons interact early and exhibit a shower profile in the
calorimeters similar to electrons. Such backgrounds are addressed by the
subtraction of the same-sign
${\mathrm{Z}}\rightarrow{\mathrm{e}^{\pm}}{\mathrm{e}^{\pm}}$ candidates. To
check whether this procedure is reliable, event samples are studied in which
one electron is tagged using the standard requirements, while the second
electron satisfies the same criteria except that the requirement on HCAL
energy is not satisfied, suggesting that the probe is likely to be a hadron.
The numbers of same-sign and opposite-sign pairs satisfying these criteria
agree within 5.5%. Treating this as an uncertainty on the background
corresponds to an uncertainty of 0.4% in the signal yield, which is taken as
the systematic uncertainty on the cross-section. There is no significant
variation with $y_{{\mathrm{Z}}}$ or $\phi^{*}$, so the uncertainty is taken
to be the same in all bins and fully correlated between bins.

Physics backgrounds that could give correlated pairs of genuine electron and
positron are not necessarily removed by the same-sign subtraction. Production
of heavy quark pairs, ${\mathrm{c}}{\overline{\mathrm{c}}}$ or
${\mathrm{b}}{\overline{\mathrm{b}}}$, followed by semileptonic decay could
mimic the signal. This contribution is expected to be small, and is found to
be negligible using studies of the distribution of the vertex-fit $\chi^{2}$
for the candidates in data and simulation. The decay
${\mathrm{Z}}\rightarrow{\uptau^{+}\uptau^{-}}$ provides a background if both
$\tau$-leptons decay to electrons. After the selection, the background from
this source is estimated to be 0.15% of the signal using simulated samples,
and the prediction is subtracted in each bin of $y_{{\mathrm{Z}}}$ and
$\phi^{*}$ as indicated in Eq. (1) with its statistical uncertainty included
in the statistical error. The background arising from production of pairs of
gauge bosons, such as ${\mathrm{W}^{+}}{\mathrm{W}^{-}}$ or
${\mathrm{W}^{\pm}}{\mathrm{Z}}$, or of ${\mathrm{t}}{\overline{\mathrm{t}}}$
pairs, is neglected, being well below the 0.1% level, based on expectations
from simulation.

##  5 Results

The measured differential cross-sections as functions of $y_{{\mathrm{Z}}}$
and $\phi^{*}$ are tabulated in Tables 2 and 3. The uncertainties in the bins
of these distributions are significantly correlated because the luminosity
uncertainty and some of the systematic uncertainties are assumed to be common
between bins. The correlation matrices between bins of the distributions are
presented in Tables 4 and 5 of the Appendix.

The results are given as Born-level cross-sections, which do not include the
effects of final-state radiation. Tables 2 and 3 also include the factors
$f_{\rm FSR}$ that permit the measurements to be converted to the particle
level after FSR. These are determined using the true momenta of the electrons
before and after the generation of FSR in the simulation.

