EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-118 LHCb-PAPER-2015-021 September 8, 2015

Study of $W$ boson production in association with beauty and charm

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

The associated production of a $W$ boson with a jet originating from either a
light parton or heavy-flavor quark is studied in the forward region using
proton-proton collisions. The analysis uses data corresponding to integrated
luminosities of 1.0 and $2.0\mbox{\,fb}^{-1}$ collected with the LHCb detector
at center-of-mass energies of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$,
respectively. The $W$ bosons are reconstructed using the $W\to\mu\nu$ decay
and muons with a transverse momentum, $p_{\rm T}$, larger than
20$\mathrm{\,Ge\kern-1.00006ptV}$ in the pseudorapidity range $2.0<\eta<4.5$.
The partons are reconstructed as jets with $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and $2.2<\eta<4.2$. The sum of the muon
and jet momenta must satisfy $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$. The fraction of $W+$jet events that
originate from beauty and charm quarks is measured, along with the charge
asymmetries of the $W\\!+\\!b$ and $W\\!+\\!c$ production cross sections. The
ratio of the $W+$jet to $Z+$jet production cross sections is also measured
using the $Z\to\mu\mu$ decay. All results are in agreement with Standard Model
predictions.

Phys. Rev. D. 92 (2015) 052001

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

##  1 Introduction

Measurements of $W+$jet production in hadron collisions provide important
tests of the Standard Model (SM), especially of perturbative quantum
chromodynamics (QCD) in the presence of heavy-flavor quarks. Such measurements
are also sensitive probes of the parton distribution functions (PDFs) of the
proton. The ratio of the $W+$jet to $Z+$jet production cross sections is a
test of perturbative QCD methods and constrains the light-parton PDFs of the
proton.

The jet produced in association with the $W$ boson may originate either from a
$b$ quark ($W\\!+\\!b$), $c$ quark ($W\\!+\\!c$) or light parton. Several
processes contribute to the $W\\!+\\!b$ and $W\\!+\\!c$ final states at next-
to-leading order (NLO) in perturbative QCD. The dominant mechanism for
$W\\!+\\!c$ production is $gs\to Wc$, but there are also important
contributions from $gs\to Wcg$, $gg\to Wc\bar{s}$, and $q\bar{q}\to
Wc\bar{c}$[1]. Therefore, measuring the ratio of the $W\\!+\\!c$ to $W+$jet
production cross sections in the forward region at the LHC provides important
constraints on the $s$ quark PDF [2, 3] at momentum transfers of $Q\approx
100\mathrm{\,Ge\kern-1.00006ptV}$ ($c=1$ throughout this article) and momentum
fractions down to $x\approx 10^{-5}$. Previous measurements of the proton $s$
quark PDF were primarily based on deep inelastic scattering experiments with
$Q\approx 1\mathrm{\,Ge\kern-1.00006ptV}$ and $x$ values $\mathcal{O}(0.1)$
[4, 5, 6]. The $W\\!+\\!c$ cross section has been measured at the Tevatron [7,
8] and at the LHC [9, 10] in the central region.

In the so-called four-flavor scheme, theoretical calculations are performed
considering only the four lightest quarks in the proton [11]. Production of
$W\\!+\\!b$ proceeds via $q\bar{q}\to Wg$ with $g\to b\bar{b}$ at leading
order. If the $b$ quark content of the proton is considered, i.e. the five-
flavor scheme, then single-$b$ production via $qb\to Wbq$ also contributes
[12]. The ratio of the $W\\!+\\!b$ to $W+$jet cross sections thus places
constraints both on the intrinsic $b$ quark content of the proton and the
probability of gluon splitting into $b\bar{b}$ pairs. The $W\\!+\\!b$ cross
section has been measured in the central region at the Tevatron [13, 14] and
at the LHC [15].

LHCb has measured the cross sections for inclusive $W$ and $Z$ production in
proton-proton ($pp$) collisions at center-of-mass energy
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ [16, 17, 18, 19], providing
precision tests of the SM in the forward region. Additionally, measurements of
the $Z+$jet and $Z\\!+\\!b$ cross sections have been made[20, 21]. In this
article, the associated production of a $W$ boson with a jet originating from
either a light parton or a heavy-flavor quark is studied using $pp$ collisions
at center-of-mass energies of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$. The
production of the $W\\!+\\!b$ final state via top quark decay is not included
in the signal definition in this analysis, but is reported separately in Ref.
[22].

A comprehensive approach is taken, where the inclusive $W+$jet, $W\\!+\\!b$
and $W\\!+\\!c$ contributions are measured simultaneously, rather than split
across multiple measurements as in Refs. [23, 9, 24, 25, 10, 15, 26]. The
identification of $c$ jets, in conjunction with $b$ jets, is performed using
the tagging algorithm described in Ref.[27], which improves upon previous
$c$-tagging methods where muons or exclusive decays were required to identify
the jet[9, 10]. For each center-of-mass energy, the following production cross
section ratios are measured: $\sigma(Wb)/\sigma(Wj)$, $\sigma(Wc)/\sigma(Wj)$,
$\sigma(W^{+}j)/\sigma(Zj)$, $\sigma(W^{-}j)/\sigma(Zj)$, $\mathcal{A}(Wb)$,
and $\mathcal{A}(Wc)$, where

$\mathcal{A}(Wq)\equiv\frac{\sigma(W^{+}q)-\sigma(W^{-}q)}{\sigma(W^{+}q)+\sigma(W^{-}q)}.$
(1)

