EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-101 LHCb-PAPER-2015-016 May 28, 2015

Identification of beauty and charm quark jets at LHCb

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

Identification of jets originating from beauty and charm quarks is important
for measuring Standard Model processes and for searching for new physics. The
performance of algorithms developed to select $b$\- and $c$-quark jets is
measured using data recorded by LHCb from proton-proton collisions at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ in 2011 and at
$\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$ in 2012. The efficiency for
identifying a $b(c)$ jet is about 65%(25%) with a probability for
misidentifying a light-parton jet of 0.3% for jets with transverse momentum
$\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and pseudorapidity
$2.2<\eta<4.2$. The dependence of the performance on the $p_{\rm T}$ and
$\eta$ of the jet is also measured.

JINST 10 (2015) P06013

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

##  1 Introduction

Identification of jets that originate from the hadronization of beauty ($b$)
and charm ($c$) quarks is important for studying Standard Model (SM) processes
and for searching for new physics. For example, the ability to efficiently
identify $b$ jets with minimal misidentification of $c$ and $\rm
light\mbox{-}parton$ jets is crucial for the measurement of top-quark
production. The study of $t\bar{t}$ production in the forward region probes
the structure of the proton [1] and can be used to search for physics beyond
the SM [2]. Measuring charge asymmetries in di-$b$-jet production also probes
beyond the SM physics [3, 4]. Furthermore, identification of $c$ jets is
important for probing the structure of the proton, e.g. in $W\\!+\\!c$
production.

The signature of a $b$ or $c$ jet is the presence of a long-lived $b$ or $c$
hadron that carries a sizable fraction of the jet energy. The LHCb detector
was designed to identify $b$ and $c$ hadrons, and so is expected to perform
well at identifying, or tagging, $b$ and $c$ jets. This paper describes two
algorithms for identifying $b$ and $c$ jets, one designed to identify both $b$
and $c$ jets offline, and another initially designed to identify $b$-hadron
decays in the trigger. The performance of each algorithm is measured using
several subsamples of the $3\mbox{\,fb}^{-1}$ of proton-proton collision data
collected at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ in 2011 and at
8$\mathrm{\,Te\kern-1.00006ptV}$ in 2012 by the LHCb detector. The
distributions of observable quantities used to discriminate between $b$, $c$
and $\rm light\mbox{-}parton$ jets are compared between data and simulation.

##  2 The LHCb detector

The LHCb detector [5, 6] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region [7], 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 [8] placed
downstream of the magnet. The tracking system provides a measurement of
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at 200$\mathrm{\,Ge\kern-1.00006ptV}$ ($c=1$
throughout this paper). The minimum distance of a track to a primary vertex,
the impact parameter, is measured with a resolution of $(15+29/\mbox{$p_{\rm
T}$}){\,\upmu\rm m}$, where $p_{\rm T}$ is the component of the momentum
transverse to the beam, in $\mathrm{\,Ge\kern-1.00006ptV}$. 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 an energy resolution 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
[9].

The trigger [10] 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 that either a high-$p_{\rm
T}$ muon or a $(b,c)$-hadron111The notation $(b,c)$ is used to mean $b$ or $c$
throughout this paper. candidate satisfies the trigger requirements. Events
recorded due to the presence of a high-$p_{\rm T}$ muon are required to have a
muon candidate with $\mbox{$p_{\rm T}$}>10\mathrm{\,Ge\kern-1.00006ptV}$.
Events recorded due to the presence of a $(b,c)$-hadron decay require that at
least one track should have $\mbox{$p_{\rm
T}$}>1.7\mathrm{\,Ge\kern-1.00006ptV}$ and $\chi^{2}_{\rm IP}$ with respect to
any primary interaction greater than 16, where $\chi^{2}_{\rm IP}$ is defined
as the difference in $\chi^{2}$ of a given primary $pp$ interaction vertex
(PV) reconstructed with and without the considered track. Decays of $b$
hadrons are inclusively identified by requiring a two-, three- or four-track
secondary vertex (SV) with a large sum of $p_{\rm T}$ of the tracks and a
significant displacement from the PV. A specialized boosted decision tree
(BDT) [11] algorithm is used for the identification of SVs consistent with the
decay of a $b$ hadron [12]. This inclusive trigger algorithm is called the
topological trigger (TOPO) and is studied as a $b$-jet tagger in this paper.
Decays of long-lived $c$ hadrons are identified either exclusively using decay
modes with large branching fractions, or in $D^{*}(2010)^{\pm}\rightarrow
D^{0}\pi^{\pm}$ decays where the $D^{0}$ is selected inclusively by the
presence of a two-track SV.

In the simulation, $pp$ collisions are generated using Pythia [13] with a
specific LHCb configuration [14]. Decays of hadronic particles are described
by EvtGen [15], in which final-state radiation is generated using Photos [16].
The interaction of the generated particles with the detector, and its
response, are implemented using the Geant4 toolkit [17, *Agostinelli:2002hh]
as described in Ref. [19].

##  3 Jet identification algorithms

Jets are clustered using the anti-$k_{T}$ algorithm [20] with a distance
parameter $0.5$, as implemented in Fastjet [21]. Information from all the
detector sub-systems is used to create charged and neutral particle inputs to
the jet algorithm using a particle flow approach [22]. During 2011 and 2012,
LHCb collected data with a mean number of $pp$ collisions per 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 to the same PV. The identification of $(b,c)$
jets is performed using SVs from the decays of $(b,c)$ hadrons. The choice of
using SVs and not single-track or other non-SV-based jet properties, e.g. the
number of particles in the jet, is driven by the need for a small
misidentification probability of $\rm light\mbox{-}parton$ jets in the
analyses performed at LHCb. Furthermore, the properties of SVs from
$(b,c)$-hadron decays are known to be well modeled in LHCb simulation.

###  3.1 The SV tagger

The tracks used as inputs to the SV-tagger algorithm are required to have
$\mbox{$p_{\rm T}$}>0.5\mathrm{\,Ge\kern-1.00006ptV}$ and
$\chi^{2}_{\mathrm{IP}}>16$. The $\chi^{2}_{\mathrm{IP}}$ requirement is
rarely satisfied by tracks reconstructed from particles originating directly
from the PV. Hadronic particle identification is not used and, instead, all
particles are assigned the pion mass. In contrast to many other jet-tagging
algorithms, tracks are not required to have $\Delta
R\equiv\sqrt{\Delta\eta^{2}+\Delta\phi^{2}}<0.5$, where
$\Delta\eta(\Delta\phi)$ is the difference in pseudorapidity (azimuthal angle)
between the track momentum and jet axis, since for low $p_{\rm T}$ jets tracks
outside of the jet cone help to discriminate between $c$ and $b$ jets.