Table 2: Differential cross-section for ${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ as a function of $\mathrm{Z}$-boson rapidity. The first error is statistical, the second the uncorrelated experimental systematic, the third the correlated experimental systematic and the last error is the uncertainty in luminosity. The cross-sections are at the Born level, i.e. before FSR. The rightmost column gives values of the additional factor, $f_{\rm FSR}$, by which the results should be multiplied in order to give the cross-sections after FSR.  $y_{{\mathrm{Z}}}$ |  ${\rm d}\sigma/{\rm d}y_{{\mathrm{Z}}}$ [pb] | $f_{\rm FSR}$
---|---|---
2.000– | 2.125 |  | 8.27$\,\pm\,$ | 0.37 $\,\pm\,$ | 0.21 $\,\pm\,$ | 0.14 $\,\pm\,$ | 0.10 |  | 0.953 $\,\pm\,$ | 0.003
2.125– | 2.250 |  | 26.17$\,\pm\,$ | 0.61 $\,\pm\,$ | 0.32 $\,\pm\,$ | 0.43 $\,\pm\,$ | 0.32 |  | 0.955 $\,\pm\,$ | 0.002
2.250– | 2.375 |  | 40.29$\,\pm\,$ | 0.72 $\,\pm\,$ | 0.36 $\,\pm\,$ | 0.62 $\,\pm\,$ | 0.49 |  | 0.959 $\,\pm\,$ | 0.001
2.375– | 2.500 |  | 52.16$\,\pm\,$ | 0.80 $\,\pm\,$ | 0.39 $\,\pm\,$ | 0.81 $\,\pm\,$ | 0.64 |  | 0.960 $\,\pm\,$ | 0.001
2.500– | 2.625 |  | 61.92$\,\pm\,$ | 0.86 $\,\pm\,$ | 0.40 $\,\pm\,$ | 1.01 $\,\pm\,$ | 0.77 |  | 0.958 $\,\pm\,$ | 0.001
2.625– | 2.750 |  | 72.32$\,\pm\,$ | 0.93 $\,\pm\,$ | 0.45 $\,\pm\,$ | 1.10 $\,\pm\,$ | 0.88 |  | 0.958 $\,\pm\,$ | 0.001
2.750– | 2.875 |  | 76.29$\,\pm\,$ | 0.98 $\,\pm\,$ | 0.47 $\,\pm\,$ | 1.16 $\,\pm\,$ | 0.93 |  | 0.956 $\,\pm\,$ | 0.001
2.875– | 3.000 |  | 77.67$\,\pm\,$ | 0.99 $\,\pm\,$ | 0.48 $\,\pm\,$ | 1.18 $\,\pm\,$ | 0.95 |  | 0.952 $\,\pm\,$ | 0.001
3.000– | 3.125 |  | 77.72$\,\pm\,$ | 1.03 $\,\pm\,$ | 0.51 $\,\pm\,$ | 1.18 $\,\pm\,$ | 0.95 |  | 0.952 $\,\pm\,$ | 0.001
3.125– | 3.250 |  | 69.58$\,\pm\,$ | 1.02 $\,\pm\,$ | 0.50 $\,\pm\,$ | 1.06 $\,\pm\,$ | 0.85 |  | 0.949 $\,\pm\,$ | 0.001
3.250– | 3.375 |  | 62.03$\,\pm\,$ | 1.01 $\,\pm\,$ | 0.51 $\,\pm\,$ | 0.96 $\,\pm\,$ | 0.76 |  | 0.950 $\,\pm\,$ | 0.001
3.375– | 3.500 |  | 46.26$\,\pm\,$ | 0.92 $\,\pm\,$ | 0.46 $\,\pm\,$ | 0.71 $\,\pm\,$ | 0.56 |  | 0.949 $\,\pm\,$ | 0.001
3.500– | 3.625 |  | 33.49$\,\pm\,$ | 0.84 $\,\pm\,$ | 0.41 $\,\pm\,$ | 0.53 $\,\pm\,$ | 0.41 |  | 0.947 $\,\pm\,$ | 0.002
3.625– | 3.750 |  | 22.81$\,\pm\,$ | 0.74 $\,\pm\,$ | 0.37 $\,\pm\,$ | 0.36 $\,\pm\,$ | 0.28 |  | 0.951 $\,\pm\,$ | 0.002
3.750– | 3.875 |  | 13.56$\,\pm\,$ | 0.64 $\,\pm\,$ | 0.33 $\,\pm\,$ | 0.28 $\,\pm\,$ | 0.17 |  | 0.946 $\,\pm\,$ | 0.002