The analysis is performed using the $W\to\mu\nu$ decay and jets clustered with
the anti-$k_{\rm T}$ algorithm [28] using a distance parameter $R=0.5$. The
following fiducial requirements are applied: both the muon and the jet must
have momentum transverse to the beam, $p_{\rm T}$, greater than
20$\mathrm{\,Ge\kern-1.00006ptV}$; the pseudorapidity of the muon must fall
within $2.0<\eta(\mu)<4.5$; the jet pseudorapidity must satisfy
$2.2<\eta(j)<4.2$; the muon and jet must be separated by $\Delta
R(\mu,j)>0.5$, where $\Delta R\equiv\sqrt{\Delta\eta^{2}+\Delta\phi^{2}}$ and
$\Delta\eta(\Delta\phi)$ is the difference in pseudorapidity (azimuthal angle)
between the muon and jet momenta; and the transverse component of the sum of
the muon and jet momenta must satisfy $\mbox{$p_{\rm
T}$}(\mu+j)\equiv\left(\vec{p}(\mu)+\vec{p}(j)\right)_{\rm
T}>20\mathrm{\,Ge\kern-1.00006ptV}$. All results reported in this article are
for within this fiducial region, i.e. no extrapolation outside of this region
is performed.

The article is organized as follows: the detector, data sample and simulation
are described in Sect. 2; the event selection is given in Sect. 3; the signal
yields are determined in Sect. 4; the systematic uncertainties are outlined in
Sect. 5; and the results are presented in Sect. 6.

##  2 The LHCb detector and data set

The LHCb detector [29, 30] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, 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 [31], 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 [32] 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}$}){\,\upmu\rm m}$, with $p_{\rm T}$ 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 and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. The electromagnetic and hadronic
calorimeters have energy resolutions of $\sigma(E)/E=10\%/\sqrt{E}\oplus 1\%$
and $\sigma(E)/E=69\%/\sqrt{E}\oplus 9\%$ (with $E$ in GeV), respectively.
Muons are identified by a system composed of alternating layers of iron and
multiwire proportional chambers [33].

The trigger [34] 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. This analysis requires at least one muon candidate
that satisfies the trigger requirement of $\mbox{$p_{\rm
T}$}>10\mathrm{\,Ge\kern-1.00006ptV}$. Global event cuts (GECs), which prevent
high-occupancy events from dominating the processing time of the software
trigger, are also applied and have an efficiency of about $90\%$ for $W+$jet
and $Z+$jet events.

Two sets of $pp$ collision data collected with the LHCb detector are used:
data collected during 2011 at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$,
corresponding to an integrated luminosity of 1.0 ${\rm fb}^{-1}$, and data
collected during 2012 at $\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$,
corresponding to an integrated luminosity of 2.0 ${\rm fb}^{-1}$. Simulated
$pp$ collisions, used to study the detector response, to define the event
selection and to validate data-driven techniques, are generated using Pythia
[35, *Sjostrand:2007gs] with an LHCb configuration [37]. Decays of hadronic
particles are described by EvtGen [38] in which final-state radiation (FSR) is
generated using Photos [39]. The interaction of the generated particles with
the detector, and its response, are implemented using the Geant4 toolkit [40,
*Agostinelli:2002hh] as described in Ref. [42].

Results are compared with theoretical calculations at NLO using MCFM [43] and
the CT10 PDF set [44]. The theoretical uncertainty is a combination of PDF,
scale, and strong-coupling ($\alpha_{s}$) uncertainties. The PDF and scale
uncertainties are evaluated following Refs. [44] and [45], respectively. The
$\alpha_{s}$ uncertainty is evaluated as the envelope obtained using
$\alpha_{s}(M_{Z})\in[0.117,0.118,0.119]$ in the theory calculations.

##  3 Event selection

The signature for $W+$jet events is an isolated high-$p_{\rm T}$ muon and a
well-separated jet, both produced in the same $pp$ interaction. Muon
candidates are identified with tracks that have associated hits in the muon
system. The muon candidate must have $\mbox{$p_{\rm
T}$}(\mu)>20\mathrm{\,Ge\kern-1.00006ptV}$ and pseudorapidity within
${2.0<\eta(\mu)<4.5}$. Background muons from $W\to\tau\to\mu$ decays or
semileptonic decays of heavy-flavor hadrons are suppressed by requiring the
muon impact parameter to be less than $0.04\rm\,mm$ [16]. Background from
high-momentum kaons and pions that enter the muon system and are misidentified
as muons, is reduced by requiring that the sum of the energy of the associated
electromagnetic and hadronic calorimeter deposits does not exceed 4% of the
momentum of the muon candidate.

Jets are clustered using the anti-$k_{T}$ algorithm with a distance parameter
$R=0.5$, as implemented in Fastjet [46]. Information from all the detector
subsystems is used to create charged and neutral particle inputs to the jet-
clustering algorithm using a particle flow approach [20]. During 2011 and
2012, LHCb collected data with a mean number of $pp$ collisions per beam
crossing of about 1.7. To reduce contamination from multiple $pp$
interactions, charged particles reconstructed within the vertex detector may
only be clustered into a jet if they are associated with the same $pp$
collision.

