EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-193 LHCb-PAPER-2015-027 5 October 2015

$B$ flavour tagging using charm decays at the LHCb experiment

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

An algorithm is described for tagging the flavour content at production of
neutral $B$ mesons in the LHCb experiment. The algorithm exploits the
correlation of the flavour of a $B$ meson with the charge of a reconstructed
secondary charm hadron from the decay of the other $b$ hadron produced in the
proton-proton collision. Charm hadron candidates are identified in a number of
fully or partially reconstructed Cabibbo-favoured decay modes. The algorithm
is calibrated on the self-tagged decay modes
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ and
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ using
$3.0\mbox{\,fb}^{-1}$ of data collected by the LHCb experiment at $pp$ centre-
of-mass energies of $7\mathrm{\,Te\kern-1.00006ptV}$ and
$8\mathrm{\,Te\kern-1.00006ptV}$. Its tagging power on these samples of
$B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}X$ decays is
$(0.30\pm 0.01\pm 0.01)\%$.

Submitted to J. Instrum.

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

##  1 Introduction

Measurements that involve mixing and time-dependent $C\\!P$ asymmetries in
decays of neutral $B$ mesons require the identification of their flavour
content at production. This is achieved via various flavour tagging algorithms
that exploit information from the rest of the $pp$ collision event. Same-side
(SS) taggers look for particles produced in association with the signal $B$
meson during the hadronization of the $b$ quark [1]. The $d$ or $s$ partner of
the light valence quark of the signal $B$ has a roughly $50\%$ chance of
hadronizing into a charged pion or kaon. Since $b$ quarks are mostly produced
in $b\overline{}b$ pairs, the flavour content of the signal $B$ meson can also
be deduced from available information on the opposite-side (OS) $b$ hadron,
whose flavour is the opposite of the signal $B$ meson at the production time.
OS muon and electron taggers look for leptons originating from semileptonic
$b\rightarrow cW$ transitions of the $b$ hadron, and an OS kaon tagger looks
for kaons coming from $b\rightarrow c\rightarrow s$ transitions. A vertex-
charge tagger reconstructs the decay vertex of the OS $b$ hadron and predicts
its charge by weighting the charges of its decay products according to their
transverse momentum. The OS taggers employed by LHCb are described in Ref. [2]
and the SS taggers in Refs. [3, 4]. This paper reports a new flavour tagging
algorithm for the LHCb experiment that relies on reconstructed decays of charm
hadrons produced in the OS $b$ hadron decay. For the development and
evaluation of the tagging algorithm, signal $B$ meson and charm hadron
candidates are reconstructed using data from 3 fb-1 of integrated luminosity
collected by LHCb at $7\mathrm{\,Te\kern-1.00006ptV}$ and
$8\mathrm{\,Te\kern-1.00006ptV}$ centre-of-mass energies in 2011 and 2012,
respectively.

The performance of a flavour tagging algorithm is defined by its tagging
efficiency, $\varepsilon_{\rm tag}$, mistag fraction, $\omega$, and dilution,
$\mathcal{D}=1-2\omega$. For a simple tagging algorithm with discrete
decisions – $B^{0}$, $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$, or
untagged – these metrics are directly related to the numbers of rightly tagged
($R$), wrongly tagged ($W$), and untagged events ($U$) in a signal sample:

${\varepsilon_{\rm
tag}}=\frac{R+W}{R+W+U},\quad\omega=\frac{W}{R+W},\quad\mathcal{D}=\frac{R-W}{R+W}.$
(1)