3.875– | 4.000 |  | 6.28$\,\pm\,$ | 0.57 $\,\pm\,$ | 0.28 $\,\pm\,$ | 0.13 $\,\pm\,$ | 0.08 |  | 0.939 $\,\pm\,$ | 0.004
4.000– | 4.250 |  | 1.85$\,\pm\,$ | 0.33 $\,\pm\,$ | 0.16 $\,\pm\,$ | 0.04 $\,\pm\,$ | 0.02 |  | 0.928 $\,\pm\,$ | 0.005
Table 3: Differential cross-section for ${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ as a function of $\phi^{*}$. The first error is statistical, the second the uncorrelated experimental systematic, the third the correlated experimental systematic and the last error is the uncertainty in luminosity. The cross-sections are at the Born level, i.e. before FSR. The rightmost column gives values of the additional factor, $f_{\rm FSR}$, by which the results should be multiplied in order to give the cross-sections after FSR.  $\phi^{*}$ |  ${\rm d}\sigma/{\rm d}\phi^{*}$ [pb] | $f_{\rm FSR}$
---|---|---
0.00– | 0.01 | 996$\,\pm\,$ | 13 $\,\pm\,$ | 7 $\,\pm\,$ | 15 $\,\pm\,$ | 12 | 0.954 $\,\pm\,$ | 0.001
0.01– | 0.02 | 933$\,\pm\,$ | 13 $\,\pm\,$ | 7 $\,\pm\,$ | 14 $\,\pm\,$ | 11 | 0.955 $\,\pm\,$ | 0.001
0.02– | 0.03 | 851$\,\pm\,$ | 12 $\,\pm\,$ | 6 $\,\pm\,$ | 13 $\,\pm\,$ | 10 | 0.954 $\,\pm\,$ | 0.001
0.03– | 0.05 | 664$\,\pm\,$ | 8 $\,\pm\,$ | 4 $\,\pm\,$ | 10 $\,\pm\,$ | 8 | 0.954 $\,\pm\,$ | 0.001
0.05– | 0.07 | 505$\,\pm\,$ | 7 $\,\pm\,$ | 3 $\,\pm\,$ | 7 $\,\pm\,$ | 6 | 0.953 $\,\pm\,$ | 0.001
0.07– | 0.10 | 346$\,\pm\,$ | 5 $\,\pm\,$ | 2 $\,\pm\,$ | 5 $\,\pm\,$ | 4 | 0.952 $\,\pm\,$ | 0.001
0.10– | 0.15 | 221.5$\,\pm\,$ | 2.9 $\,\pm\,$ | 1.4 $\,\pm\,$ | 3.4 $\,\pm\,$ | 2.7 | 0.953 $\,\pm\,$ | 0.001
0.15– | 0.20 | 126.9$\,\pm\,$ | 2.2 $\,\pm\,$ | 1.1 $\,\pm\,$ | 2.0 $\,\pm\,$ | 1.6 | 0.952 $\,\pm\,$ | 0.001
0.20– | 0.30 | 65.8$\,\pm\,$ | 1.1 $\,\pm\,$ | 0.5 $\,\pm\,$ | 1.0 $\,\pm\,$ | 0.8 | 0.949 $\,\pm\,$ | 0.001
0.30– | 0.40 | 32.2$\,\pm\,$ | 0.8 $\,\pm\,$ | 0.4 $\,\pm\,$ | 0.5 $\,\pm\,$ | 0.4 | 0.951 $\,\pm\,$ | 0.002
0.40– | 0.60 | 13.86$\,\pm\,$ | 0.36 $\,\pm\,$ | 0.17 $\,\pm\,$ | 0.22 $\,\pm\,$ | 0.17 | 0.951 $\,\pm\,$ | 0.002
0.60– | 0.80 | 5.63$\,\pm\,$ | 0.23 $\,\pm\,$ | 0.11 $\,\pm\,$ | 0.09 $\,\pm\,$ | 0.07 | 0.955 $\,\pm\,$ | 0.003
0.80– | 1.20 | 1.64$\,\pm\,$ | 0.09 $\,\pm\,$ | 0.04 $\,\pm\,$ | 0.03 $\,\pm\,$ | 0.02 | 0.957 $\,\pm\,$ | 0.003
1.20– | 2.00 | 0.334$\,\pm\,$ | 0.026 $\,\pm\,$ | 0.013 $\,\pm\,$ | 0.006 $\,\pm\,$ | 0.004 | 0.957 $\,\pm\,$ | 0.005
2.00– | 4.00 | 0.031$\,\pm\,$ | 0.006 $\,\pm\,$ | 0.002 $\,\pm\,$ | 0.001 $\,\pm\,$ | 0.001 | 0.966 $\,\pm\,$ | 0.007