Signal events are selected by requiring a muon candidate and at least one jet
with $\Delta R(\mu,j)>0.5$. For each event the highest-$p_{\rm T}$ muon
candidate that satisfies the trigger requirements is selected, along with the
highest-$p_{\rm T}$ jet from the same $pp$ collision. The high-$p_{\rm T}$
muon candidate is not removed from the anti-$k_{T}$ inputs and so is clustered
into a jet. This jet, referred to as the muon jet and denoted as $j_{\mu}$, is
used to discriminate between $W+$jet and dijet events. The requirement
$\mbox{$p_{\rm T}$}(j_{\mu}+j)>20\mathrm{\,Ge\kern-1.00006ptV}$ is made to
suppress dijet backgrounds, which are well balanced in $p_{\rm T}$, unlike
$W+$jet events where there is undetected energy from the neutrino.
Furthermore, the distribution of the fractional muon candidate $p_{\rm T}$
within the muon jet, $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$, is
used to separate vector bosons from jets. For vector-boson production, this
ratio deviates from unity only due to muon FSR, activity from the underlying
event, or from neutral-particle production in a separate $pp$ collision,
whereas for jet production this ratio is driven to smaller values by the
presence of additional radiation produced in association with the muon
candidate.

Events with a second, oppositely charged, muon candidate from the same $pp$
collision are vetoed. However, when the dimuon invariant mass is in the range
$60<M(\mu^{+}\mu^{-})<120\mathrm{\,Ge\kern-1.00006ptV}$, such events are
selected as $Z+$jet candidates and the $\mbox{$p_{\rm T}$}(j_{\mu}+j)$
requirement is not applied. Two $Z+$jet data samples are selected at each
center-of-mass energy: a data sample where only the $\mu^{+}$ is required to
satisfy the trigger requirements and one where only the $\mu^{-}$ is required
to satisfy them. The first sample is used to measure
$\sigma(W^{+}j)/\sigma(Zj)$, while the second is used for
$\sigma(W^{-}j)/\sigma(Zj)$. This strategy leads to approximate cancellation
of the uncertainty in the trigger efficiency in the measurement of these
ratios.

The reconstructed jets must have $\mbox{$p_{\rm
T}$}(j)>20\mathrm{\,Ge\kern-1.00006ptV}$ and $2.2<\eta(j)<4.2$. The reduced
$\eta(j)$ acceptance ensures nearly uniform jet reconstruction and heavy-
flavor tagging efficiencies. The momentum of a reconstructed jet is scaled to
obtain an unbiased estimate of the true jet momentum. The scaling factor,
typically between 0.9 and 1.1, is determined from simulation and depends on
the jet $p_{\rm T}$ and $\eta$, the fraction of the jet transverse momentum
measured with the tracking systems, and the number of $pp$ interactions in the
event. No scaling is applied to the momentum of the muon jet. Migration of
events in and out of the jet $p_{\rm T}$ fiducial region due to the detector
response is corrected for by an unfolding technique. Data-driven methods are
used to obtain the unfolding matrix, with the resulting corrections to the
measurements presented in this article being at the percent level.

The jets are identified, or tagged, as originating from the hadronization of a
heavy-flavor quark by the presence of a secondary vertex (SV) with $\Delta
R<0.5$ between the jet axis and the SV direction of flight, defined by the
vector from the $pp$ interaction point to the SV position. Two boosted
decision trees (BDTs) [47, 48], ${\rm BDT}(bc|udsg)$ and ${\rm BDT}(b|c)$,
trained on the characteristics of the SV and the jet, are used to separate
heavy-flavor jets from $\rm light\mbox{-}parton$ jets, and to separate $b$
jets from $c$ jets. The two-dimensional distribution of the BDT response
observed in data is fitted to obtain the SV-tagged $b$, $c$ and $\rm
light\mbox{-}parton$ jet yields. The SV-tagger algorithm is detailed in Ref.
[27], where the heavy-flavor tagging efficiencies and $\rm
light\mbox{-}parton$ mistag probabilities are measured in data.

##  4 Background determination

Contributions from six processes are considered in the $W+$jet data sample:
$W+$jet signal events; $Z+$jet events where one muon is not reconstructed; top
quark events producing a $W+$jet final state; $Z\to\tau\tau$ events where one
$\tau$ lepton decays to a muon and the other decays hadronically; QCD dijet
events; and vector boson pair production. Simulations based on NLO predictions
show that the last contribution is negligible.

The signal yields are obtained for each muon charge and center-of-mass energy
independently. The $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$
distribution is fitted to determine the $W+$jet yield of each data sample. To
determine the $W\\!+\\!b$ and $W\\!+\\!c$ yields, the subset of candidates
with an SV-tagged jet is binned according to $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$. In each $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ bin, the two-dimensional SV-tagger BDT-
response distributions are fitted to determine the yields of $b$-tagged and
$c$-tagged jets, which are used to form the $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ distributions for candidates with
$b$-tagged and $c$-tagged jets. These $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})$ distributions are fitted to determine the SV-tagged $W\\!+\\!b$
and $W\\!+\\!c$ yields. Finally, to obtain $\sigma(Wb)/\sigma(Wj)$ and
$\sigma(Wc)/\sigma(Wj)$, the jet-tagging efficiencies of $\epsilon_{\rm
tag}(b)\approx 65\%$ and $\epsilon_{\rm tag}(c)\approx 25\%$ are accounted
for. In all fits performed in this analysis, the templates are histograms with
fixed shapes.

The $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ distributions are
shown in Fig. 1 (in this and subsequent figures the pull represents the
difference between the data and the fit, in units of standard deviations). The
$W$ boson yields are determined by performing binned extended-maximum-
likelihood fits to these distributions with the following components:

  * •

The $W$ boson template is obtained by correcting the $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ distribution observed in $Z+$jet events
for small differences between $W$ and $Z$ decays derived from simulation.