The performance of the flavour tagging algorithms is improved by assigning
confidence weights to their tagging decisions. For each tagger, a multivariate
classifier is trained using simulated data to distinguish between correct and
incorrect decisions [2]. The inputs to the classifier are a selection of
kinematic and geometric quantities describing the tagging track(s), the signal
$B$ meson, and the event. This classifier then calculates a predicted mistag
probability $\eta$ for each decision made. The predicted mistag probability is
calibrated to data using an appropriate flavour self-tagged mode, such as
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$, or a
mode involving neutral $B$ oscillation, which self-tags its flavour at the
decay-time, such as $B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{*0}$ or $B^{0}_{s}\\!\rightarrow D^{-}_{s}\pi^{+}$ [5, 4] (the use of
charge-conjugate modes is implied throughout this paper). This calibration
procedure provides a function $\omega(\eta)$, which relates the actual mistag
probability $\omega$ to the predicted mistag probability $\eta$. Weighting
each signal candidate by $1-2\omega(\eta)$ leads to an improved effective
mistag fraction $\omega$ and associated dilution $\mathcal{D}=1-2\omega$. The
statistical power of a $C\\!P$ asymmetry measurement using a tagging algorithm
is proportional to the effective tagging efficiency (or tagging power)
$\varepsilon_{\rm eff}$, defined as

$\varepsilon_{\rm eff}={\varepsilon_{\rm tag}}\mathcal{D}^{2}.$ (2)

The typical combined tagging power of the current set of OS tagging algorithms
used by LHCb is approximately $2.5\%$ [6, 7, 3, 8]. Any augmentation to this
tagging power increases the statistical precision achievable in $C\\!P$
measurements at LHCb.

##  2 Detector and simulation

The LHCb detector [9, 10] is a single-arm forward spectrometer covering the
pseudorapidity range between $2$ and $5$, 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 [11], 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 [12] placed
downstream of the magnet. The tracking system provides a measurement of
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at
200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum distance of a track to
a primary vertex (PV), the impact parameter, is measured with a resolution of
$(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm m}$, where $p_{\rm T}$ is the component
of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons in
the momentum range $2\text{--}100\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ are
distinguished using information from two ring-imaging Cherenkov detectors
[13]. Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers
[14]. The online event selection is performed by a trigger [15], which
consists of a hardware stage, based on information from the calorimeter and
muon systems, followed by a software stage, which applies a full event
reconstruction.

In the simulation, $pp$ collisions are generated using Pythia [16, 17] with a
specific LHCb configuration [18]. Decays of hadronic particles are described
by EvtGen [19], in which final-state radiation is generated using Photos [20].
The interaction of the generated particles with the detector, and its
response, are implemented using the Geant4 toolkit [21, *Agostinelli:2002hh]
as described in Ref. [23].

##  3 Tagging potential of OS charm hadrons

In events containing a signal $B$ decay, the opposite-side $D^{+}$, $D^{0}$,
and $\mathchar 28931\relax^{+}_{c}$ charm hadrons are primarily produced
through the quark-level $b\rightarrow c$ transition. The charge of the $D^{+}$
or $\mathchar 28931\relax^{+}_{c}$ determines the flavour of the $b$ hadron
parent. For $D^{0}$ decays through the dominant Cabibbo-favoured process
$D^{0}\rightarrow K^{-}X$, the kaon charge determines the flavour of the charm
hadron, and thereby that of the parent $B$ hadron (the effect of $D^{0}$
mixing is negligible). The OS charm tagging algorithm uses charm hadron
candidates reconstructed in a number of decay modes, chosen for their
relatively large branching fractions, listed in Table 1. These include fully
reconstructed hadronic modes with a single charged kaon in the final state,
partially reconstructed hadronic modes with an unobserved neutral pion, and
partially reconstructed semileptonic modes. Table 1 also reports the breakdown
of the charm tagger’s performance by decay mode. The relative rate and
relative power of each mode are the amounts that it contributes to the
algorithm’s total tagging rate ${\varepsilon_{\rm tag}}$ and tagging power
$\varepsilon_{\rm eff}$, which are presented in Section 6 and Table 3. The
algorithm predicts the flavour of the signal $B$ meson using the charge of the
kaon in the same manner as the OS kaon tagger; however, the selection based on
the reconstruction of $c$ hadrons (rather than the selection of kaons based on
their individual kinematic properties) results in a different set of selected
kaons and provides a complementary source of tagging information.