The overall cross-section, obtained by integration of the rapidity
distribution, is

$\sigma({\mathrm{p}}{\mathrm{p}}\rightarrow{\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}})=93.81\pm
0.41({\rm stat})\pm 1.48({\rm syst})\pm 1.14({\rm lumi})\;{\rm pb}\,,$

where the first uncertainty is statistical, the second includes all
experimental systematic effects apart from the contribution from the
luminosity, which forms the third uncertainty. When combining the experimental
systematic uncertainties, those associated with $\epsilon_{\rm trig}$, and
those parts of $\epsilon_{\rm track}$, $\epsilon_{\rm kin}$ and $\epsilon_{\rm
PID}$ arising from the size of the Monte Carlo sample, are treated as
uncorrelated between bins and therefore combined quadratically; other
contributions are treated as fully correlated, as is the luminosity
uncertainty, and combined linearly.

The measured cross-section is compared in Fig. 3 with next-to-next-to-leading
order (NNLO; ${\cal O}({\alpha_{s}}^{2})$) QCD predictions, based on Fewz
version 3.1.b2 [14] using five different PDF sets, MSTW08 [15], CTEQ10 [16],
ABM12 [17], NNPDF23 [18] and NNPDF30 [19]. Of these, MSTW08 and CTEQ10 predate
the start of LHC data-taking, while ABM12 and NNPDF have included some LHC
measurements in their analyses. The uncertainties in the predictions include
the effect of varying the renormalisation and factorisation scales by factors
of two around the nominal values (set to the $\mathrm{Z}$ mass), combined in
quadrature with the PDF uncertainties evaluated at 68% confidence level. All
predictions are in good agreement with the data.

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

The differential distribution with respect to $y_{{\mathrm{Z}}}$ is presented
in Fig. 4 (left) and compared with the NNLO calculations based on Fewz, all of
which are compatible with the integrated cross-section, and model the rapidity
distribution as well. In comparing the shapes of the differential cross-
sections with theoretical predictions it can be beneficial to normalise them
to the integrated cross-section in the acceptance, since most of the
correlated systematic uncertainties in the data cancel. This is useful when
comparing with models based on LO or NLO calculations, which may predict the
integrated cross-section well. The normalised differential distribution with
respect to $y_{{\mathrm{Z}}}$ is presented in Fig. 4 (right) and compared with
calculations that partially take account of higher-order effects. A QCD
calculation that takes multiple soft gluon emissions into account through
resummation is provided by ResBos [20, *Balazs:1997xd, *Landry:2002ix].444The
P branch of ResBos is used with grids for LHC at
$\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$ based on CTEQ6.6. Alternatively,
Powheg [22, *Alioli:2010qp] provides a framework whereby a NLO (${\cal
O}({\alpha_{s}})$) calculation can be interfaced to a parton shower model such
as Pythia, which can approximate higher-order effects. The parton shower model
of Pythia 8.1 [7, *Sjostrand:2007gs] is also compared with the data. All
approaches reproduce the main features of the rapidity distribution.

Studies at 7 TeV [4] showed that the NNLO calculations based on Fewz fail to
model the $\phi^{*}$ distribution. It is expected that the $\phi^{*}$
distribution, like that of $p_{\rm T}$, is significantly affected by multiple
soft gluon emissions, which are not sufficiently accounted for in fixed-order
calculations. The present data exhibit the same behaviour, and this comparison
is not shown. The normalised distribution with respect to $\phi^{*}$ is
therefore presented in Fig. 5 (left) and compared with the ResBos, Powheg and
Pythia 8.1 calculations. These all model the data reasonably well, especially
at lower $\phi^{*}$ where differences are typically up to the 10% level, while
larger discrepancies are seen for $\phi^{*}>1$. To show this more clearly, the
ratios between the calculations that include higher orders and the data for
the $\phi^{*}$ distribution are also shown in Fig. 5 (right). The data tend to
fall between the different models, indicating no clear preference for any of
them.