All possible two-track SVs are built using pairs of the input tracks such that
the distance of closest approach between the tracks is less than 0.2$\rm\,mm$,
the vertex fit $\chi^{2}<10$ and the two-body mass is in the range
$0.4\mathrm{\,Ge\kern-1.00006ptV}<M<M(B)$, where $M(B)$ is the nominal
${B}^{0}$ mass [23]. Since all particles are assigned a pion mass, the upper
mass requirement rarely removes SVs from any long-lived $b$ hadrons. The lower
mass requirement removes SVs from most strange-particle decays, including the
$\Lambda$ baryon whose computed mass is always below
0.4$\mathrm{\,Ge\kern-1.00006ptV}$ when the proton is assigned a pion mass. At
this stage tracks are allowed to belong to multiple SVs. Next, all two-track
SVs with $\Delta R<0.5$ relative to the jet axis, where the direction of
flight is taken as the PV to SV vector, are collected as candidates for a so-
called linking procedure. This procedure involves merging SVs that share
tracks until none of the remaining SVs with $\Delta R<0.5$ share tracks. The
SV position is taken to be the weighted average of the 2-body SV positions
using the inverse of the 2-body vertex $\chi^{2}$ values as the weights.

The linking procedure can produce SVs that contain any number of tracks. The
linked $n$-track SVs are required to have $\mbox{$p_{\rm
T}$}>2\mathrm{\,Ge\kern-1.00006ptV}$, significant spatial separation from the
PV, and to contain at most one track with $\Delta R>0.5$ relative to the jet
axis. If the SV has only two tracks and a mass consistent with that of the
${K}^{0}_{\rm\scriptscriptstyle S}$ [23], the SV is rejected. Interactions
with material, and strange-particle decays, are suppressed by requiring that
the flight distance divided by the momentum of the SV is less than
1.5$\rm\,mm$/GeV; this quantity serves as a proxy for the hadron lifetime. The
SV position is also required to be within a restricted region consistent with
that of $(b,c)$-hadron decays.

An important quantity for discriminating between hadron types is the so-called
corrected mass defined as

$M_{\rm cor}=\sqrt{M^{2}+p^{2}\sin^{2}{\theta}}+p\sin{\theta},$ (1)

where $M$ and $p$ are the invariant mass and momentum of the particles that
form the SV and $\theta$ is the angle between the momentum and the direction
of flight of the SV. The corrected mass is the minimum mass that the long-
lived hadron can have that is consistent with the direction of flight. The
linked $n$-track SVs are required to have $M_{\rm
cor}>0.6\mathrm{\,Ge\kern-1.00006ptV}$ to remove any remaining kaon or hyperon
decays. A few percent of jets contain multiple SVs that pass all requirements;
in such cases the SV with the highest $p_{\rm T}$ is chosen. The fraction of
multi-SV-tagged jets is consistent in data and simulation.

Two BDTs are used to identify $b$ and $c$ jets: ${\rm BDT}(bc|udsg)$ trained
to separate $(b,c)$ jets from $\rm light\mbox{-}parton$ jets and ${\rm
BDT}(b|c)$ trained to separate $b$ jets from $c$ jets. Both BDTs are trained
on simulated samples of $b$, $c$ and $\rm light\mbox{-}parton$ jets. The
inputs to both BDTs are as follows:

  * •

the SV mass $M$;

  * •

the SV corrected mass $M_{\rm cor}$;

  * •

the transverse flight distance of the two-track SV closest to the PV;

  * •

the fraction of the jet $p_{\rm T}$ carried by the SV, $\mbox{$p_{\rm
T}$}({\rm SV})/\mbox{$p_{\rm T}$}({\rm jet})$;

  * •

$\Delta R$ between the SV flight direction and the jet;

  * •

the number of tracks in the SV;

  * •

the number of SV tracks with $\Delta R<0.5$ relative to the jet axis;

  * •

the net charge of the tracks that form the SV;

  * •

the flight distance $\chi^{2}$;

  * •

the sum of all SV track $\chi^{2}_{\mathrm{IP}}$.

For jets that contain an SV passing all of the requirements, the two BDT
responses are used to identify the jet as either $b$, $c$ or $\rm
light\mbox{-}parton$.

###  3.2 The topological trigger

The topological trigger algorithm uses SVs that satisfy similar criteria to
those used in the SV-tagger algorithm to build two-, three- and four-track
SVs. The TOPO SVs are required to have large $p_{\rm T}$ and significant
flight distance from the PV. The TOPO provides an efficient trigger option for
generic $b$-jet events, as the SV used by the TOPO to trigger recording of the
event can also be used to tag a $b$ jet. The BDT used in the TOPO algorithm
uses the following inputs:

  * •

the SV mass;

  * •

the SV corrected mass;

  * •

the sum of the $p_{\rm T}$ of the SV tracks;

  * •

the maximum distance of closest approach between the SV tracks;

  * •

the $\chi^{2}_{\mathrm{IP}}$ of the SV formed using the momentum of the tracks
that form the SV and SV position;

  * •

the flight distance $\chi^{2}$ of the SV from the PV;

  * •

the minimum $p_{\rm T}$ of the SV tracks.

To ensure stability during data-taking the TOPO BDT uses discretized inputs as
described in detail in Ref. [12]. Further details about the TOPO algorithm and
its performance on $b$-hadron decays as measured in LHCb data can be found in
Ref. [10].

###  3.3 Performance in simulation

Figure 1 shows the SV-tagger BDT distributions obtained from simulated
$W\\!+$jet events for each jet type. The distributions in the two-dimensional
BDT plane of SV-tagged $b$, $c$, and $\rm light\mbox{-}parton$ jets are
clearly distinguishable. The full two-dimensional distribution is fitted in
data to determine the jet flavor content. However, to aid in comparison to
other jet-tagging algorithms, a requirement of ${\rm BDT}(bc|udsg)>0.2$ is
applied to display the performance obtained from simulated events in Fig. 2.
This requirement is about 90% efficient on SV-tagged $(b,c)$ jets and highly
suppresses $\rm light\mbox{-}parton$ jets. The $(b,c)$-jet efficiencies are
nearly uniform for jet $\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$
and for $2.2<\eta<4.2$, but are lower for low-$p_{\rm T}$ jets and for jets
near the edges of the detector. The misidentification probability of $\rm
light\mbox{-}parton$ jets is less than 0.1% for low-$p_{\rm T}$ jets and
increases to about 1% at 100$\mathrm{\,Ge\kern-1.00006ptV}$. Figure 3 shows
the $(b,c)$-jet efficiencies versus the mistag probability of $\rm
light\mbox{-}parton$ jets obtained by increasing the ${\rm BDT}(bc|udsg)$ cut.

For the TOPO algorithm, in the trigger a BDT requirement is always applied;
the requirement is looser when the SV contains a muon. In the LHCb measurement
of the charge asymmetry in $b\bar{b}$ production [24], this same looser BDT
requirement was applied to tag a second jet in the event. Figure 2 shows the
performance of the TOPO algorithm, obtained from simulated events, for both
the nominal and loose BDT requirements. The nominal trigger BDT requirement
strongly suppresses $c$ and $\rm light\mbox{-}parton$ jets, with the
misidentification probability of $\rm light\mbox{-}parton$ jets being 0.01%
for low-$p_{\rm T}$ jets. Such a strong suppression is required during online
running due to output rate limitations.