Several effects contribute an irreducible component to the mistag probability
for the OS charm tagging algorithm. The dominant impact comes from
$B^{0}$–$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ oscillation and
from the contributions of “wrong sign” charm hadrons produced in $b\rightarrow
c\overline{}cq$ transitions. The impact of Cabibbo-suppressed
$D^{0}\rightarrow K^{+}X$ decays is negligible, as these typically produce
additional kaons and do not mimic modes used by the tagging algorithm, and
doubly Cabibbo-suppressed decays such as $D^{0}\rightarrow K^{+}\pi^{-}$ have
a negligibly small branching fraction. Accounting for relative production
rates of $b$ hadrons, neutral $B$ oscillation, and branching fractions of the
decay modes used in the tagger, the irreducible mistag probabilities for
$D^{0}$, $D^{+}$ and $\mathchar 28931\relax^{+}_{c}$ modes are estimated to be
$23\%$, $19\%$, and $6\%$, respectively.

In addition to the irreducible mistag probability arising from physics
effects, the charm hadron candidates are contaminated by combinatorial and
partially reconstructed $b$ and $c$ hadron background that can lead to an
incorrect flavour tag result. For each mode, the charm tagger uses a
multivariate algorithm that combines geometric and kinematic quantities and
properties of the $c$ hadron candidate and its daughters. The resulting
discriminating variable is used both to suppress the combinatorial background
and to predict the corresponding mistag probability for the surviving
candidate.

##  4 Selection of charm candidates

Charm decay candidates are formed by combining kaon, pion, and proton
candidates that satisfy particle identification criteria. These particles are
required to have momentum $p>1000{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$,
transverse momentum with respect to the beam axis
$p_{\mathrm{T}}>100{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, and to be
significantly displaced from any PV. For the candidates in the partially
reconstructed modes and the decay $D^{0}\rightarrow
K^{-}\pi^{+}\pi^{+}\pi^{-}$, which contain large combinatorial backgrounds,
more stringent requirements are imposed on the displacement of the final-state
particles from the PV. In addition, particles are required to have
$p_{\mathrm{T}}>150{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ for candidates in the
mode $D^{0}\rightarrow K^{-}\pi^{+}\pi^{+}\pi^{-}$.

Table 1: Decay modes used in the OS charm tagger. The symbol $H_{c}$ stands for any $c$ hadron. The definition of the two right-most columns is given in the text. Decay mode | Relative rate | Relative power
---|---|---
$D^{0}\rightarrow K^{-}\pi^{+}$ | 10.0% | 24.0%
$D^{0}\rightarrow K^{-}\pi^{+}\pi^{+}\pi^{-}$ | 5.9% | 8.4%
$D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ | 10.3% | 2.6%
$H_{c}\rightarrow K^{-}\pi^{+}X$ | 69.7% | 61.5%
$H_{c}\rightarrow K^{-}e^{+}X$ | 0.5% | 0.2%
$H_{c}\rightarrow K^{-}\mu^{+}X$ | 3.4% | 0.3%
$\mathchar 28931\relax^{+}_{c}\rightarrow p^{+}K^{-}\pi^{+}$ | 0.2% | 2.4%

Charm hadron candidates are required to pass a number of selection
requirements. These include a maximum distance of closest approach between
each pair of daughter tracks and a minimum quality of the decay vertex fit.
Each candidate is required to be well separated from any PV and to have a
trajectory that leads back to the best PV, chosen to be the PV for which the
impact parameter significance of the charm hadron is smallest. The invariant
mass of the charm hadron candidate is required to be consistent with the known
mass of the corresponding charm hadron, within
$100{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for the $\mathchar
28931\relax^{+}_{c}$ channel and $50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
for all other fully reconstructed $D$ decay modes. For the partially
reconstructed $D\rightarrow K^{-}\pi^{+}X$ modes, the $K^{-}\pi^{+}$ mass is
required to be in a
$\left[-400{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},+0{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}\right]$
window around the known $D^{0}$ mass or in a window of $\pm
50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the $K^{*}(892)^{0}$
resonance. The former is favoured by the invariant mass distribution of
$K^{-}\pi^{+}$ pairs from the quasi-two body decay $D^{0}\rightarrow
K^{-}\rho^{+}$, and the latter selects $D\rightarrow K^{*}(892)^{0}X$ decays.
Charm candidates surviving these criteria still contain significant background
contamination, which must be further reduced in order to lower the mistag
probability of the algorithm.