Figure 4: (left) Differential cross-section ${\rm d}\sigma/{\rm
d}y_{{\mathrm{Z}}}$ and (right) normalised differential cross-section
$(1/\sigma){\rm d}\sigma/{\rm d}y_{{\mathrm{Z}}}$ as a function of
$y_{{\mathrm{Z}}}$. The measured data are shown as the shaded bands, with the
inner (orange) bands indicating the statistical error and the outer (yellow)
bands the total uncertainty. For comparison, the NNLO predictions of Fewz
using five different sets of PDFs are shown on the left-hand plot. The same
data are compared with leading log calculations in the right-hand plot. To aid
clarity, small horizontal displacements are applied to some of the
predictions.

Figure 5: (left) Normalised differential cross-section $(1/\sigma){\rm
d}\sigma/{\rm d}\phi^{*}$ as a function of $\phi^{*}$. The measured data are
shown as the shaded bands, with the inner (orange) bands indicating the
statistical error and the outer (yellow) bands the total uncertainty. For
comparison, the predictions of the leading-log calculations described in the
text are shown. (right) The same data and predictions normalised to the
measurement in data, so that the measurements are shown as the shaded bands at
unity. To aid clarity, small horizontal displacements are applied to some of
the predictions.

##  6 Summary

A measurement of the cross-section for ${\mathrm{Z}}$-boson production in the
forward region of $\mathrm{p}$ $\mathrm{p}$ collisions at
8$\mathrm{\,Te\kern-1.00006ptV}$ centre-of-mass energy is presented. The
measurement, using an integrated luminosity of 2.0 $\mbox{\,fb}^{-1}$ recorded
using the LHCb detector, is based on the
${\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}}$ decay. The acceptance
is defined by the requirements $2.0<\eta<4.5$ and $\mbox{$p_{\rm
T}$}>20$$\mathrm{\,Ge\kern-1.00006ptV}$ for the leptons while their invariant
mass is required to lie in the range 60–120$\mathrm{\,Ge\kern-1.00006ptV}$.
The cross-section is determined to be

$\sigma({\mathrm{p}}{\mathrm{p}}\rightarrow{\mathrm{Z}}\rightarrow{\mathrm{e}^{+}\mathrm{e}^{-}})=93.81\pm
0.41({\rm stat})\pm 1.48({\rm syst})\pm 1.14({\rm lumi})\;{\rm pb}\,,$

where the first uncertainty is statistical and the second reflects all
systematic uncertainties apart from that associated with the luminosity, which
is given as the third uncertainty. Differential cross-sections are also
presented as functions of the Z-boson rapidity, and the angular variable
$\phi^{*}$. The rapidity distribution is well modelled by NNLO calculations,
and is compared with several recent sets of parton distribution functions. A
reasonable description of the $\phi^{*}$ distribution requires the use of
calculations that implement approximations of higher orders, either through
resummation or using parton shower techniques.

## 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, 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).

Appendix

## Correlation Matrices

Table 4: Correlation matrix between bins of $y_{\rm Z}$. The bin numbering
follows the same sequence as Table 2.