The jet-tagging performance is measured in simulated events with one $pp$
collision and two or more $pp$ collisions and found to be consistent. The
tagging performance is also studied in simulation using different event types,
e.g. top-quark and QCD di-jet events, with only small changes in the tagging
efficiencies and BDT templates observed for $(b,c)$ jets. The mistag
probability of $\rm light\mbox{-}parton$ jets is found to be higher for
high-$p_{\rm T}$ jets in events that also contain $(b,c)$ jets. This is
discussed in detail in Sec. 5.

Figure 1:  SV-tagger algorithm ${\rm BDT}(b|c)$ versus ${\rm BDT}(bc|udsg)$
distributions obtained from simulation for (left) $b$, (middle) $c$ and
(right) $\rm light\mbox{-}parton$ jets.

Figure 2:  Efficiencies and mistag probabilities obtained from simulation for
the SV-tagger and TOPO algorithms for (top) $b$, (middle) $c$ and (bottom)
$\rm light\mbox{-}parton$ jets. The left plots show the dependence on $p_{\rm
T}$ for $2.2<\eta<4.2$, while the right plots show the dependence on $\eta$
for $\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ (see text for
details). The “loose” label for the TOPO refers to the BDT requirement used in
the trigger for SVs that contain muon candidates.  Figure 3:  Efficiencies for
SV-tagging a $(b,c)$-jet versus mistag probability for a $\rm
light\mbox{-}parton$ jet from simulation. The curves are obtained by varying
the ${\rm BDT}(bc|udsg)$ requirement.

##  4 Efficiency measurements in data

The tagging efficiencies for $b$ and $c$ jets are measured in data and
compared with expectations from simulation. To measure the tagging
efficiencies in a given data sample, both the number of tagged $(b,c)$ jets
and the total number of $(b,c)$ jets must be determined. The tagged $(b,c)$
yields are obtained by fitting the SV-tagger or TOPO BDT distributions in the
subsample of jets that are tagged by an SV. The total number of $(b,c)$ jets
is determined by fitting the $\chi^{2}_{\mathrm{IP}}$ distribution of the
highest-$p_{\rm T}$ track in the jet. The $(b,c)$-tagging efficiency is the
ratio of the tagged over total $(b,c)$-jet yields.

An alternative approach employed by other experiments (see, e.g. Ref. [25]) is
to measure the efficiency using the subsample of jets that contain a muon.
This approach has the advantage that the $(b,c)$-jet content is enhanced due
to the presence of muons from the semileptonic decays of $(b,c)$ hadrons;
however, the disadvantage is that this method assumes that mismodeling of the
tagging performance is the same for semileptonic and inclusive decays. Both
the highest-$p_{\rm T}$ track and muon-jet methods are used in this analysis
to study the jet-tagging performance.

Combined fits of several data samples enriched in $(b,c)$ jets are performed
to obtain the tagging efficiencies. It is important to include the systematic
uncertainties on both the tagged and total $(b,c)$-jet yields for each data
sample in the combined fits.

This section is arranged as follows: the data samples used are described in
Sec. 4.1; the BDT fits used to obtain the tagged $(b,c)$-jet yields are given
in Sec. 4.2; the highest-$p_{\rm T}$-track $\chi^{2}_{\mathrm{IP}}$ fits used
to obtain the total $(b,c)$-jet yields are described in Sec. 4.3; the muon-jet
subsample method is discussed in Sec. 4.4; the systematic uncertainties on the
tagged and total $(b,c)$-jet yields are presented in Sec. 4.5; and the
$(b,c)$-tagging efficiency results are given in Sec. 4.6.

###  4.1 Data samples

Events that contain either a high-$p_{\rm T}$ muon or a fully reconstructed
$(b,c)$ hadron, referred to here as an event-tag, are used to measure the jet-
tagging efficiencies in data. The highest-$p_{\rm T}$ jet in the event that
does not have any overlap with the event-tag is chosen as the test jet. Each
event-tag is required to have satisfied specific trigger requirements and to
have $\Delta\phi>2.5$ relative to the test-jet axis to reduce the possibility
of contamination of the jet from the event-tag222The event-tag samples are
highly pure; however, when the event-tag is not properly reconstructed the
non-overlap requirements are not guaranteed to hold. Requiring that the event-
tag and test jet are back-to-back in the transverse plane greatly reduces the
probability that a particle originating from the event-tag decay but not
reconstructed in the event-tag is reconstructed as part of the test jet..
Therefore, all events used to measure the $(b,c)$-tagging efficiency have
passed the trigger independently of the presence of the test jet, which
ensures that the trigger does not bias the efficiency measurement. The
following event-tags are used (labeled by the data-set identifier):

  * •

($B+$jet) a fully reconstructed $b$-hadron decay which enriches the $b$-jet
content of the test-jet sample;

  * •

($D+$jet) a fully reconstructed $c$-hadron decay which enriches the $c$-jet
and $b$-jet content of the test-jet sample (due to $b\rightarrow c$ decays);

  * •

($\mu(b,c)+$jet) a displaced high-$p_{\rm T}$ muon which enriches the $c$-jet
and $b$-jet content of the test-jet sample;

  * •

($W\\!+$jet) a prompt isolated high-$p_{\rm T}$ muon indicative of $W\\!+$jet
events that consists of about 95% $\rm light\mbox{-}parton$ jets.

The first three samples are used to measure the $(b,c)$-jet identification
efficiencies and properties. The final sample is used to study
misidentification of $\rm light\mbox{-}parton$ jets. In all samples the event-
tag and test jet are required to originate from the same PV. The range
$10<\mbox{$p_{\rm T}$}({\rm jet})<100\mathrm{\,Ge\kern-1.00006ptV}$ is
considered since there are no large enough data samples to measure the
efficiency for jet $\mbox{$p_{\rm T}$}>100\mathrm{\,Ge\kern-1.00006ptV}$.

###  4.2 Tagged-jet yields

The presence of an SV and its kinematic properties are used to discriminate
between $b$, $c$ and $\rm light\mbox{-}parton$ jets. As described in Section
3, the SV-tagger algorithm uses two BDTs while the TOPO uses one BDT for each
SV. The tagged yields for each algorithm are obtained by fitting to data BDT
templates obtained from simulation for $b$, $c$ and $\rm light\mbox{-}parton$
jets. In all fits the template shapes are fixed and only the yields of each
jet type are free to vary.

Figures 4–6 show the results of fits performed to the two-dimensional SV-
tagger BDT distributions in the $B+$jet, $D+$jet and $\mu(b,c)+$jet data
samples. The $b$ and $c$ jets are clearly distinguishable in the two-
dimensional BDT distributions: $b$ jets are mostly found in the upper right
corner, while $c$ jets are found in the center-right and lower-right regions.
The $\rm light\mbox{-}parton$ jets cluster near the origin but are difficult
to see due to the low SV-tag probability of $\rm light\mbox{-}parton$ jets.
The BDT templates for $b$, $c$ and $\rm light\mbox{-}parton$ jets describe the
data well. A dedicated study of the modeling of the $\rm
light\mbox{-}parton$-jet BDT distributions is discussed in Sec. 5.

Figure 4:  SV-tagger BDT fit results for the $B+$jet data sample with
$10<\mbox{$p_{\rm T}$}({\rm jet})<100\mathrm{\,Ge\kern-1.00006ptV}$: (top
left) distribution in data; (top right) two-dimensional template-fit result;
and (bottom) projections of the fit result with the $b$, $c$, and $\rm
light\mbox{-}parton$ contributions shown as stacked histograms.