  * •

The template for $Z$ boson events where one muon is not reconstructed is
obtained by correcting, using simulation, the $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ distribution observed in fully
reconstructed $Z+$jet events for small differences expected in partially
reconstructed $Z+$jet events. The yield is fixed from the fully reconstructed
$Z+$jet data sample, where simulation is used to obtain the probability that
the muon is missed, either because it is out of acceptance or it is not
reconstructed.

  * •

The templates for $b$, $c$ and $\rm light\mbox{-}parton$ jets are obtained
using dijet-enriched data samples. These samples require $\mbox{$p_{\rm
T}$}(j_{\mu}+j)<10\mathrm{\,Ge\kern-1.00006ptV}$ and, for the heavy-flavor
samples, either a stringent $b$-tag or $c$-tag requirement on the associated
jet. The templates are corrected for differences in the $\mbox{$p_{\rm
T}$}(j_{\mu})$ spectra between the dijet-enriched and signal regions. The
contributions of $b$, $c$ and $\rm light\mbox{-}parton$ jets are each free to
vary in the $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ fits.

The $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ fits determine the
$W+$jet yields, which include contributions from top quark and $Z\to\tau\tau$
production. The top quark and $Z\to\tau\tau$ contributions cannot be separated
from $W+$jet since their $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$
distributions are nearly identical to that of $W+$jet events. The subtraction
of these backgrounds is described below.

Figure 1:  Distributions of $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})$ with fits overlaid from (top)
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ and (bottom)
$8\mathrm{\,Te\kern-1.00006ptV}$ data for (left) $\mu^{+}$ and (right)
$\mu^{-}$.

The yields of events with $W$ bosons associated with $b$-tagged and $c$-tagged
jets are obtained by fitting the two-dimensional SV-tagger BDT-response
distributions for $\sqrt{s}=7$ and 8$\mathrm{\,Te\kern-1.00006ptV}$ and for
each muon charge separately in bins of $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})$. The SV-tagger BDT templates used in this analysis are obtained
from the data samples enriched in $b$ and $c$ jets used in Ref. [27]. As a
consistency check, the two-dimensional BDT distributions are fitted using
templates from simulation; the yields shift only by a few percent. Figure 2
shows the BDT distributions combining all data in the most sensitive region,
$W+$jet events with $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})>0.9$.
This is the region where the muon carries a large fraction of the muon-jet
momentum and is, therefore, highly isolated. Figure 3 shows the distributions
in a dijet dominated region ($0.5<\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})<0.6$). In the dijet region the majority of SV-tagged jets
associated with the high-$p_{\rm T}$ muon candidate are found to be $b$ jets.
This is due to the large semileptonic branching fraction of $b$ hadrons. In
the $W+$jet signal region there are significant contributions from both $b$
and $c$ jets.

Figure 2: (top left) Two-dimensional SV-tag BDT distribution and (top right)
fit for events in the subsample with $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})>0.9$, projected onto the (bottom left) ${\rm BDT}(bc|udsg)$ and
(bottom right) ${\rm BDT}(b|c)$ axes. Combined data for $\sqrt{s}=7$ and 8 TeV
for both muon charges are shown.

Figure 3: (top left) Two-dimensional SV-tag BDT distribution and (top right)
fit for events in the subsample with $0.5<\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})<0.6$, projected onto the (bottom left)
${\rm BDT}(bc|udsg)$ and (bottom right) ${\rm BDT}(b|c)$ axes. Combined data
for $\sqrt{s}=7$ and 8 TeV for both muon charges are shown.

As a consistency check, the $b$, $c$, and $\rm light\mbox{-}parton$ yields are
obtained in the $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})>0.9$
signal region from a fit using only two of the BDT inputs, both of which rely
only on basic SV properties, the track multiplicity and the corrected mass,
which is defined as

$M_{\rm
cor}=\sqrt{M^{2}+|\vec{p}|^{2}\sin^{2}{\theta}}+|\vec{p}|\sin{\theta},$ (2)

where $M$ and $\vec{p}$ are the invariant mass and momentum of the particles
that form the SV, and $\theta$ is the angle between $\vec{p}$ and the flight
direction. The corrected mass, which is the minimum mass for a long-lived
hadron whose trajectory is consistent with the flight direction, peaks near
the $D$ meson mass for $c$ jets and consequently provides excellent
discrimination against other jet types. The SV track multiplicity identifies
$b$ jets well, since $b$-hadron decays typically produce many displaced
tracks. In Fig. 4, the distributions of $M_{\rm cor}$ and SV track
multiplicity for a subsample of SV-tagged events with ${\rm BDT}(bc|udsg)>0.2$
(see Fig. 2) are fitted simultaneously. The templates used in these fits are
obtained from data in the same manner as the SV-tagger BDT templates. After
correcting for the efficiency of requiring ${\rm BDT}(bc|udsg)>0.2$, the $b$
and $c$ yields determined from the fits to $M_{\rm cor}$ and SV track
multiplicity and from the two-dimensional BDT fits are consistent. The mistag
probability for $W+$$\rm light\mbox{-}parton$ events in this sample is found
to be approximately $0.3\%$, which agrees with the value obtained from
simulation.

Figure 4:  Projections of simultaneous fits of (left) $M_{\rm cor}$ and
(right) SV track multiplicity for the SV-tagged subsample with ${\rm
BDT}(bc|udsg)>0.2$ and $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})>0.9$. The highest $M_{\rm cor}$ bin includes candidates with
$M_{\rm cor}>10\mathrm{\,Ge\kern-1.00006ptV}$. Combined data for $\sqrt{s}=7$
and 8 TeV for both muon charges are shown.