For each mode, an adaptive-boosted decision tree (BDT) [24, 25] is used both
to suppress background candidates and to estimate mistag probabilities. The
inputs to the BDT are variables describing the decay kinematics, decay vertex
and displacement, and particle identification information on the decay
products. A variable related to the decay-time is calculated from the distance
between the $c$ hadron’s decay vertex and the corresponding best PV; this
approximates the sum of the decay-times of the $c$ hadron and its parent $b$
hadron. The BDT algorithms are trained using Monte Carlo (MC) simulations of
$b\overline{}b$ events containing
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$,
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$, and
$B^{0}_{s}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$
decays on the signal side and inclusive decays of the $b$ hadron on the
opposite-side. These $B$ decays are used to model the various sources and
amounts of background when reconstructing OS $c$ hadrons recoiling against
signal $B$ decays.

The output of the BDT, along with the simulation record of candidate
identification, is used to compute the predicted mistag probability $\eta$ for
each $c$ hadron candidate. Candidates with $\eta<45\%$ are used in the flavour
tagging decision. Removing candidates that fail this criterion significantly
reduces the computing time of the algorithm at little cost to tagging
performance. In cases where multiple charm candidates are present, the
candidate with the lowest predicted mistag probability is retained. The
combined efficiency of these requirements for retaining tagged events is
$(59.00\pm 0.07)\%$ and $(53.4\pm 0.3)\%$ in simulation and data,
respectively.

##  5 Calibration

While simulated data are used to develop and optimize the charm tagging
algorithm, its performance is calibrated with collision data by comparing the
algorithm’s predictions to the known flavours of signal $B$ candidates,
according to the procedure detailed in Ref. [2]. The calibration parameters
$p_{0}$, $p_{1}$, $\Delta p_{0}$, and $\Delta p_{1}$ are defined by

$\displaystyle\omega$
$\displaystyle=p_{0}+p_{1}\left(\eta-\langle\eta\rangle\right)$
$\displaystyle\Delta\omega$ $\displaystyle=\Delta p_{0}+\Delta
p_{1}\left(\eta-\langle\eta\rangle\right)$

where $\langle\eta\rangle$ is the average predicted mistag probability,
$\omega$ is the actual mistag probability averaged over $B^{+}$ and $B^{-}$
signal mesons, and $\Delta\omega$ is the excess mistag probability for $B^{+}$
mesons with respect to $B^{-}$ mesons; equivalent definitions hold for
$B^{0}$/$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ signal. In the
ideal case, the offset parameter $p_{0}$ should equal $\langle\eta\rangle$,
and so the related parameter $\delta p_{0}=p_{0}-\langle\eta\rangle$ is often
more convenient.

