EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-173 LHCb-PAPER-2016-020

Measurement of the ratio of branching fractions
${\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})/{\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$

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

The ratio of branching fractions
${R}_{K/\pi}\equiv{\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})/{\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$ is measured with $pp$ collision data collected by the
LHCb experiment at centre-of-mass energies of $7\mathrm{\,Te\kern-1.00006ptV}$
and $8\mathrm{\,Te\kern-1.00006ptV}$, corresponding to an integrated
luminosity of 3$\mbox{\,fb}^{-1}$. It is found to be ${R}_{K/\pi}=0.079\pm
0.007\pm 0.003$, where the first uncertainty is statistical and the second is
systematic. This measurement is consistent with the previous LHCb result,
while the uncertainties are significantly reduced.

Published in JHEP 09(2016)153

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

##  1 Introduction

The ${B}_{c}^{+}$ meson, the lightest $\bar{b}c$ bound state, can only decay
weakly. Since it contains only heavy quarks, its decays can be analysed using
various theoretical approaches, including QCD-based methods [1, 2, 3] and QCD-
inspired phenomenological models [4, 5]. A measurement of the weak decay
properties of ${{B}_{c}^{+}}$ mesons can test these approaches and provide
insight into the dynamics of the heavy quarks in the ${{B}_{c}^{+}}$ meson.

The exclusive decay111The inclusion of charge-conjugate processes is implied
throughout the paper.
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ is of particular interest since it proceeds via a
${\overline{b}}\rightarrow{\overline{c}}{u}{\overline{s}}$ transition and thus
is CKM-suppressed by a factor $|V_{us}/V_{ud}|^{2}\sim 0.05$ with respect to
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$, where the dominant amplitude is a
${\overline{b}}\rightarrow{\overline{c}}{u}{\overline{d}}$ transition. In
addition to the CKM matrix elements, the ratio of branching fractions
${R}_{K/\pi}\equiv{\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})/{\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$ depends on the form factors of the two decays.
Theoretical calculations of ${R}_{K/\pi}$ have been carried out using
approaches that handle the non-factorisable and non-perturbative contributions
in different ways, yielding values in the range from $0.05$ to $0.10$ [6, 7,
8, 9, 10, 1, 11, 12, 13, 5, 14, 15].

The decay ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ was first observed by the LHCb collaboration, which reported
a measurement of ${R}_{K/\pi}=0.069\pm 0.019\pm 0.005$ [16]. The uncertainty
on this value is too large to discriminate between the predictions quoted
above. The $pp$ data sample used in Ref. [16], taken at a centre-of-mass
energy of $7\mathrm{\,Te\kern-1.00006ptV}$ and corresponding to an integrated
luminosity of $1\mbox{\,fb}^{-1}$, is now reanalysed in this paper together
with an additional sample taken at a centre-of-mass energy of
$8\mathrm{\,Te\kern-1.00006ptV}$ and corresponding to an integrated luminosity
of $2\mbox{\,fb}^{-1}$. Owing to improvements in the analysis method as well
as the increase in the data sample size, the statistical uncertainty is
reduced by a factor of more than two. The systematic uncertainty is also
reduced.

##  2 Detector and simulation

The LHCb detector [17, 18] 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, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of charged particle
momentum, $p$, 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_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
(in GeV/$c$) is the component of the momentum transverse to the beam
direction. Different types of charged hadrons are distinguished using
information from two ring-imaging Cherenkov (RICH) 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. Muons are identified by a system composed of
alternating layers of iron and multiwire proportional chambers.

The trigger comprises a hardware stage and a software stage. The hardware
trigger employed in this analysis uses information from the muon system to
select single muons or muon pairs, applying $p_{\mathrm{T}}$ requirements. The
subsequent software trigger is composed of two stages, the first of which
performs a partial reconstruction and requires either a pair of well-
reconstructed, oppositely charged muons having an invariant mass above
$2.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, or a single well-reconstructed
muon. The second stage of the software trigger applies a full event
reconstruction, and requires at least one of the following two conditions to
be fulfilled: either two opposite-sign muons must form a good-quality vertex
that is well separated from all of the primary vertices and must have an
invariant mass within $120{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the
known ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass [19], or an
algorithm using a boosted decision tree must identify a two- or three-track
vertex that is well separated from all of the primary vertices and includes a
muon among the constituent tracks. The same trigger requirements are used to
select both ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ decays, due to the similarity in their kinematic
distributions.