Bin |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17
1 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2 | 0.23 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
3 | 0.26 | 0.43 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
4 | 0.22 | 0.36 | 0.41 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
5 | 0.30 | 0.49 | 0.56 | 0.47 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
6 | 0.30 | 0.50 | 0.56 | 0.47 | 0.64 | 1.00 |  |  |  |  |  |  |  |  |  |  |
7 | 0.30 | 0.50 | 0.57 | 0.47 | 0.65 | 0.65 | 1.00 |  |  |  |  |  |  |  |  |  |
8 | 0.30 | 0.50 | 0.57 | 0.47 | 0.65 | 0.65 | 0.65 | 1.00 |  |  |  |  |  |  |  |  |
9 | 0.30 | 0.49 | 0.56 | 0.47 | 0.64 | 0.64 | 0.65 | 0.64 | 1.00 |  |  |  |  |  |  |  |
10 | 0.28 | 0.47 | 0.54 | 0.45 | 0.61 | 0.62 | 0.62 | 0.62 | 0.61 | 1.00 |  |  |  |  |  |  |
11 | 0.27 | 0.45 | 0.51 | 0.43 | 0.58 | 0.59 | 0.59 | 0.59 | 0.58 | 0.56 | 1.00 |  |  |  |  |  |
12 | 0.25 | 0.41 | 0.46 | 0.39 | 0.53 | 0.53 | 0.54 | 0.54 | 0.53 | 0.51 | 0.49 | 1.00 |  |  |  |  |
13 | 0.22 | 0.36 | 0.41 | 0.34 | 0.47 | 0.47 | 0.47 | 0.47 | 0.47 | 0.45 | 0.43 | 0.39 | 1.00 |  |  |  |
14 | 0.18 | 0.30 | 0.34 | 0.28 | 0.39 | 0.39 | 0.39 | 0.39 | 0.39 | 0.37 | 0.35 | 0.32 | 0.28 | 1.00 |  |  |
15 | 0.15 | 0.26 | 0.29 | 0.24 | 0.33 | 0.33 | 0.33 | 0.33 | 0.33 | 0.32 | 0.30 | 0.27 | 0.24 | 0.20 | 1.00 |  |
16 | 0.09 | 0.14 | 0.16 | 0.14 | 0.18 | 0.19 | 0.19 | 0.19 | 0.18 | 0.18 | 0.17 | 0.15 | 0.13 | 0.11 | 0.10 | 1.00 |
17 | 0.04 | 0.07 | 0.08 | 0.07 | 0.10 | 0.10 | 0.10 | 0.10 | 0.10 | 0.09 | 0.09 | 0.08 | 0.07 | 0.06 | 0.05 | 0.03 | 1.00

Table 5: Correlation matrix between bins of $\phi^{*}$. The bin numbering
follows the same sequence as Table 3.

Bin index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |  |
2 | 0.63 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |  |
3 | 0.62 | 0.61 | 1.00 |  |  |  |  |  |  |  |  |  |  |  |
4 | 0.82 | 0.80 | 0.79 | 1.00 |  |  |  |  |  |  |  |  |  |  |
5 | 0.64 | 0.63 | 0.62 | 0.82 | 1.00 |  |  |  |  |  |  |  |  |  |
6 | 0.64 | 0.63 | 0.62 | 0.82 | 0.64 | 1.00 |  |  |  |  |  |  |  |  |
7 | 0.65 | 0.64 | 0.63 | 0.83 | 0.65 | 0.65 | 1.00 |  |  |  |  |  |  |  |
8 | 0.58 | 0.57 | 0.56 | 0.74 | 0.58 | 0.58 | 0.59 | 1.00 |  |  |  |  |  |  |
9 | 0.58 | 0.58 | 0.57 | 0.75 | 0.59 | 0.59 | 0.59 | 0.53 | 1.00 |  |  |  |  |  |
10 | 0.48 | 0.48 | 0.47 | 0.62 | 0.49 | 0.49 | 0.49 | 0.44 | 0.44 | 1.00 |  |  |  |  |
11 | 0.46 | 0.46 | 0.45 | 0.59 | 0.47 | 0.47 | 0.47 | 0.42 | 0.43 | 0.35 | 1.00 |  |  |  |
12 | 0.35 | 0.34 | 0.34 | 0.44 | 0.35 | 0.35 | 0.35 | 0.31 | 0.32 | 0.26 | 0.25 | 1.00 |  |  |
13 | 0.30 | 0.30 | 0.30 | 0.39 | 0.31 | 0.31 | 0.31 | 0.28 | 0.28 | 0.23 | 0.22 | 0.16 | 1.00 |  |
14 | 0.22 | 0.22 | 0.21 | 0.28 | 0.22 | 0.22 | 0.22 | 0.20 | 0.20 | 0.17 | 0.16 | 0.12 | 0.10 | 1.00 |
15 | 0.10 | 0.10 | 0.10 | 0.13 | 0.10 | 0.10 | 0.10 | 0.09 | 0.09 | 0.08 | 0.07 | 0.06 | 0.05 | 0.04 | 1.00