Figure 5:  Same as Fig. 4 for the $D+$jet data sample.

Figure 6:  Same as Fig. 4 for the $\mu(b,c)+$jet data sample.

A simple cross-check on the $b$, $c$ and $\rm light\mbox{-}parton$ yields is
performed by fitting only two of the BDT inputs: the corrected mass defined in
Eq. 1 and the number of tracks in the SV. The corrected mass provides the best
discrimination between $c$ jets and other jet types due to the fact that
$M_{\rm cor}$ peaks near the $D$ meson mass for $c$ jets333This is true for
all long-lived $c$ hadrons when all tracks are assigned a pion mass.. The
number of tracks in the SV identifies $b$ jets well since $b$-hadron decays
often produce many displaced tracks. Figure 7 shows the results of a two-
dimensional fit to these two SV properties. The absolute fractions of $b$, $c$
and $\rm light\mbox{-}parton$ SV tags agree with the BDT fit results to within
1–2%. The corrected mass has been previously used in LHCb jet analyses for
determining the $c$-jet yield [24] and for extracting the $b$-jet yield [26].
The clear peaking structure for $c$ jets, which relies on the excellent vertex
resolution of the LHCb detector, makes them easily identifiable.

Figure 7:  Two-dimensional $M_{\rm cor}$ versus SV track multiplicity fit
results for (top) $B+$jet, (middle) $D+$jet and (bottom) $\mu(b,c)+$jet data
samples. The left plots show the projection onto the $M_{\rm cor}$ axis, while
the right plots show the projection onto the track multiplicity. The highest
$M_{\rm cor}$ bin includes candidates with $M_{\rm
cor}>10\mathrm{\,Ge\kern-1.00006ptV}$.

Figure 8 shows the results of fitting the TOPO BDT distributions in the
various data samples using $b$, $c$ and $\rm light\mbox{-}parton$ jet template
shapes obtained from simulation. The ratios of SV-tagger to TOPO SV-tagged
$b$, $c$ and $\rm light\mbox{-}parton$ jets are each consistent with
expectations from simulation. Modeling of both the SV-tagger and TOPO SV
properties are sufficient to allow the SV-tagged content to be accurately
determined.

Figure 8:  Fits to the TOPO BDT distribution in (left) $B+$jet, (middle)
$D+$jet and (right) $\mu(b,c)+$jet data samples with $10<\mbox{$p_{\rm
T}$}({\rm jet})<100\mathrm{\,Ge\kern-1.00006ptV}$.

###  4.3 Efficiency measurement using highest-$p_{\rm T}$ tracks

To determine the jet-tagging efficiency, the jet composition prior to applying
the SV tag must be determined. This is necessarily more difficult than
determining the SV-tagged composition. The $\chi^{2}_{\mathrm{IP}}$
distribution of the highest-$p_{\rm T}$ track in the jet is used for this
task. For $\rm light\mbox{-}parton$ jets the highest-$p_{\rm T}$ track will
mostly originate from the PV, while for $(b,c)$ jets the highest-$p_{\rm T}$
track will often originate from the decay of the $(b,c)$ hadron. To avoid
possible issues with modeling of soft radiation, only the subset of jets for
which the highest-$p_{\rm T}$ track satisfies $\mbox{$p_{\rm
T}$}($track$)/\mbox{$p_{\rm T}$}($jet$)>10\%$, which is about 95% of all jets,
is used.

Since the $W\\!+$jet sample is dominantly composed of $\rm
light\mbox{-}parton$ jets, the $\chi^{2}_{\mathrm{IP}}$ detector response can
be obtained in a data-driven way using this data sample. First, the two-
dimensional SV-tagger BDT response is fitted to determine the SV-tagged $b$,
$c$ and $\rm light\mbox{-}parton$ jet yields. The tagging efficiencies
obtained in simulation for $b$ and $c$ jets are used to estimate the total
number of $b$ and $c$ jets in the $W\\!+$jet data sample. Since the $b$ and
$c$ jets combined make up only 5% of the total data sample, any mismodeling of
the SV-tagging efficiency will have negligible impact on this study. The IP
resolution is studied by comparing the observed $\chi^{2}_{\mathrm{IP}}$
distributions in data with templates obtained from simulation in bins of jet
$p_{\rm T}$. The resolution in data is found to be about 10% worse than in the
simulation which is consistent with previous LHCb studies of the IP resolution
[7]. Figure 9 shows that the data-driven templates describe the data well. The
difference in the detector response between data and simulation is assumed to
be universal and is applied to correct the $\chi^{2}_{\mathrm{IP}}$ templates
for $b$ and $c$ jets.

Figure 9:  Results of $\chi^{2}_{\mathrm{IP}}$ calibration using $W\\!+$jet
data for $10<\mbox{$p_{\rm T}$}({\rm jet})<100\mathrm{\,Ge\kern-1.00006ptV}$.
The tail out to large $\chi^{2}_{\mathrm{IP}}$ values in the $\rm
light\mbox{-}parton$-jet sample is largely due to strange particle decays.

Figure 10 shows the results of fitting the $\chi^{2}_{\mathrm{IP}}$
distributions in the $B+$jet, $D+$jet and $\mu(b,c)+$jet data samples. Each
sample consists of mostly $\rm light\mbox{-}parton$ jets prior to applying an
SV tag. While these data samples require that an event-tag containing a
$(b,c)$ quark is reconstructed, the associated $(b,c)$ quarks produced in hard
scattering processes are often not produced within the LHCb acceptance.
Furthermore, for the $(B,D)+$jet samples, the event-tags often have low
$p_{\rm T}$ so that the associated $(b,c)$ quarks may be within the LHCb
acceptance but do not form a high-$p_{\rm T}$ jet. The $\rm
light\mbox{-}parton$-jet $\chi^{2}_{\mathrm{IP}}$ template has a long tail out
to large values which arises due to hyperon and kaon decays. In the
$\chi^{2}_{\mathrm{IP}}$ fits, the $\log{\chi^{2}_{\mathrm{IP}}}>3$ component
of the $\rm light\mbox{-}parton$ template is allowed to vary independently to
allow for different $s$-quark content from the $W\\!+$jet calibration sample.
Apart from this, all $\chi^{2}_{\mathrm{IP}}$ templates are fixed in shape.
The efficiency for tagging a jet originated by a quark of type $q$ is
determined as

$\epsilon_{q}=N_{q}({\rm SV})/N_{q}(\chi^{2}_{\mathrm{IP}}),$ (2)

i.e. it is the ratio of the yield determined from fits to the SV-tagged BDT
distributions, either for the SV-tagger or TOPO algorithm, to the yield
obtained from fits to the $\chi^{2}_{\mathrm{IP}}$ distributions.

Figure 10:  Fits to the $\chi^{2}_{\mathrm{IP}}$ distribution in (top left)
$B+$jet, (top right) $D+$jet and (bottom) $\mu(b,c)+$jet data samples.