From the SV-tagger BDT fits, the $b$ and $c$ yields are obtained in bins of
$\sqrt{s}$, muon charge, and $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})$. The $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$
distributions for muons associated with $b$-tagged and $c$-tagged jets are
shown in Figs. 5 and 6. These distributions are fitted to determine the
$W\\!+\\!b$ and $W\\!+\\!c$ final-state yields as in the inclusive $W+$jet
sample. The $Z\\!+\\!b$ and $Z\\!+\\!c$ yields are obtained by fitting the SV-
tagger BDT distributions in the fully reconstructed $Z+$jet data samples and
then correcting for the missed-muon probability. The fits are shown in Figs. 5
and 6 for each muon charge and center-of-mass energy. The yields obtained
still include contributions from top quark production and $Z\to\tau\tau$.

Figure 5:  Fits to $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$
distributions for $b$-tagged data samples for $\sqrt{s}=7$ and 8 TeV.

Figure 6:  Fits to $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$
distributions for $c$-tagged data samples for $\sqrt{s}=7$ and 8 TeV.

The $Z\to\tau\tau$ background, where one $\tau$ lepton decays into a muon and
the other into a hadronic jet, contaminates the $W\\!+\\!c$ sample due to the
similarity of the $c$-hadron and $\tau$ lepton masses. The $\mbox{$p_{\rm
T}$}({\rm SV})/\mbox{$p_{\rm T}$}(j)$ distribution, where $\mbox{$p_{\rm
T}$}({\rm SV})$ is the transverse momentum of the particles that form the SV,
is used to discriminate between $c$ and $\tau$ jets, since SVs produced from
$\tau$ decays usually carry a larger fraction of the jet energy than SVs from
$c$-hadron decays. Figure 7 shows fits to the $\mbox{$p_{\rm T}$}({\rm
SV})/\mbox{$p_{\rm T}$}(j)$ distributions observed in data where the $b$ and
$\rm light\mbox{-}parton$ yields are fixed using the results of BDT fits
performed on the data samples. A requirement of ${\rm BDT}(bc|udsg)>0.2$ is
applied to this sample to remove the majority of SV-tagged $\rm
light\mbox{-}parton$ jets while retaining 90% of $b$, $c$ and $\tau$ jets. The
only free parameter in these fits is the fraction of jets identified as charm
in the SV-tagger BDT fits that originate from $\tau$ leptons. The
$\mbox{$p_{\rm T}$}({\rm SV})/\mbox{$p_{\rm T}$}(j)$ templates are obtained
from simulation. The $Z\to\tau\tau$ yields are consistent with SM expectations
and are about 25 times smaller than the $W\\!+\\!c$ yields. These results are
extrapolated to the inclusive sample using simulation.

Figure 7: Fits to the $\mbox{$p_{\rm T}$}(\mathrm{SV})/\mbox{$p_{\rm T}$}(j)$
distributions in (left) $7\mathrm{\,Te\kern-1.00006ptV}$ and (right)
$8\mathrm{\,Te\kern-1.00006ptV}$ data for candidates with $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})>0.9$ and ${\rm BDT}(bc|udsg)>0.2$.

The top quark background is determined in the dedicated analysis of Ref. [22],
where a reduced fiducial region is used to enrich the relative top quark
content. The yields and charge asymmetries of the $W\\!+\\!b$ final state as
functions of $\mbox{$p_{\rm T}$}(\mu+b)$ are used to discriminate between
$W\\!+\\!b$ and top quark production. The results obtained in Ref. [22] are
consistent with SM expectations and are extrapolated to the fiducial region of
this analysis using simulation based on NLO calculations. The extrapolated top
quark yields are subtracted from the observed number of $W\\!+\\!b$ candidates
to obtain the signal yields. Top quark production is found to be responsible
for about 1/3 of events that contain a $W$ boson and $b$ jet. A summary of all
signal yields is given in Table 1.

Table 1:  Summary of signal yields. The two $Zj$ yields denote the charge of the muon on which the trigger requirement is made. The $Zj$ yields given are the numbers of candidates observed, while the $W$ boson yields are obtained from fits. The yield due to top quark production is subtracted in these results.  | $7\mathrm{\,Te\kern-1.00006ptV}$ | $8\mathrm{\,Te\kern-1.00006ptV}$
---|---|---
Mode | $\mu^{+}$ | $\mu^{-}$ | $\mu^{+}$ | $\mu^{-}$
$Zj$ | 2364 | 2357 | 6680 | 6633
$Wj$ | $27\,400\pm 500$ | $17\,500\pm 400$ | $70\,700\pm 1100$ | $44\,800\pm 800$
$Wb$-tag | $160\pm 31$ | $51\pm 27$ |  $400\pm 43$11 | $236\pm 45$
$Wc$-tag | $295\pm 36$ | $338\pm 31$ |  $795\pm 56$11 | $802\pm 55$

##  5 Systematic uncertainties

A summary of the relative systematic uncertainties separated by source for
each measurement is provided in Table 2. A detailed description of each
contribution is given below.

The $p_{\rm T}$ distributions of muons from $W$ and $Z$ bosons produced in
association with $b$, $c$ and $\rm light\mbox{-}parton$ jets are nearly
identical. This results in a negligible uncertainty from muon trigger and
reconstruction efficiency on cross section ratios involving only $W$ bosons.
In the ratios $\sigma(W^{+}j)/\sigma(Zj)$ and $\sigma(W^{-}j)/\sigma(Zj)$, the
muon from the $Z$ boson decay with the same charge as that from the $W$ decay
is required to satisfy the same trigger and selection requirements as the $W$
boson muon, giving negligible uncertainty from the trigger and selection
efficiency. The efficiency for reconstructing and selecting the additional
muon from the $Z$ boson decay is obtained from the data-driven studies of Ref.
[17]. A further data-driven correction is applied to account for the higher
occupancy in events with jets [20]; a 2% systematic uncertainty is assigned to
this correction.

The GEC efficiency is obtained following Ref. [20]: an alternative dimuon
trigger requirement with a looser GEC is used to determine the fraction of
events that are rejected. The GEC efficiencies for all final states are found
to be consistent within a statistical precision of 1%, which is assigned as a
systematic uncertainty. As a further check, the number of jets per event
reconstructed in association with $W$ or $Z$ bosons is compared and found to
be consistent.

The jet reconstruction efficiencies for heavy-flavor and $\rm
light\mbox{-}parton$ jets in simulation are found to be consistent within
$2\%$, which is assigned as a systematic uncertainty for flavor-dependencies
in the jet-reconstruction efficiency. The jet $p_{\rm T}$ detector response is
studied with a data sample enriched in $b$ jets using SV tagging. The
$\mbox{$p_{\rm T}$}({\rm SV})/\mbox{$p_{\rm T}$}(j)$ distribution observed in
data is compared to templates obtained from simulation in bins of jet $p_{\rm
T}$. The resolution and scale in simulation for each jet $p_{\rm T}$ bin are
varied to find the best description of the data and to construct a data-driven
unfolding matrix. The results obtained using this unfolding matrix are
consistent with those obtained using a matrix determined by studies of $p_{\rm
T}$ balance in $Z+$jet events [20], where no heavy-flavor tagging is applied.
The unfolding corrections are at the percent level and their statistical
precision is assigned as the uncertainty.

The heavy-flavor tagging efficiencies are measured from data in Ref. [27],
where a 10% uncertainty is assigned for $b$ and $c$ jets. The cross-check fits
of Sect. 4, using the corrected mass and track multiplicity, remove
information associated with jet quantities, such as $p_{\rm T}$, from the
yield determination and produce yields consistent at the 5% level. This is
assigned as the uncertainty for the SV-tagged yield determination.

The $W$ boson template for the $\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm
T}$}(j_{\mu})$ distribution is derived from data, as described in Sect. 4. The
fit is repeated using variations of this template, e.g. using a template taken
directly from simulation and using separate templates for $W^{+}$ and $W^{-}$,
to assess a systematic uncertainty. The dijet templates are obtained from data
in a dijet-enriched region. The residual, small $W$ boson contamination is
subtracted using two methods: the $W$ boson yield expected in the dijet-
enriched region is taken from simulation; and the $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ distribution in the dijet-enriched
region is fitted to a parametric function to estimate the $W$ boson yield. The
difference in the $W$ boson yields obtained using these two sets of dijet
templates is at most 2%. The uncertainty on $W/Z$ ratios due to the $W$ boson
and dijet templates is 4%. The uncertainty due to the $W$ boson template
cancels to good approximation in the measurements of $\sigma(Wb)/\sigma(Wj)$
and $\sigma(Wc)/\sigma(Wj)$; however, the uncertainty due to the dijet
templates is larger due to the enhanced dijet background levels. Variations of
the dijet templates are considered, with 10% and 5% uncertainties assigned on
$\sigma(Wb)/\sigma(Wj)$ and $\sigma(Wc)/\sigma(Wj)$.

The systematic uncertainty from top quark production is taken from Ref. [22],
while the systematic uncertainty from $Z\to\tau\tau$ is evaluated by fitting
the data using variations of the $\mbox{$p_{\rm T}$}({\rm SV})/\mbox{$p_{\rm
T}$}(j)$ templates. All other electroweak backgrounds are found to be
negligible from NLO predictions. All $W\to\mu\nu$ yields have a small
contamination from $W\to\tau\to\mu$ decays that cancels in all cross section
ratios except for the $W/Z$ ratios. A scaling factor of 0.975, obtained from
simulation, is applied to the $W$ boson yields. A 1% uncertainty is assigned
to the scale factor, which is obtained from the difference between the
correction factor from simulation and a data-driven study of this background
[16] for inclusive $W\to\mu\nu$ production.

The trigger, reconstruction and selection requirements are consistent with
being charge symmetric [16], which results in negligible uncertainty on
$\mathcal{A}(Wb)$ and $\mathcal{A}(Wc)$. Unfolding of the jet $p_{\rm T}$
detector response is performed independently for $W^{+}$ and $W^{-}$ bosons,
with the statistical uncertainties on the corrections to the charge
asymmetries assigned as systematic uncertainties. The uncertainty on the
$W\\!+\\!b$ and $W\\!+\\!c$ yields from the BDT templates is included in the
charge asymmetry uncertainty due to the fact that the fractional jet content
of the SV-tagged samples is charge dependent. The uncertainty on the charge
asymmetries due to determination of the $W$ boson yields is evaluated using an
alternative method for obtaining the charge asymmetries. The raw charge
asymmetry in the $b$-jet and $c$-jet yields in the $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})>0.9$ region is obtained from the SV-
tagger BDT fits. The $Z+$jet and dijet backgrounds are charge symmetric at the
percent level and contribute at most to 20% of the events in this
$\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ region. Therefore,
$\mathcal{A}(Wb)$ and $\mathcal{A}(Wc)$ are approximated by scaling the raw
asymmetries by the inverse of the $W$ boson purity in the $\mbox{$p_{\rm
T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})>0.9$ region. A small correction must
also be applied to $\mathcal{A}(Wb)$ to account for top quark production. The
difference between the asymmetries from this method and the nominal method is
assigned as a systematic uncertainty from $W$ boson signal determination. The
uncertainty on $\mathcal{A}(Wb)$ due to top quark production is taken from
Ref. [22].

Table 2: Systematic uncertainties. Relative uncertainties are given for cross section ratios and absolute uncertainties for charge asymmetries. Source | $\frac{\sigma(Wb)}{\sigma(Wj)}$ | $\frac{\sigma(Wc)}{\sigma(Wj)}$ | $\frac{\sigma(Wj)}{\sigma(Zj)}$ | $\mathcal{A}(Wb)$ | $\mathcal{A}(Wc)$
---|---|---|---|---|---
Muon trigger and selection | $-$ | $-$ | 2% | $-$ | $-$
GEC | 1% | 1% | 1% | $-$ | $-$
Jet reconstruction | 2% | 2% | $-$ | $-$ | $-$
Jet $p_{\rm T}$ | 2% | 2% | 1% | 0.02 | 0.02
$(b,c)$-tag efficiency | 10% | 10% |  | $-$ | $-$
SV-tag BDT templates | 5% | 5% |  | 0.02 | 0.02
$\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}(j_{\mu})$ templates | 10% | 5% | 4% | 0.08 | 0.03
Top quark | 13% | $-$ | $-$ | 0.02 |
$Z\to\tau\tau$ | $-$ | 3% | $-$ | $-$ | $-$
Other electroweak | $-$ | $-$ | $-$ | $-$ | $-$
$W\to\tau\to\mu$ | $-$ | $-$ | 1% | $-$ | $-$
Total | 20% | 13% | 5% | 0.09 | 0.04
Table 3: Summary of the results and SM predictions. For each measurement the first uncertainty is statistical, while the second is systematic. All results are reported within a fiducial region that requires a jet with $\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ in the pseudorapidity range $2.2<\eta<4.2$, a muon with $\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ in the pseudorapidity range $2.0<\eta<4.5$, $\mbox{$p_{\rm T}$}(\mu+j)>20\mathrm{\,Ge\kern-1.00006ptV}$, and $\Delta R(\mu,j)>0.5$. For $Z+$jet events both muons must fulfill the muon requirements and $60<M(\mu\mu)<120\mathrm{\,Ge\kern-1.00006ptV}$; the $Z+$jet fiducial region does not require $\mbox{$p_{\rm T}$}(\mu+j)>20\mathrm{\,Ge\kern-1.00006ptV}$.  | Results | SM prediction
---|---|---
| $7\mathrm{\,Te\kern-1.00006ptV}$ | $8\mathrm{\,Te\kern-1.00006ptV}$ | $7\mathrm{\,Te\kern-1.00006ptV}$ | $8\mathrm{\,Te\kern-1.00006ptV}$
$\frac{\sigma(Wb)}{\sigma(Wj)}\times 10^{2}$ | $0.66\pm 0.13\pm 0.13$ | $0.78\pm 0.08\pm 0.16$ | $0.74_{-0.13}^{+0.17}$ | $0.77_{-0.13}^{+0.18}$
$\frac{\sigma(Wc)}{\sigma(Wj)}\times 10^{2}$ | $5.80\pm 0.44\pm 0.75$ | $5.62\pm 0.28\pm 0.73$ | $5.02_{-0.69}^{+0.80}$ | $5.31_{-0.52}^{+0.87}$
$\mathcal{A}(Wb)$ | $0.51\pm 0.20\pm 0.09$ | $0.27\pm 0.13\pm 0.09$ | $0.27_{-0.03}^{+0.03}$ | $0.28_{-0.03}^{+0.03}$
$\mathcal{A}(Wc)$ | $-0.09\pm 0.08\pm 0.04$ | $-0.01\pm 0.05\pm 0.04$ | $-0.15_{-0.04}^{+0.02}$ | $-0.14_{-0.03}^{+0.02}$
$\frac{\sigma(W^{+}j)}{\sigma(Zj)}$ | $10.49\pm 0.28\pm 0.53$ | $9.44\pm 0.19\pm 0.47$ | $9.90_{-0.24}^{+0.28}$ | $9.48_{-0.33}^{+0.16}$
$\frac{\sigma(W^{-}j)}{\sigma(Zj)}$ | $6.61\pm 0.19\pm 0.33$ | $6.02\pm 0.13\pm 0.30$ | $5.79_{-0.18}^{+0.21}$ | $5.52_{-0.25}^{+0.13}$

##  6 Results

The results for $\sqrt{s}=7$ and 8$\mathrm{\,Te\kern-1.00006ptV}$ are
summarized in Table 3. Each result is compared to SM predictions calculated at
NLO using MCFM [43] and the CT10 PDF set [44] as described in Sect. 2.
Production of $W+$jet events in the forward region requires a large imbalance
in $x$ of the initial partons. In the four-flavor scheme at leading order,
$W\\!+\\!b$ production proceeds via $q\bar{q}\to Wg(b\bar{b})$, where the
charge of the $W$ boson has the same sign as that of the initial parton with
larger $x$. Therefore, $\mathcal{A}(Wb)\approx+1/3$ is predicted due to the
valence quark content of the proton. The dominant mechanism for $W\\!+\\!c$
production is $gs\to Wc$, which is charge symmetric assuming symmetric $s$ and
$\bar{s}$ quark PDFs. However, the Cabibbo-suppressed contribution from $gd\to
Wc$ leads to a prediction of a small negative value for $\mathcal{A}(Wc)$.