In the simulation, $pp$ collisions are generated using Pythia 6 [20] with a
specific LHCb configuration [21], or, for the hard process
$gg\rightarrow{{B}_{c}^{+}}+b+{\overline{c}}$ that is the dominant source of
${{B}_{c}^{+}}$ mesons, using the dedicated generator Bcvegpy [22, 23]. Decays
of hadronic particles are described by EvtGen [24], in which final-state
radiation is generated using Photos [25]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [26, *Agostinelli:2002hh] as described in Ref. [28].

##  3 Event selection

Candidate ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\,h^{+}$ decays, with ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$ and $h^{+}$ being a $K^{+}$ or $\pi^{+}$,
are reconstructed as follows. First a loose preselection is applied. Pairs of
oppositely charged, well-reconstructed muon tracks with
$\mbox{$p_{\mathrm{T}}$}>550{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ consistent
with originating from a common vertex are combined to form
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$
candidates. Hadron ($h^{+}$) candidates are selected from well-reconstructed
tracks with $\mbox{$p_{\mathrm{T}}$}>500{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$,
inconsistent with originating from any PV and with the muon hypothesis.
Candidate ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ decays are formed from
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}h^{+}$ combinations that
originate from a common vertex. They must also be within
$500{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${{B}_{c}^{+}}$
mass [19]. The impact parameter $\chi^{2}$, $\chi^{2}_{\rm IP}$, which is
defined as the difference in the vertex fit $\chi^{2}$ of the PV with and
without the particle under consideration, is required to be less than 16 for
the ${{B}_{c}^{+}}$ candidates.

A multivariate classifier using a boosted decision tree (BDT) [29] is
constructed to further suppress the combinatorial background. The kinematic
variables used as inputs to the BDT are chosen to discriminate between signal
and background. The twelve variables chosen are: the $\chi^{2}_{\rm IP}$ of
the ${B}_{c}^{+}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$, $\mu^{+}$,
$\mu^{-}$ and $h^{+}$ candidates; the $p_{\mathrm{T}}$ of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$, $\mu^{+}$, $\mu^{-}$ and
$h^{+}$ candidates; the $\chi^{2}$ per degree of freedom of the
${{B}_{c}^{+}}$ vertex fit; and the decay time and the decay length of the
${{B}_{c}^{+}}$ candidate. Since the kaon-pion mass difference is small
compared with the energy release of
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}h^{+}$
decays, the distributions of the BDT variables are similar for
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$
and ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}$ decays. The BDT is trained with simulated
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}$ decays to represent both the
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$
and the ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}$ signals, and with events from the upper mass sideband of the
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ candidates in data,
$[6444,~{}6528]{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, to represent the
combinatorial background. For one third of the events in the training samples
the centre-of-mass energy is $7\mathrm{\,Te\kern-1.00006ptV}$, and for the
rest it is $8\mathrm{\,Te\kern-1.00006ptV}$ in accordance with the ratio of
integrated luminosities. Since the BDT does not use any particle
identification information, it selects both
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ candidates. Particle identification requirements using
information from the RICH subdetectors are then applied to the hadrons to
obtain two mutually exclusive samples of
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ candidates.

The BDT and particle identification requirements are optimised sequentially on
the sample of ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ candidates that pass the loose preselection to maximise
$N_{K}/\sqrt{N_{\rm tot}}$, where $N_{\rm tot}$ is the total number of
candidates within $\pm 3$ times the mass resolution around the known
${{B}_{c}^{+}}$ mass. Here $N_{K}$ refers to the
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ signal yield and is estimated to be $(N_{\rm tot}-N_{\rm
comb})/(1+1/(r_{\rm eff}{R}_{K/\pi}))$, where the value of ${R}_{K/\pi}$ is
taken from the previous LHCb measurement [16], $N_{\rm comb}$ is the number of
combinatorial background events in the signal region extrapolated from the
upper sideband, and $r_{\rm eff}$ represents the ratio of the numbers of
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}$ events that pass the
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ selection and fall in the signal window. After this
optimisation, the BDT rejects more than $99.8\%$ of the combinatorial
background and keeps around $70\%$ of
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}h^{+}$
events. This particle identification requirement has an efficiency of about
$70\%$ for ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and $87\%$ for
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$, while the probabilities for a charged kaon to be
misidentified as a pion and a charged pion to be misidentified as a kaon are
below $7\%$ and $1\%$, respectively.