###  4.4 Efficiency measurement using muon jets

The approach described in the previous subsection has the advantage that it
involves measuring the efficiency on almost all of the jets in the data
sample; however, its disadvantage is the large $\rm light\mbox{-}parton$-jet
content, which results in 10–20% uncertainties on the pre-SV-tag jet content.
An approach used by other experiments is to measure the efficiency on the
subset of jets that contain muons. The tagging efficiencies are also obtained
using Eq. 2 for the muon-jet subsamples. Figures 11–13 show the SV-tagger BDT
and $\chi^{2}_{\mathrm{IP}}$ fit results for the muon-jet subsample of each
data set. In these subsamples the $\chi^{2}_{\mathrm{IP}}$ is that of the
highest-$p_{\rm T}$ muon in the jet. The muon is required to satisfy
$\mbox{$p_{\rm T}$}(\mu)/\mbox{$p_{\rm T}$}({\rm jet})>10\%$. The initial $\rm
light\mbox{-}parton$-jet content is greatly reduced in these data subsamples;
however, this approach only uses about $10\%$ of the jets and it is possible
that mismodeling of the jet-tagging performance in semileptonic decays is not
the same as for other decays.

Figure 11:  (top) SV-tagger two dimensional BDT fit results projected onto the
(left) ${\rm BDT}(bc|udsg)$ and (right) ${\rm BDT}(b|c)$ axes and (bottom)
$\chi^{2}_{\mathrm{IP}}$ fit results for the $B+$muon-jet subsample with
$10<\mbox{$p_{\rm T}$}({\rm jet})<100\mathrm{\,Ge\kern-1.00006ptV}$.

Figure 12:  Same as Fig. 11 but for the $D+$muon-jet data sample.

Figure 13:  Same as Fig. 11 but for the $\mu(b,c)+$muon-jet data sample.

###  4.5 Systematic uncertainties

The systematic uncertainty on $N_{(b,c)}({\rm SV})$ is estimated using the
difference between the $(b,c)$ SV-tagged yields obtained from two different
fits: the fit to the BDT distributions and the fit to the $M_{\rm cor}$ versus
track multiplicity distributions. The latter approach removes jet quantities
such as jet $p_{\rm T}$ from the yield determination. While the absolute
uncertainty on the SV-tagged quark content as determined by the difference in
these two methods is only a few percent, the relative uncertainty is large for
cases where a given jet type makes up a small fraction of the SV-tagged data
sample. For example, the relative uncertainty on the $c$-jet yield in the
$B+$jet data sample is large. As a further cross-check the $(B,D)+$jet data
samples are used to obtain data-driven BDT templates. The difference in
$(b,c)$ yields obtained by fitting the $W\\!+$jet data sample using the data-
driven and simulation templates is found to be negligible.

The systematic uncertainty on $N_{(b,c)}(\chi^{2}_{\mathrm{IP}})$ has several
components. The nominal $\chi^{2}_{\mathrm{IP}}$ fits allow the large-IP
component of the $\rm light\mbox{-}parton$-jet template to vary. The
$\chi^{2}_{\mathrm{IP}}$ fits are repeated fixing this component to that
observed in $W\\!+$jet data, with the difference in $(b,c)$-jet yields
assigned as a systematic uncertainty. This uncertainty is sizable for the case
of high-$p_{\rm T}$ $c$ jets whose $\chi^{2}_{\mathrm{IP}}$ template is less
distinct from that of $\rm light\mbox{-}parton$ jets which has a variable
large-IP component in the fit. Possible dependence of the mismodeling of the
IP resolution on the origin point of the particle is studied and found to be
negligible.

For the case of muon jets, the misidentification probability of hadrons as
muons and the jet track multiplicity must be modeled properly to obtain an
accurate $\chi^{2}_{\mathrm{IP}}$ distribution. Mismodeling of these
properties does not lead to large uncertainty on
$N_{b}(\chi^{2}_{\mathrm{IP}})$, since the vast majority of reconstructed
muons in $b$ jets are truly muons that arise due to semileptonic decays. For
$c$ jets, however, mismodeling of these properties can produce sizable shifts
in $N_{c}(\chi^{2}_{\mathrm{IP}})$ due to the smaller fraction of $c$ jets
that contain muons from semileptonic decays. A comparison between $W\\!+$jet
data and simulation of the jet fraction that satisfies the muon-jet
requirements, in bins of jet $p_{\rm T}$, is used to obtain an estimate of the
probability of misidentifying a jet as a muon jet. Based on this study a 5%
relative uncertainty is assigned to $N_{b}(\chi^{2}_{\mathrm{IP}})$ and 20% to
$N_{c}(\chi^{2}_{\mathrm{IP}})$ for muon jets. Another possible way of
misidentifying muon jets is if the semileptonic decay of a $b$ hadron outside
of the jet produces a muon reconstructed as part of the jet444This can also
happen for semileptonic $c$-hadron decays; however, such decays rarely produce
particles with $\Delta R>0.5$ to the jet axis due to the much lower mass of
$c$ hadrons compared to that of $b$ hadrons.. The $\Delta R$ distribution
between the SV direction of flight and jet axis for all muons found in an SV
is used to conclude that this effect is at the per mille level; it is taken to
be negligible.

Jets produced in different types of events can have different properties. The
$b$-tag efficiency is found to agree to about 1% in simulated $W\\!+\\!b$, top
and QCD multi-jet events. The BDT shapes are studied in simulated single-jet
$b$ and di-jet $b\bar{b}$ events and found to be consistent for low-$p_{\rm
T}$ jets but to show small discrepancies for large jet $p_{\rm T}$. For
example, the absolute difference in efficiency of requiring ${\rm
BDT}(bc|udsg)>0.2$ for $b$ jets is less than 1% up to a jet $p_{\rm T}$ of
50$\mathrm{\,Ge\kern-1.00006ptV}$ but reaches about 3% at a jet $p_{\rm T}$ of
100$\mathrm{\,Ge\kern-1.00006ptV}$. In the data samples considered in this
study, such effects are negligible as using BDT templates from different event
types results in differences in the SV-tagged yields of less than 1%.

Events where multiple $b$ hadrons are produced could affect the SV BDT shapes.
The fraction of SVs that contain a track with $\Delta R>0.5$ relative to the
jet axis is studied in data with the back-to-back requirement for the event-
tag and test jet removed. The fraction of SVs that contain such a track is
found to vary by at most a few percent as a function of $\Delta R$ between the
event-tag and test jet. This could indicate percent-level cross-talk between
multiple $b$ jets or could be due to changes in the jet composition. For the
efficiency measurements presented in this paper the effect of $(b,c)$-hadron
decays outside of the jet is negligible; however, such decays could have an
important impact on the tagging performance in some event types, e.g. in four
$b$-jet events.

Gluon splitting to $b\bar{b}$ or $c\bar{c}$ can produce jets that contain
multiple $(b,c)$ hadrons which have a higher tagging efficiency. The
requirement that a $(b,c)$-hadron-decay signature is back-to-back with the
test jet suppresses gluon-splitting contributions. The fraction of jets that
contain multiple SVs in data is a few percent, which agrees to about 1% in all
bins with simulated jets that contain only a single $(b,c)$ hadron. The
systematic uncertainty due to jets that contain multiple $(b,c)$ hadrons from
$g\rightarrow(b\bar{b},c\bar{c})$ is taken to be 1%. Finally, there is no
evidence in simulation of dependence on the number of $pp$ interactions in the
event, so the uncertainty due to mismodeling of the number of $pp$
interactions is taken to be negligible. The systematic uncertainties are
summarized in Table 1.