The $\sigma(Wb)/\sigma(Wj)$ ratio in conjunction with the $W\\!+\\!b$ charge
asymmetry is consistent with MCFM calculations performed in the four-flavor
scheme, where $W\\!+\\!b$ production is primarily from gluon splitting. This
scheme assumes no intrinsic $b$ quark content in the proton. The data do not
support a large contribution from intrinsic $b$ quark content in the proton
but the precision is not sufficient to rule out such a contribution at
$\mathcal{O}(10\%)$. The ratio $[\sigma(Wb)+\sigma({\rm top})]/\sigma(Wj)$ is
measured to be $1.17\pm 0.13\mathrm{\,(stat)}\pm 0.18\mathrm{\,(syst)}$% at
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ and $1.29\pm
0.08\mathrm{\,(stat)}\pm 0.19\mathrm{\,(syst)}$% at
$\sqrt{s}=8$$\mathrm{\,Te\kern-1.00006ptV}$, which agree with the NLO SM
predictions of $1.23\pm 0.24\%$ and $1.38\pm 0.26\%$, respectively.

The $\sigma(Wc)/\sigma(Wj)$ ratio is much larger than $\sigma(Wb)/\sigma(Wj)$,
which is consistent with $Wc$ production from intrinsic $s$ quark content of
the proton. The measured charge asymmetry for $W\\!+\\!c$ is about $2\sigma$
smaller than the predicted value obtained with CT10, which assumes symmetric
$s$ and $\bar{s}$ quark PDFs. This could suggest a larger than expected
contribution from scattering off of strange quarks or a charge asymmetry
between $s$ and $\bar{s}$ quarks in the proton. The ratio
$\sigma(W^{+}j)/\sigma(Zj)$ is consistent within $1\sigma$ with NLO
predictions, while the observed $\sigma(W^{-}j)/\sigma(Zj)$ ratio is higher
than the predicted value by about $1.5\sigma$.

## Acknowledgments

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).

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R. Aaij38, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
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Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1,
L.J. Bel41, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson38, J.
Benton46, A. Berezhnoy32, R. Bernet40, A. Bertolin22, M.-O. Bettler38, M. van
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Bondar30,38, W. Bonivento15, S. Borghi54, M. Borsato7, T.J.V. Bowcock52, E.
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Cassina20,k, L. Castillo Garcia38, M. Cattaneo38, Ch. Cauet9, G. Cavallero19,
R. Cenci23,t, M. Charles8, Ph. Charpentier38, M. Chefdeville4, S. Chen54,
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Silva57, P. De Simone18, C.-T. Dean51, D. Decamp4, M. Deckenhoff9, L. Del
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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. Ferrari14, F. Ferreira Rodrigues1, M.
Ferro-Luzzi38, S. Filippov33, M. Fiore16,38,f, M. Fiorini16,f, M. Firlej27, C.
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Frosini17, J. Fu21, E. Furfaro24,l, A. Gallas Torreira37, D. Galli14,d, S.
Gallorini22,38, S. Gambetta50, 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,
D. Gerick11, E. Gersabeck11, M. Gersabeck54, T. Gershon48, Ph. Ghez4, A.
Gianelle22, S. Gianì39, V. Gibson47, O. G. Girard39, L. Giubega29, V.V.
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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, T. Hadavizadeh55, C. Hadjivasiliou59, G. Haefeli39, C.
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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.
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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, M. Kozeiha5, L. Kravchuk33, K. Kreplin11, M.
Kreps48, G. Krocker11, P. Krokovny34, F. Kruse9, W. Kucewicz26,o, M.
Kucharczyk26, V. Kudryavtsev34, A. K. Kuonen39, 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. Leflat32,38, J. Lefrançois7, O. Leroy6, T. Lesiak26, B.
Leverington11, Y. Li7, T. Likhomanenko65,64, M. Liles52, R. Lindner38, C.
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J.H. Lopes2, D. Lucchesi22,r, M. Lucio Martinez37, H. Luo50, A. Lupato22, E.
Luppi16,f, O. Lupton55, F. Machefert7, F. Maciuc29, O. Maev30, K. Maguire54,
S. Malde55, A. Malinin64, G. Manca7, G. Mancinelli6, P. Manning59, A.
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Marino23,38,t, R. Märki39, J. Marks11, G. Martellotti25, M. Martin6, M.
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A. Massafferri1, R. Matev38, A. Mathad48, Z. Mathe38, C. Matteuzzi20, K.
Matthieu11, A. Mauri40, B. Maurin39, A. Mazurov45, M. McCann53, J. McCarthy45,
A. McNab54, R. McNulty12, B. Meadows57, F. Meier9, M. Meissner11, D.
Melnychuk28, M. Merk41, D.A. Milanes62, M.-N. Minard4, D.S. Mitzel11, J.
Molina Rodriguez60, S. Monteil5, M. Morandin22, P. Morawski27, A. Mordà6, M.J.
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Rodrigues1, J.M. Otalora Goicochea2, A. Otto38, P. Owen53, A. Oyanguren66, A.
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L. Pescatore45, K. Petridis46, A. Petrolini19,j, M. Petruzzo21, E. Picatoste
Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, A. Piucci11, S.
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1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
63Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
64National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
65Yandex School of Data Analysis, Moscow, Russia, associated to 31
66Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
67Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 41

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