A calibration of the algorithm has been performed using the flavour self-
tagged mode $B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$. The signal candidates are selected by combining pairs of
oppositely charged muons, with invariant mass consistent with the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass, with charged kaons, and
are required to pass a set of cuts to obtain a good signal to background ratio
[2]. When multiple candidates are present for a single event, that with the
best decay vertex fit is kept. A fit to the reconstructed $B^{+}$ mass
distribution is used to separate signal and background via the sPlot
procedure, which computes signal and background weights for each candidate
[26]. The empirical model for the signal is a sum of two Crystal Ball
functions [27], while background is modeled by an exponential distribution. A
total of $1.1\times 10^{6}$ signal candidates in this channel are found in the
full dataset. The parameters $p_{0}$ and $p_{1}$ are determined by splitting
the data into 13 bins of $\eta$ between 0.19 and 0.45, calculating
$\omega_{i}$ and $\bar{\eta}_{i}$ (the average $\eta$) in each bin, and
performing a linear fit to the set of values $(\omega_{i},\bar{\eta}_{i})$.
The calibration parameters $\Delta p_{0}$ and $\Delta p_{1}$ are obtained from
fits to the $B^{+}$ and $B^{-}$ data each split into 5 bins of $\eta$. The
quantities $\Delta\omega_{i}$ and $\bar{\eta}_{i}$ are calculated in each of
the 5 bins, and a linear fit is performed to the set of values
$(\Delta\omega_{i},\bar{\eta}_{i})$. These fits are shown in Figs. 1 and 2.
The resulting calibration parameters are given in Table 2.

Figure 1: Mistag probability $\omega$ as a function of the predicted mistag probability $\eta$ for the $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ data sample. A straight line fit to extract the parameters $p_{0}$ and $p_{1}$ is superimposed. The dark (green) and light (yellow) bands are the regions within $1\sigma$ and $2\sigma$ of the fitted value, respectively. Figure 2: Excess mistag probability $\Delta\omega$ as a function of the predicted mistag probability $\eta$ for the $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ data sample. A straight line fit to extract the parameters $\Delta p_{0}$ and $\Delta p_{1}$ is superimposed. The dark (green) and light (yellow) bands are the regions within $1\sigma$ and $2\sigma$ of the fitted value, respectively. Table 2: Calibration parameters as determined from the $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ and $B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ control samples. For both calibration modes, the average predicted mistag probability $\langle\eta\rangle$ is $0.379$. The first uncertainties are statistical and the second are systematic. The systematic uncertainties are evaluated using simulation. Sample |  $\phantom{-}\delta p_{0}$ ($10^{-3}$) | $p_{1}$ |  $\Delta p_{0}$ ($10^{-3}$) | $\Delta p_{1}$
---|---|---|---|---
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ | $-25\pm 3\pm 3$ | $1.00\pm 0.06\pm 0.02$ | $15\pm 5\pm 4$ | $-0.08\pm 0.12\pm 0.04$
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ | $-18\pm 8\pm 3$ | $1.16\pm 0.17\pm 0.02$ | $23\pm 11\pm 4$ | $\phantom{-}0.21\pm 0.25\pm 0.04$

A cross-check of the calibration has been carried out using a
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$
control sample. For this calibration, $B^{0}$–$\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ oscillation must be taken into
account. The Hypatia function [28] is used to model the signal’s mass
distribution, while the background is modeled with a sum of two exponential
functions. A set of simultaneous fits to the $B^{0}$ lifetime distribution in
bins of $\eta$ is performed, in which $p_{0}$, $p_{1}$, $\Delta p_{0}$, and
$\Delta p_{1}$ are parameters of the fit model. In each bin, the raw
$B^{0}$–$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ mixing asymmetry is
defined as

$\mathcal{A}_{\text{mixing}}=\frac{\mathcal{N}(\mathcal{D}=\mathcal{P})-\mathcal{N}(\mathcal{D}\neq\mathcal{P})}{\mathcal{N}(\mathcal{D}=\mathcal{P})+\mathcal{N}(\mathcal{D}\neq\mathcal{P})},$
(3)

where $\mathcal{D}$ is the $B$ meson flavour at decay-time and $\mathcal{P}$
is the production flavour predicted by the charm tagger. The amplitude of this
asymmetry is governed by the actual mistag fraction $\omega_{i}$ in the bin,
while the bin’s average predicted mistag probability is $\bar{\eta}_{i}$. The
fit attempts to match the calibrated value $\omega(\bar{\eta}_{i})$ to
$\omega_{i}$ in each bin by adjusting the calibration parameters. A projection
of the fitted model to the mixing asymmetry is shown in Fig. 3. The values of
the calibration parameters obtained from the fit are given in Table 2. The
parameters are compatible with those obtained in the
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ mode,
with the total $\chi^{2}$ per degree of freedom equal to $0.65$.