Table 1:  Summary of relative systematic uncertainties ($-$ denotes negligible). Systematic uncertainties that dependent on jet type and $p_{\rm T}$ are marked by a $*$ (see text for details). source |  $b$ jets |  $c$ jets
---|---|---
BDT templates∗ | $\approx 2\%$ | $\approx 2\%$
$\rm light\mbox{-}parton$-jet large IP component∗ | $\approx 5\%$ | $\approx 10-30\%$
IP resolution | $-$ | $-$
hadron-as-muon probability (muon-jet subsample only) | 5% | 20%
out-of-jet $(b,c)$-hadron decay | $-$ | $-$
gluon splitting | $1\%$ | $1\%$
number of $pp$ interactions per event | $-$ | $-$

###  4.6 Results

A combined fit to the $B+$jet, $D+$jet and $\mu(b,c)+$jet data samples,
including the systematic uncertainties in Table 1, is performed to obtain the
$(b,c)$-jet tagging efficiencies. In these fits, both $N_{(b,c)}({\rm SV})$
and $N_{(b,c)}(\chi^{2}_{\mathrm{IP}})$ are determined simultaneously under
the constraint that the $(b,c)$-tagging efficiency in a given jet $p_{\rm T}$
and $\eta$ region must be the same in each data sample. The highest-$p_{\rm
T}$ track and muon-jet subsamples are fitted independently since the scale
factors between data and simulation could be different for semileptonic and
inclusive decays. The scale factors for $b$ and $c$ jets are allowed to vary
independently since these may be different for different jet types. The
misidentification probability of $\rm light\mbox{-}parton$ jets is allowed to
vary freely in each data sample, although the results obtained are all
consistent and agree with simulation.

The scale factors for the SV-tagger algorithm are measured versus jet $p_{\rm
T}$ in the region $2.2<\eta<4.2$, where the efficiencies are expected to be
nearly uniform versus $\eta$, and in the region $2<\eta<2.2$ for jet
$\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$, where the efficiencies
are nearly uniform versus jet $p_{\rm T}$ (there are not sufficient statistics
to measure the efficiencies in the $\eta>4.2$ region). The results versus jet
$p_{\rm T}$ are shown in Fig. 14 and are summarized as follows:

  * •

The scale factors obtained from the highest-$p_{\rm T}$ track approach are all
consistent with unity at the $\pm 20\%$ level. They show no trend in $p_{\rm
T}$ for $b$ or $c$ jets.

  * •

The scale factors for muon jets are found to be consistent, albeit with large
uncertainties, with those obtained using the highest-$p_{\rm T}$ track
approach. The results are combined assuming that the scale factors are the
same for semileptonic and inclusive $(b,c)$-hadron decays (see Fig. 14) and
are summarized in Table 2. The scale factors are consistent with unity for jet
$\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$, but 10-20% below unity
for low-$p_{\rm T}$ jets.

  * •

The scale-factor results obtained from the global fits are strongly anti-
correlated between $b$ and $c$ jets. It is likely that the true scale factors
are similar between $b$ and $c$ jets since many of the contributing factors,
e.g. mismodeling of the SV position resolution, are expected to affect $b$ and
$c$ jets in a similar manner. The highest-$p_{\rm T}$ track fits are repeated
assuming that the scale factors are the same for $b$ and $c$ jets (see Fig.
14) and summarized in Table 2. The results for jet $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ are consistent with unity at about the
5% level, while at low jet $p_{\rm T}$ the scale factor is again less than
unity by about 10%. The muon jet results are not combined for $b$ and $c$ jets
since the $b$-jet results are much more precise.

Neither of the assumptions made in the combinations has to be completely
valid; however, they should each be a good approximation. Overall, the
efficiencies measured in data are consistent with those in simulation for jet
$\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ with a conservative
systematic uncertainty estimate of 10%. At low jet $p_{\rm T}$ the scale
factors are about 0.9 for $b$ jets and 0.8 for $c$ jets. Using the difference
in central values obtained from the highest-$p_{\rm T}$ track, combined
highest-$p_{\rm T}$ track and muon jet, and combined $b$ and $c$ jet results,
produces a conservative systematic uncertainty estimate of 10%. The absolute
efficiencies measured assuming the scale factors are the same for $b$ and $c$
jets are given in Table 2. For jet $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and $2.2<\eta<4.2$, the mean SV-tagging
efficiency is about 65% for $b$ jets and 25% for $c$ jets. Finally, the TOPO
algorithm efficiencies are measured in data and found to be consistent with
simulation to about 5% for $b$ jets and 20% for $c$ jets (see Fig. 15). The
absolute efficiencies measured using the TOPO for $b$ jets are: $21\pm 1\%$
for 10–20$\mathrm{\,Ge\kern-1.00006ptV}$; $44\pm 4\%$ for
20–30$\mathrm{\,Ge\kern-1.00006ptV}$; $60\pm 5\%$ for
30–50$\mathrm{\,Ge\kern-1.00006ptV}$; and $66\pm 6\%$ for
50–100$\mathrm{\,Ge\kern-1.00006ptV}$.

Figure 14:  Efficiencies of the SV-tagger algorithm measured in data relative to those obtained from simulation for $2.2<\eta<4.2$: (top left) results from the (closed markers) highest-$p_{\rm T}$ track and (open markers) muon-jet samples; (top right) the combined results assuming the scale factors are the same for semileptonic and inclusive $(b,c)$-hadron decays; and (bottom left) the combined results for $(b,c)$-jet using the highest-$p_{\rm T}$-track approach assuming the scale factors are the same for $b$ and $c$ jets. The absolute efficiencies corresponding to the combined $(b,c)$-jet results (bottom right).  Table 2:  SV-tagger algorithm $(b,c)$-tagging efficiencies measured in data compared to those obtained in simulation. The $b$ and $c$ results are obtained by combining the highest-$p_{\rm T}$ track and muon-jet results under the assumption that the scale factors are the same for semileptonic and inclusive $(b,c)$-hadron decays. The $(b,c)$ results are obtained by fitting the highest-$p_{\rm T}$-track sample under the assumption that the scale factors are the same for $b$ and $c$ jets. The absolute efficiencies observed in data are provided using the “$(b,c)$ jets” results.  |  |  $\epsilon($data$)/\epsilon($simulation$)$ |  $\epsilon($data$)$ (%)
---|---|---|---
jet $p_{\rm T}$ ($\mathrm{\,Ge\kern-1.00006ptV}$) | jet $\eta$ |  $b$ jets |  $c$ jets |  $(b,c)$ jets |  $b$ jets |  $c$ jets
10–200 | 2.2–4.2 | $0.89\pm 0.04$ | $0.81\pm 0.09$ | $0.91\pm 0.04$ | $38\pm 2$ | $14\pm 1$
20–300 | 2.2–4.2 | $0.92\pm 0.07$ | $0.97\pm 0.09$ | $0.97\pm 0.04$ | $61\pm 3$ | $23\pm 1$
30–500 | 2.2–4.2 | $1.06\pm 0.08$ | $1.04\pm 0.09$ | $0.97\pm 0.04$ | $65\pm 3$ | $25\pm 1$
50–100 | 2.2–4.2 | $1.10\pm 0.09$ | $0.81\pm 0.15$ | $1.05\pm 0.06$ | $70\pm 4$ | $28\pm 4$
20–100 |  .22–2.2 | $1.00\pm 0.07$ | $1.12\pm 0.10$ | $1.05\pm 0.03$ | $56\pm 2$ | $20\pm 1$
Figure 15:  TOPO algorithm $(b,c)$-tagging efficiencies, using the “loose” BDT
requirement, in data relative to those obtained in simulation.