##  4 Signal yields and efficiency correction

The measurement is made by evaluating

${R}_{K/\pi}\equiv\frac{{\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})}{{\mathcal{B}}({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})}=\frac{N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})}{N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})}\times\frac{\epsilon({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})}{\epsilon({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})},$ (1)

where $N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})$ and
$N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$ are the signal yields, and
$\epsilon({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})$ and
$\epsilon({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$ are the total efficiencies estimated with simulation and
control samples of data.

The signal yields
$N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})$ and
$N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$ are obtained from a simultaneous unbinned maximum
likelihood fit to the distribution of ${B}_{c}^{+}$ candidate masses in the
range 6000 to 6600 ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. These
candidates include the part of the background training sample that passes the
full selection; the effect of doing so has been investigated and found not to
lead to any systematic bias. The fit model includes components due to signal,
combinatorial background and misidentified decays
(${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ misidentified as
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$, or vice versa).

A partially reconstructed background component is included for
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$. This background is mainly due to
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{+}$ decays followed by
$\rho^{+}\rightarrow{{\pi}^{+}}{{\pi}^{0}}$. The data show no clear indication
of partially reconstructed background for
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$. A systematic uncertainty is assigned due to the non-
inclusion of this background component.

The signal mass distribution of
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\,h^{+}$ is described by the sum of two double-sided Crystal Ball
($F^{\rm DSCB}$) functions consisting of a Gaussian core and power law tails
on both sides,

$\displaystyle f_{\rm sig}(M_{{{B}_{c}^{+}}})=\alpha F^{\rm
DSCB}_{1}(M_{{{B}_{c}^{+}}})+(1-\alpha)F^{\rm DSCB}_{2}(M_{{{B}_{c}^{+}}}),$
(2)

where $M_{{{B}_{c}^{+}}}$ is the invariant mass of the
${\mu^{+}\mu^{-}}\,h^{+}$ combination with the mass of the ${\mu^{+}\mu^{-}}$
pair constrained to the known ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$
mass. In the simultaneous fit, the Gaussian mean and the core mass resolution
$\sigma_{1}$ of $F^{\rm DSCB}_{1}$ are allowed to vary, and set to be the same
for both the ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ and the
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ decays. The tail parameters, the fraction $\alpha$ and the
ratio $\sigma_{2}/\sigma_{1}$ of the core-mass resolutions of $F^{\rm
DSCB}_{1}$ and $F^{\rm DSCB}_{2}$ are fixed to the values obtained in
simulation.

The combinatorial background for each decay mode is modelled by an exponential
distribution. Background arising from misidentified ${{B}_{c}^{+}}\rightarrow
J/\psi h^{+}$ decays is described by a DSCB function, with shape and mass
offset relative to the signal peak derived from simulation for each mode
separately. The invariant mass distribution of the partially reconstructed
background is taken to be an ARGUS function[30] convolved with a Gaussian
resolution function. The mean and the width parameters of the resolution
function are set to be zero and
$\sqrt{\alpha\sigma_{1}^{2}+(1-\alpha)\sigma_{2}^{2}}$.

The parameters estimated from the simultaneous fit are: the yield
$N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$, the yield ratio
$N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})/N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$, the numbers of combinatorial background events for
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ decays, the number of misidentification background events
for each of the decay modes, the number of partially reconstructed background
events for the ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ decay, and the shape parameters describing the signal and
background distributions.

The results of the separate fits to the 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$
samples are shown in Fig. 1. In the 7$\mathrm{\,Te\kern-1.00006ptV}$ sample,
the yield $N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$ is found to be $954\pm 36$ and the yield ratio
$N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})/N({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})$ is found to be $0.069\pm 0.010$. The corresponding values
in the 8$\mathrm{\,Te\kern-1.00006ptV}$ sample are $2253\pm 53$ and $0.059\pm
0.006$.

The ratio of branching fractions ${R}_{K/\pi}$ is obtained by correcting the
yield ratio with the relative efficiency, as shown in Eq. 1. The total
efficiencies include contributions from the LHCb detector acceptance and from
selection, trigger and particle identification requirements. The selection and
trigger efficiencies are calculated from simulated samples. The simulated
events are weighted to account for differences from data in the track
multiplicity distribution. It has been checked that after this weighting, the
distributions of the variables used as inputs to the BDT are similar in data
and simulation. The particle identification efficiencies for hadrons are
evaluated from simulation calibrated with a control sample of
$D^{*+}\rightarrow{{D}^{0}}{{\pi}^{+}}$,
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays. The efficiency ratio is
determined to be
$\epsilon({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}})/\epsilon({{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})=1.277\pm 0.007$ and $1.284\pm 0.006$ for
$7\mathrm{\,Te\kern-1.00006ptV}$ and $8\mathrm{\,Te\kern-1.00006ptV}$ data,
respectively. The efficiency difference between
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ mainly arises from particle identification for the hadrons.