## References

  * [1] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [2] R. S. Thorne, A. D. Martin, W. J. Stirling, and G. Watt, _Parton distributions and QCD at LHCb_ , arXiv:0808.1847
  * [3] 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
  * [4] 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
  * [5] 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
  * [6] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , arXiv:1412.6352, to appear in Int. J. Mod. Phys. A
  * [7] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [8] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [9] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , Nuclear Science Symposium Conference Record (NSS/MIC) IEEE (2010) 1155
  * [10] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [11] Geant4 collaboration, S. Agostinelli et al., _Geant4: a simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [12] M. Clemencic et al., _The LHCb simulation application, Gauss: design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [13] LHCb collaboration, R. Aaij et al., _Precision luminosity measurements at LHCb_ , JINST 9 (2014) 12005, arXiv:1410.0149
  * [14] Y. Li and F. Petriello, _Combining QCD and electroweak corrections to dilepton production in FEWZ_ , Phys. Rev. D86 (2012) 094034, arXiv:1208.5967
  * [15] A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, _Parton distributions for the LHC_ , Eur. Phys. J. C63 (2009) 189, arXiv:0901.0002
  * [16] H.-L. Lai et al., _New parton distributions for collider physics_ , Phys. Rev. D82 (2010) 074024, arXiv:1007.2241
  * [17] S. Alekhin, J. Bluemlein, and S. Moch, _The ABM parton distributions tuned to LHC data_ , Phys. Rev. D89 (2014) 054028, arXiv:1310.3059
  * [18] The NNPDF collaboration, R. D. Ball et al., _Parton distributions with LHC data_ , Nucl. Phys. B867 (2013) 244, arXiv:1207.1303
  * [19] The NNPDF collaboration, R. D. Ball et al., _Parton distributions for the LHC Run II_ , arXiv:1410.8849
  * [20] G. A. Ladinsky and C. P. Yuan, _The nonperturbative regime in QCD resummation for gauge boson production at hadron colliders_ , Phys. Rev. D50 (1994) 4239(R), arXiv:hep-ph/9311341
  * [21] C. Balazs and C. P. Yuan, _Soft gluon effects on lepton pairs at hadron colliders_ , Phys. Rev. D56 (1997) 5558, arXiv:hep-ph/9704258
  * [22] 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
  * [23] S. Alioli, P. Nason, C. Oleari, and E. Re, _Vector boson plus one jet production in POWHEG_ , JHEP 01 (2011) 095, arXiv:1009.5594

LHCb collaboration

R. Aaij41, 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, 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, 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. 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. Bowcock52, E. Bowen40, C. Bozzi16, S. Braun11,
D. Brett54, M. Britsch10, T. Britton59, J. Brodzicka54, N.H. Brook46, A.
Bursche40, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, M. Calvi20,k, M.
Calvo Gomez36,p, P. Campana18, D. Campora Perez38, L. Capriotti54, A.
Carbone14,d, G. Carboni24,l, R. Cardinale19,j, A. Cardini15, P. Carniti20, L.
Carson50, K. Carvalho Akiba2,38, R. Casanova Mohr36, G. Casse52, L.
Cassina20,k, L. Castillo Garcia38, M. Cattaneo38, Ch. Cauet9, G. Cavallero19,
R. Cenci23,t, M. Charles8, Ph. Charpentier38, M. Chefdeville4, S. Chen54,
S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26, X. Cid Vidal38, G.
Ciezarek41, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47, J. Closier38, V.
Coco38, J. Cogan6, E. Cogneras5, V. Cogoni15,e, L. Cojocariu29, G.
Collazuol22, P. Collins38, A. Comerma-Montells11, A. Contu15,38, A. Cook46, M.
Coombes46, S. Coquereau8, G. Corti38, M. Corvo16,f, I. Counts56, B.
Couturier38, G.A. Cowan50, D.C. Craik48, A.C. Crocombe48, M. Cruz Torres60, S.
Cunliffe53, R. Currie53, C. D’Ambrosio38, J. Dalseno46, P.N.Y. David41, A.
Davis57, K. De Bruyn41, S. De Capua54, M. De Cian11, J.M. De Miranda1, L. De
Paula2, W. De Silva57, P. De Simone18, C.-T. Dean51, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach55, O. Deschamps5, F.
Dettori38, B. Dey40, A. Di Canto38, F. Di Ruscio24, H. Dijkstra38, S.
Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Suárez37, D. Dossett48, A.
Dovbnya43, K. Dreimanis52, G. Dujany54, F. Dupertuis39, P. 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. Evans47, T.
Evans55, A. Falabella14, C. Färber11, C. Farinelli41, N. Farley45, S. Farry52,
R. Fay52, D. Ferguson50, V. Fernandez Albor37, 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. Gandini55, Y. Gao3, J. García Pardiñas37, J.
Garofoli59, J. Garra Tico47, L. Garrido36, D. Gascon36, C. Gaspar38, U.
Gastaldi16, R. Gauld55, L. Gavardi9, G. Gazzoni5, A. Geraci21,v, 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,
J. Molina Rodriguez60, S. Monteil5, M. Morandin22, P. Morawski27, A. Mordà6,
M.J. Morello23,t, J. Moron27, A.-B. Morris50, R. Mountain59, F. Muheim50, K.
Müller40, 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, E. Pesen68, K. Petridis46, A. Petrolini19,j, 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, J.A. Rodriguez Lopez62, 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. Sanmartin
Sedes37, R. Santacesaria25, C. Santamarina Rios37, E. Santovetti24,l, A.
Sarti18,m, C. Satriano25,n, A. Satta24, D.M. Saunders46, D. Savrina31,32, M.
Schiller38, H. Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O.
Schneider39, A. Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18, A.
Sciubba25,m, A. Semennikov31, I. Sepp53, N. Serra40, J. Serrano6, L.
Sestini22, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T.
Shears52, L. Shekhtman34, V. Shevchenko64, A. Shires9, R. Silva Coutinho48, G.
Simi22, M. Sirendi47, N. Skidmore46, I. Skillicorn51, T. Skwarnicki59, N.A.
Smith52, E. Smith55,49, E. Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D.
Sokoloff57,38, F.J.P. Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2, B.
Spaan9, P. Spradlin51, S. Sridharan38, F. Stagni38, M. Stahl11, S. Stahl38, O.
Steinkamp40, O. Stenyakin35, F Sterpka59, S. Stevenson55, S. Stoica29, S.
Stone59, B. Storaci40, S. Stracka23,t, M. Straticiuc29, U. Straumann40, R.
Stroili22, L. Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V.
Syropoulos42, M. Szczekowski28, P. Szczypka39,38, T. Szumlak27, S. T’Jampens4,
M. Teklishyn7, G. Tellarini16,f, F. Teubert38, C. Thomas55, E. Thomas38, J.
van Tilburg41, V. Tisserand4, M. Tobin39, J. Todd57, S. Tolk42, L.
Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,
S. Tourneur39, K. Trabelsi39, M.T. Tran39, M. Tresch40, A. Trisovic38, A.
Tsaregorodtsev6, P. Tsopelas41, N. Tuning41,38, M. Ubeda Garcia38, A.
Ukleja28, A. Ustyuzhanin65, U. Uwer11, C. Vacca15,e, V. Vagnoni14, G.
Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37, C. Vázquez
Sierra37, S. Vecchi16, J.J. Velthuis46, M. Veltri17,h, G. Veneziano39, M.
Vesterinen11, J.V. Viana Barbosa38, B. Viaud7, D. Vieira2, M. Vieites Diaz37,
X. Vilasis-Cardona36,p, A. Vollhardt40, D. Volyanskyy10, D. Voong46, A.
Vorobyev30, V. Vorobyev34, C. Voß63, J.A. de Vries41, R. Waldi63, C.
Wallace48, R. Wallace12, J. Walsh23, S. Wandernoth11, J. Wang59, D.R. Ward47,
N.K. Watson45, D. Websdale53, A. Weiden40, M. Whitehead48, D. Wiedner11, G.
Wilkinson55,38, M. Wilkinson59, M. Williams38, M.P. Williams45, M. Williams56,
H.W. Wilschut67, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M.
Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, K. Wyllie38, Y. Xie61, Z.
Xu39, Z. Yang3, X. Yuan34, O. Yushchenko35, M. Zangoli14, M. Zavertyaev10,b,
L. Zhang3, 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
68Celal Bayar University, Manisa, Turkey, associated to 38

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