##  5 Light-parton jet misidentification

Light-parton jets contain SVs due to any of the following: (1)
misreconstruction of prompt particles as displaced tracks; (2) decays of long-
lived strange particles; or (3) interactions with material. Type (1) can be
studied in data using jets that contain an SV whose inverted direction of
flight lies in the jet cone (referred to as a backward SV). Types (2) and (3)
can be studied using SVs for which the ratio of the SV flight distance divided
by the SV momentum is too large for the decay of a $(b,c)$ hadron (referred to
as a too-long-lived SV). The mistag probability for simulated $\rm
light\mbox{-}parton$ jets using backward and too-long-lived SVs is consistent
with the nominal mistag probability at the 20% level (the nominal mistag
probability is shown in Fig. 2). Furthermore, the SV BDT distributions
obtained using backward and too-long-lived SVs are similar to the nominal $\rm
light\mbox{-}parton$-jet BDT distributions. Therefore, the mistag probability
of $\rm light\mbox{-}parton$ jets and SV properties can be studied in data
using backward and too-long-lived SV-tagged jets.

Such a study is complicated by the fact that prompt tracks in $(b,c)$ jets can
also be misreconstructed as displaced, and that $(b,c)$ jets also produce
strange particles and material interactions. Therefore, both backward and too-
long-lived SVs are also found in $(b,c)$ jets. The $W\\!+$jet data sample,
which is dominantly composed of $\rm light\mbox{-}parton$ jets, is used to
mitigate effects from mistagged $(b,c)$ jets. Figure 16 shows the BDT
distributions from backward and too-long-lived SVs observed in data compared
to simulation. The backward and too-long-lived BDT templates are similar for
all jet types. The $(b,c)$ yields here are fixed by fitting the nominal SV-
tagged data to obtain the total $(b,c)$-jet content then taking the backward
and too-long-lived SV-tag probabilities for $(b,c)$ jets from simulation. The
distributions in data and simulation are consistent, which demonstrates that
the SV properties are well-modeled for $\rm light\mbox{-}parton$ jets.

The total $\rm light\mbox{-}parton$-jet composition of this sample, without
applying any SV-tagging algorithm, is found to be 95%, by fitting the nominal
SV-tagged BDT distributions and applying the data-driven $(b,c)$-tagging
efficiencies from the previous section. The mistag probability of $\rm
light\mbox{-}parton$ jets is obtained as the ratio of the number of SV-tags
for those jets (obtained by fitting the SV BDT distributions) to the total
number of $\rm light\mbox{-}parton$ jets. The ratio of this probability in
data to that in simulation is shown in Fig. 17; data and simulation agree at
about the $\pm 30\%$ level integrated over jet $p_{\rm T}$. A detailed study
of $W\\!+$jet production in LHCb using the SV-tagger algorithm introduced in
this paper, in which the jets are required to satisfy $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and $2.2<\eta<4.2$, finds that the
nominal $\rm light\mbox{-}parton$-jet mistag probability is 0.3% which is
consistent with simulation[27]. The same ratio for the TOPO algorithm is also
shown in Fig. 17.

Figure 16:  SV-tagger algorithm BDT distributions for backward and too-long-
lived SVs in the $W\\!+$jet data sample: (top left) distribution in data; (top
right) two-dimensional template-fit result; and (bottom) projections of the
fit result with the $b$, $c$, and $\rm light\mbox{-}parton$ contributions
shown as stacked histograms.

Figure 17:  Ratio of $\rm light\mbox{-}parton$-jet mistag probabilities
observed in data to those in simulation for the (left) SV-tagger and (right)
TOPO algorithms.

The performance of any tagging algorithm on $\rm light\mbox{-}parton$ jets can
be affected by the presence of $(b,c)$ jets in the event. The
misidentification probability of $\rm light\mbox{-}parton$ jets is studied in
simulated di-$b$-jet events and compared to the performance obtained in
simulated events that contain no $(b,c)$ jets. The absolute difference in the
fraction of $\rm light\mbox{-}parton$ jets that are SV-tagged and have ${\rm
BDT}(bc|udsg)>0.2$ is found to be at the per mille level for low-$p_{\rm T}$
jets, but increases to about 1% for jet $p_{\rm T}$ of
50$\mathrm{\,Ge\kern-1.00006ptV}$ and to about 2–3% at
100$\mathrm{\,Ge\kern-1.00006ptV}$. The BDT shapes are distorted relative to
those obtained in events that contain no $(b,c)$ jets, but there is still
significant discrimination between the $\rm light\mbox{-}parton$ and $(b,c)$
distributions. The difference is largely due to particles originating from a
$b$-hadron decay and produced with $\Delta R<0.5$ relative to the $\rm
light\mbox{-}parton$-jet axis. These tracks may then form SVs with
misreconstructed prompt tracks in the $\rm light\mbox{-}parton$ jets.

##  6 Summary

The LHCb collaboration has developed several algorithms that efficiently
identify jets that arise from the hadronization of $b$ and $c$ quarks. The
performance of these algorithms has been studied in data and is found to agree
with that in simulation at about the 10% level for $(b,c)$ jets, and at the
30% level for $\rm light\mbox{-}parton$ jets. The SV properties of all jet
types are found to be well modeled by LHCb simulation. The efficiency for
identifying a $b(c)$ jet is about 65%(25%) with a probability of
misidentifying a $\rm light\mbox{-}parton$ jet of 0.3% for jets with
transverse momentum $\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and
pseudorapidity $2.2<\eta<4.2$.