Figure 1:  Fits to the reconstructed
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ (left) and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ (right) mass distributions using 7 TeV (top) and 8 TeV
(bottom) data samples. The contributions from the signal, the
misidentification background, the combinatorial background and the partially
reconstructed background are indicated in the figures.

##  5 Systematic uncertainties

Since the running conditions changed between $7\mathrm{\,Te\kern-1.00006ptV}$
and $8\mathrm{\,Te\kern-1.00006ptV}$, the systematic uncertainties on
${R}_{K/\pi}$ are determined separately for the two samples. Table 1
summarises the relative systematic uncertainties associated with the mass fit
and efficiency estimates that affect the ratio of branching fractions. The
sources of these uncertainties are discussed below.

Each of the systematic uncertainties associated with the mass fit is studied
by generating an ensemble of pseudoexperiments according to the nominal model
described above and fitting them with an alternative model. The difference in
the mean values of ${R}_{K/\pi}$ obtained is taken as the systematic
uncertainty.

Changing the signal model from the sum of two DSCB functions to a single DSCB
function leads to relative systematic uncertainties of $0.5\%$ and $0.8\%$ for
the 7$\mathrm{\,Te\kern-1.00006ptV}$ and 8$\mathrm{\,Te\kern-1.00006ptV}$
data, respectively. Using a third-order polynomial in place of an exponential
function for the combinatorial background changes the mean values of
${R}_{K/\pi}$ by $1.1\%$ and $0.5\%$ for the two samples.

In the nominal fit, the partially reconstructed background is neglected for
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ decays for reasons of fit stability. The associated
systematic uncertainties are estimated by including such a component in the
same way as was done for
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ decays, and are found to be $3.3\%$ and $3.2\%$ for the 7
and $8\mathrm{\,Te\kern-1.00006ptV}$ data, respectively. Using the sum of two
DSCB functions instead of a single DSCB function for the misidentification
background events changes the mean values of ${R}_{K/\pi}$ by $0.2\%$ and
$0.0\%$ for the two samples.

The selection and trigger efficiencies are calculated with simulated samples.
Systematic effects on the efficiency evaluation due to differences between
data and simulation in the distributions of variables such as muon momentum
and ${B}_{c}^{+}$ decay time are investigated. Such effects are found to
cancel in the efficiency ratio and thus have negligible impact on
${R}_{K/\pi}$.

The kaon and pion identification efficiencies are measured as functions of
momentum and pseudorapidity with a control sample of
$D^{*+}\rightarrow{{D}^{0}}{{\pi}^{+}}$,
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays, and represented by two-
dimensional histograms. When the histogram binning is varied, the largest
changes in the efficiency ratio seen are $0.2\%$ and $0.1\%$ for the
$7\mathrm{\,Te\kern-1.00006ptV}$ and 8$\mathrm{\,Te\kern-1.00006ptV}$ samples,
and these values are assigned as the corresponding relative systematic
uncertainties.

The simulation accounts for the different interaction cross-sections of pions
and kaons with matter. However, if the amount of material in the detector is
not modelled correctly, this would alter the efficiency ratio. A systematic
uncertainty of $0.3\%$ associated with this effect is assigned for both
$7\mathrm{\,Te\kern-1.00006ptV}$ and $8\mathrm{\,Te\kern-1.00006ptV}$ samples.
Adding all of the above contributions in quadrature, the total relative
systematic uncertainties on ${R}_{K/\pi}$ are $3.5\%$ and $3.4\%$ for the
$7\mathrm{\,Te\kern-1.00006ptV}$ and $8\mathrm{\,Te\kern-1.00006ptV}$ results.