Figure 3: Raw $B^{0}$–$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$
mixing asymmetry (defined in Eq. 3) vs. decay-time for the
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ data
sample. The amplitude of the asymmetry is diluted due to mistagging by the
charm tagger. The mixing asymmetry from the fit is superimposed.

The relatively small yield of the decay $B^{0}_{s}\\!\rightarrow
D^{-}_{s}\pi^{+}$ precludes performing a data-driven calibration on a
$B^{0}_{s}$ mode. Therefore, in order to ensure that the algorithm performs
similarly for $B^{0}_{s}$ channels as well as $B^{+}$ and $B^{0}$ channels,
separate calibrations to simulated
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$,
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$, and
$B^{0}_{s}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$
events are performed. Where statistically significant differences between the
calibration parameters in the three channels are found, a systematic
uncertainty, corresponding to half of the maximum difference, is assigned to
the parameter. These systematic uncertainties are roughly the size of the
statistical uncertainties for the parameters $p_{0}$ and $\Delta p_{0}$, but
are negligible for $p_{1}$ and $\Delta p_{1}$. The propagation of these
uncertainties results in a $0.011\%$ absolute systematic uncertainty on the
tagging power, comparable to its statistical uncertainty.

Other sources of systematic uncertainty on calibration parameters have been
investigated and found to have negligible effect. These include the potential
effect of the chosen model of the invariant $B$ mass distribution for the
channel $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$. Two alternative models of the mass distribution were used and
gave nearly identical results.

There are additional systematic uncertainties related to flavour tagging that
must be considered in a $C\\!P$ asymmetry analysis. These include differences
between the signal channel sample and calibration channel sample in phase
space distribution, event multiplicity, number of primary vertices, or other
variables. These differences would require corrections and would introduce
tagging-related systematic uncertainties. Such effects are dependent on the
signal channel and selection, and must be determined separately for each
analysis.

##  6 Performance

The distribution of $\eta$ after calibration for the
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ control
sample is shown in Fig. 4. The tagging efficiency, mistag fraction, and the
tagging power of the charm tagger are reported in Table 3 for the training
sample of simulated $B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}X$ decays and for both calibration channels. The propagated statistical
uncertainty of the calibration parameters dominates the statistical
uncertainty of the tagging power. The overall tagging power is slightly higher
in simulation than in data, due to differences in the distributions of input
variables. The tagging powers in the two
$B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}X$ calibration
channels are consistent.

Figure 4: Distribution of the calibrated predicted mistag probability $\omega(\eta)$ for the $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ data sample. Table 3: Tagging efficiencies (${\varepsilon_{\rm tag}}$), effective mistag fractions ($\omega$), and tagging powers ($\varepsilon_{\rm eff}$) in the various data samples studied. The first uncertainties are statistical and the second are systematic. The sample labeled Simulation is the training sample of simulated $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$, $B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$, and $B^{0}_{s}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$ decays, which has negligible statistical uncertainties. Sample | ${\varepsilon_{\rm tag}}$ | $\omega$ | $\varepsilon_{\rm eff}$
---|---|---|---
Simulation | $4.88\%$ | $37.0\%$ | $0.33\%$
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ | $(3.11\pm 0.02)\%$ | $(34.6\pm 0.3\pm 0.3)\%$ | $(0.30\pm 0.01\pm 0.01)\%$
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ | $(3.32\pm 0.04)\%$ | $(35.0\pm 0.8\pm 0.3)\%$ | $(0.30\pm 0.03\pm 0.01)\%$
$B^{0}\\!\rightarrow D^{-}\pi^{+}$ | $(4.11\pm 0.03)\%$ | $(34.4\pm 0.4\pm 0.3)\%$ | $(0.40\pm 0.02\pm 0.01)\%$
$B^{0}_{s}\\!\rightarrow D^{-}_{s}\pi^{+}$ | $(3.99\pm 0.07)\%$ | $(34.4\pm 0.6\pm 0.3)\%$ | $(0.39\pm 0.03\pm 0.01)\%$

Table 3 also reports the tagging metrics for the decays $B^{0}\\!\rightarrow
D^{-}\pi^{+}$ and $B^{0}_{s}\\!\rightarrow D^{-}_{s}\pi^{+}$. Fits to the mass
distributions of the signal candidates are performed to separate signal from
background. In each fit, the signal is modeled by a sum of two Crystal Ball
functions and the combinatorial background is described by an exponential
function. Several fully and partially reconstructed backgrounds are also
modeled in the fit to the $B^{0}_{s}\\!\rightarrow D^{-}_{s}\pi^{+}$ sample.
The tagging efficiency for these samples is found to be higher than for the
samples of $B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}X$ decays,
due to correlations between the kinematics of the signal $B$ and the opposite-
side charm hadrons. The effective mistag fraction for these samples is
consistent with that on the $B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}X$ samples. The net effect is an increased tagging power for these
$B\rightarrow DX$ decays, similar to that observed for other opposite-side
tagging algorithms [7, 29].

To use the charm tagger in a physics analysis, the flavour tagging information
from the charm tagger can be combined with information from other tagging
algorithms. Assessing the actual gain in performance depends on the method of
combination and calibration, as well as on the set of tagging algorithms being
combined. Due to correlations with other tagging algorithms, in particular the
OS kaon and vertex-charge taggers, the maximum possible increase in tagging
power after the addition of the charm tagging algorithm is less than its
individual tagging power. The performance of the combination of the current OS
tagging algorithms with and without the addition of the charm tagger has been
measured on the $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$ data sample. The absolute net gain in tagging power using the
current combination algorithm is found to be around $0.11\%$, compared to the
current total OS tagging power of about $2.5\%$ [6, 7, 3, 8].

##  7 Conclusion

An algorithm has been developed that determines the flavour of a signal $b$
hadron at production time by reconstructing opposite-side charm hadrons from a
number of decay channels. The flavour tagger uses boosted decision tree
algorithms trained on simulated data, and has been calibrated and evaluated on
data using the self-tagged decay
$B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$. Its
tagging power for data in this channel is found to be $(0.30\pm
0.01\text{$\mathrm{\,(stat)}$}\pm 0.01\text{$\mathrm{\,(syst)}$})\%$. The
calibration has been cross-checked using the decay
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$,
giving consistent results. The tagging power is found to be higher for the
decays $B^{0}\\!\rightarrow D^{-}\pi^{+}$ and $B^{0}_{s}\\!\rightarrow
D^{-}_{s}\pi^{+}$, at $(0.40\pm 0.02\text{$\mathrm{\,(stat)}$}\pm
0.01\text{$\mathrm{\,(syst)}$})\%$ and $(0.39\pm
0.03\text{$\mathrm{\,(stat)}$}\pm 0.01\text{$\mathrm{\,(syst)}$})\%$,
respectively.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); INFN (Italy);
FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). The Tier1 computing centres are
supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted
to the communities behind the multiple open source software packages on which
we depend. We are also thankful for the computing resources and the access to
software R&D tools provided by Yandex LLC (Russia). Individual groups or
members have received support from EPLANET, Marie Skłodowska-Curie Actions and
ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and
OCEVU, Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain),
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

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K. Wyllie38, Y. Xie61, Z. Xu39, Z. Yang3, J. Yu61, X. Yuan34, O. Yushchenko35,
M. Zangoli14, M. Zavertyaev10,b, L. Zhang3, Y. Zhang3, A. Zhelezov11, A.
Zhokhov31, L. Zhong3, S. Zucchelli14.

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 Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
oLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
pHanoi University of Science, Hanoi, Viet Nam
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy
tUniversità degli Studi di Milano, Milano, Italy
†Deceased