## 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).

## References

  * [1] R. Gauld, Leptonic top-quark asymmetry predictions at LHCb, Phys. Rev. D91 (2015) 054029, arXiv:1409.8631
  * [2] A. L. Kagan, J. F. Kamenik, G. Perez, and S. Stone, Probing new top physics at the LHCb experiment, Phys. Rev. Lett. 107 (2011) 082003, arXiv:1103.3747
  * [3] B. Grinstein and C. W. Murphy, Bottom-quark forward-backward asymmetry in the Standard Model and beyond, Phys. Rev. Lett. 111 (2013) 062003, arXiv:1302.6995
  * [4] D. Kahawala, D. Krohn, and M. Strassler, Measuring the bottom-quark forward-central asymmetry at the LHC, JHEP 01 (2012) 069, arXiv:1108.3301
  * [5] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [6] LHCb, R. Aaij et al., LHCb Detector Performance, Int. J. Mod. Phys. A30 (2015), no. 07 1530022, arXiv:1412.6352
  * [7] R. Aaij et al., Performance of the LHCb Vertex Locator, JINST 9 (2014) P09007, arXiv:1405.7808
  * [8] R. Arink et al., Performance of the LHCb Outer Tracker, JINST 9 (2014) P01002, arXiv:1311.3893
  * [9] A. A. Alves Jr. et al., Performance of the LHCb muon system, JINST 8 (2013) P02022, arXiv:1211.1346
  * [10] R. Aaij et al., The LHCb trigger and its performance in 2011, JINST 8 (2013) P04022, arXiv:1211.3055
  * [11] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and regression trees, Wadsworth international group, Belmont, California, USA, 1984
  * [12] V. V. Gligorov and M. Williams, Efficient, reliable and fast high-level triggering using a bonsai boosted decision tree, JINST 8 (2013) P02013, arXiv:1210.6861
  * [13] T. Sjöstrand, S. Mrenna, and P. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [14] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, J. Phys. Conf. Ser. 331 (2011) 032047
  * [15] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A462 (2001) 152
  * [16] P. Golonka and Z. Was, PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [17] Geant4 collaboration, J. Allison et al., Geant4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [18] Geant4 collaboration, S. Agostinelli et al., Geant4: A simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250
  * [19] M. Clemencic et al., The LHCb simulation application, Gauss: Design, evolution and experience, J. Phys. Conf. Ser. 331 (2011) 032023
  * [20] M. Cacciari, G. P. Salam, and G. Soyez, The anti-kt jet clustering algorithm, JHEP 04 (2008) 063, arXiv:0802.1189
  * [21] M. Cacciari, G. P. Salam, and G. Soyez, FastJet user manual, Eur. Phys. J. C72 (2012) 1896, arXiv:1111.6097
  * [22] LHCb collaboration, R. Aaij et al., Study of forward $Z$+jet production in $pp$ collisions at $\sqrt{s}=7~{}T\kern-0.50003pteV$, JHEP 01 (2014) 033, arXiv:1310.8197
  * [23] Particle Data Group, K. A. Olive et al., Review of particle physics, Chin. Phys. C38 (2014) 090001
  * [24] LHCb collaboration, R. Aaij et al., First measurement of the charge asymmetry in beauty-quark pair production, Phys. Rev. Lett. 113 (2014) 082003, arXiv:1406.4789
  * [25] CMS collaboration, S. Chatrchyan et al., Identification of b-quark jets with the CMS experiment, JINST 8 (2013) P04013, arXiv:1211.4462
  * [26] LHCb collaboration, R. Aaij et al., Measurement of the $Z$+$b$-jet cross-section in $pp$ collisions at $\sqrt{s}=7~{}T\kern-0.50003pteV$ in the forward region, JHEP 01 (2015) 064, arXiv:1411.1264
  * [27] LHCb collaboration, R. Aaij et al., Study of $W$ boson production in association with beauty and charm, LHCb-PAPER-2015-021, submitted to Phys. Rev. D, arXiv:1505.04051

LHCb collaboration

R. Aaij38, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
Alvarez Cartelle53, A.A. Alves Jr57, S. Amato2, S. Amerio22, Y. Amhis7, L.
An3, L. Anderlini17,g, J. Anderson40, M. Andreotti16,f, J.E. Andrews58, R.B.
Appleby54, O. Aquines Gutierrez10, F. Archilli38, P. d’Argent11, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, C. Baesso60, W. Baldini16,38, R.J.
Barlow54, C. Barschel38, S. Barsuk7, W. Barter38, V. Batozskaya28, V.
Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1,
L.J. Bel41, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson38, J.
Benton46, A. Berezhnoy32, R. Bernet40, A. Bertolin22, M.-O. Bettler38, M. van
Beuzekom41, A. Bien11, S. Bifani45, T. Bird54, A. Birnkraut9, A. Bizzeti17,i,
T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N.
Bondar30,38, W. Bonivento15, S. Borghi54, 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, 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. 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, L. Dufour41, 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. Ferrari14, F.
Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M. Fiore16,38,f, M.
Fiorini16,f, M. Firlej27, C. Fitzpatrick39, T. Fiutowski27, K. Fohl38, P.
Fol53, M. Fontana10, F. Fontanelli19,j, R. Forty38, O. Francisco2, M. Frank38,
C. Frei38, M. Frosini17, J. Fu21, 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, D. Gerick11, E. Gersabeck11, M. Gersabeck54, T. Gershon48, Ph.
Ghez4, A. Gianelle22, S. Gianì39, V. Gibson47, O. G. Girard39, 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, 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. Linn38, F. Lionetto40, B.
Liu15, X. Liu3, S. Lohn38, I. Longstaff51, J.H. Lopes2, P. Lowdon40, 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. 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, 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, M. Merk41, D.A. Milanes62,
M.-N. Minard4, D.S. Mitzel11, J. Molina Rodriguez60, S. Monteil5, M.
Morandin22, P. Morawski27, A. Mordà6, M.J. Morello23,t, J. Moron27, A.B.
Morris50, R. Mountain59, F. Muheim50, J. Müller9, K. Müller40, V. Müller9, M.
Mussini14, B. Muster39, P. Naik46, T. Nakada39, R. Nandakumar49, I. Nasteva2,
M. Needham50, N. Neri21, S. Neubert11, N. Neufeld38, M. Neuner11, A.D.
Nguyen39, T.D. Nguyen39, C. Nguyen-Mau39,q, V. Niess5, R. Niet9, N. Nikitin32,
T. Nikodem11, D. Ninci23, A. Novoselov35, D.P. O’Hanlon48, A. Oblakowska-
Mucha27, V. Obraztsov35, S. Ogilvy51, O. Okhrimenko44, R. Oldeman15,e, C.J.G.
Onderwater67, B. Osorio Rodrigues1, J.M. Otalora Goicochea2, A. Otto38, P.
Owen53, A. Oyanguren66, A. Palano13,c, F. Palombo21,u, M. Palutan18, J.
Panman38, A. Papanestis49, M. Pappagallo51, L.L. Pappalardo16,f, C. Parkes54,
G. Passaleva17, G.D. Patel52, M. Patel53, C. Patrignani19,j, A. Pearce54,49,
A. Pellegrino41, G. Penso25,m, M. Pepe Altarelli38, S. Perazzini14,d, P.
Perret5, L. Pescatore45, K. Petridis46, A. Petrolini19,j, M. Petruzzo21, E.
Picatoste Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, A.
Piucci11, S. Playfer50, M. Plo Casasus37, T. Poikela38, F. Polci8, A.
Poluektov48,34, I. Polyakov31, E. Polycarpo2, A. Popov35, D. Popov10,38, 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, M. Santimaria18, 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, T. Schmelzer9, B. Schmidt38, O. Schneider39, A.
Schopper38, M. Schubiger39, 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, 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, L.
Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V. Syropoulos42, M.
Szczekowski28, P. Szczypka39,38, T. Szumlak27, S. T’Jampens4, T. Tekampe9, 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, A. Ukleja28, A. Ustyuzhanin65,64, 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, 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,
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

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