Table 1: Summary of the relative systematic uncertainties on ${R}_{K/\pi}$. | $7\mathrm{\,Te\kern-1.00006ptV}$ | $8\mathrm{\,Te\kern-1.00006ptV}$
---|---|---
Signal model | $0.5\%$ | $0.8\%$
Combinatorial background | $1.1\%$ | $0.5\%$
Partially reconstructed background | $3.3\%$ | $3.2\%$
Misidentification background | $0.2\%$ | $0.0\%$
Particle identification efficiency | $0.2\%$ | $0.1\%$
Detector material | $0.3\%$ | $0.3\%$
Total | $3.5\%$ | $3.4\%$

##  6 Results and summary

Using the yield and efficiency ratios, the ratio of branching fractions of
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}$ is evaluated as

${R}_{K/\pi}=0.089\pm 0.013\pm 0.003$

for the 7$\mathrm{\,Te\kern-1.00006ptV}$ data sample and

${R}_{K/\pi}=0.075\pm 0.008\pm 0.003$

for the 8$\mathrm{\,Te\kern-1.00006ptV}$ sample, where the first uncertainties
are statistical and the second are systematic.

The two results are combined by evaluating their weighted average. The
systematic uncertainties of both measurements are dominated by the
contribution from the non-inclusion of the partially reconstructed background
for ${{B}_{c}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ decays, and so are assumed to be fully correlated, while
their statistical uncertainties are independent. The combined measurement for
the $7\mathrm{\,Te\kern-1.00006ptV}$ and $8\mathrm{\,Te\kern-1.00006ptV}$ data
sample is

${R}_{K/\pi}=0.079\pm 0.007\pm 0.003\,.$

This is consistent with the previous LHCb measurement ${R}_{K/\pi}=0.069\pm
0.019\pm 0.005$ [16], which was based on the 7$\mathrm{\,Te\kern-1.00006ptV}$
data alone. The uncertainties are significantly reduced due to both the
increased sample size and the improved event selection. The result supersedes
the previous measurement [16] and agrees with the theoretical predictions in
Refs. [1, 6, 7, 10, 12, 13, 5, 14, 15], but disfavours that based on QCD sum
rules [11].

## Acknowledgements

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

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Vazquez Regueiro38, S. Vecchi17, M. van Veghel42, J.J. Velthuis47, M.
Veltri18,r, G. Veneziano40, A. Venkateswaran60, M. Vernet5, M. Vesterinen12,
B. Viaud7, D. Vieira1, M. Vieites Diaz38, X. Vilasis-Cardona37,m, V. Volkov33,
A. Vollhardt41, B. Voneki39, D. Voong47, A. Vorobyev31, V. Vorobyev35, C.
Voß65, J.A. de Vries42, C. Vázquez Sierra38, R. Waldi65, C. Wallace49, R.
Wallace13, J. Walsh24, J. Wang60, D.R. Ward48, H.M. Wark53, N.K. Watson46, D.
Websdale54, A. Weiden41, M. Whitehead39, J. Wicht49, G. Wilkinson56,39, M.
Wilkinson60, M. Williams39, M.P. Williams46, M. Williams57, T. Williams46,
F.F. Wilson50, J. Wimberley59, J. Wishahi10, W. Wislicki29, M. Witek27, G.
Wormser7, S.A. Wotton48, K. Wraight52, S. Wright48, K. Wyllie39, Y. Xie63, Z.
Xing60, Z. Xu40, Z. Yang3, H. Yin63, J. Yu63, X. Yuan35, O. Yushchenko36, M.
Zangoli15, K.A. Zarebski46, M. Zavertyaev11,c, L. Zhang3, Y. Zhang7, Y.
Zhang62, A. Zhelezov12, Y. Zheng62, A. Zhokhov32, X. Zhu3, V. Zhukov9, S.
Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
36Institute for High Energy Physics (IHEP), Protvino, Russia
37ICCUB, Universitat de Barcelona, Barcelona, Spain
38Universidad de Santiago de Compostela, Santiago de Compostela, Spain
39European Organization for Nuclear Research (CERN), Geneva, Switzerland
40Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
41Physik-Institut, Universität Zürich, Zürich, Switzerland
42Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
43Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
44NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
45Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
46University of Birmingham, Birmingham, United Kingdom
47H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
48Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
49Department of Physics, University of Warwick, Coventry, United Kingdom
50STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
51School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
52School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
53Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
54Imperial College London, London, United Kingdom
55School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
56Department of Physics, University of Oxford, Oxford, United Kingdom
57Massachusetts Institute of Technology, Cambridge, MA, United States
58University of Cincinnati, Cincinnati, OH, United States
59University of Maryland, College Park, MD, United States
60Syracuse University, Syracuse, NY, United States
61Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
62University of Chinese Academy of Sciences, Beijing, China, associated to 3
63Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
64Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
65Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
66National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
67Yandex School of Data Analysis, Moscow, Russia, associated to 32
68Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
69Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 42

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines