EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-154 LHCb-PAPER-2021-023 September 1, 2021

Updated search for ${B}_{c}^{+}$ decays to two charm mesons

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

A data set corresponding to an integrated luminosity of $9\text{\,fb}^{-1}$ of
proton-proton collisions collected by the LHCb experiment has been analysed to
search for ${{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{(*)0}}}$ decays. The decays are fully or partially
reconstructed, where one or two missing neutral pions or photons from the
decay of an excited charm meson are allowed. Upper limits for the branching
fractions, normalised to ${{B}^{+}}$ decays to final states with similar
topologies, are obtained for fourteen ${B}_{c}^{+}$ decay modes. For the decay
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$, an excess with a significance
of 3.4 standard deviations is found.

Submitted to JHEP

© 2024 CERN for the benefit of the LHCb collaboration. CC BY 4.0 licence.

##  1 Introduction

Heavy-flavour states with $b$ quarks are characterised by a relatively long
lifetime and a large number of decay channels, and allow for highly sensitive
studies of charge and parity ($C\\!P$) symmetry violation and quantum-loop
induced amplitudes. In the ${B}_{c}^{+}$ meson, a $\overline{b}$ quark is
accompanied by a charm quark, $c$, forming a system where decays of both the
beauty and the charm quark, as well as weak annihilation processes, contribute
to the decay amplitude [1].

Transition amplitudes between up-type quarks and down-type quarks are
described by the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [2, 3].
Figure 1 illustrates the CKM-favoured, but colour-suppressed
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ decay (unless specified
otherwise, charge conjugation is implied throughout this article) and the CKM-
suppressed, but colour-favoured
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{0}}$ decay, which are expected
to have similar amplitudes. This may result in a large, ${\mathcal{O}}(1)$,
$C\\!P$ asymmetry for final states that are common between ${D}^{0}$ and
${\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$ decays. Consequently
decays of ${B}_{c}^{+}$ mesons to two charm mesons,
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}$, have been proposed to measure the angle
$\gamma\equiv{\rm
arg}(-{V_{{u}{d}}^{\phantom{\ast}}}{V_{{u}{b}}^{\ast}}/{V_{{c}{d}}^{\phantom{\ast}}}{V_{{c}{b}}^{\ast}})$
[4, 5, 6, 7], one of the key parameters of the CKM matrix. Presently, the most
precise determinations of $\gamma$ come from measurements of the $C\\!P$
asymmetry in ${{{B}^{+}}}\\!\rightarrow{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}{{K}^{+}}$ decays [8, 9].

Predicted branching fractions of ${B}_{c}^{+}$ decays to two charm mesons are
listed in Table 1. Final-state interactions may result in an enhancement of
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}$ decay rates [10]. Moreover, contributions from
physics beyond the Standard Model could potentially affect fully hadronic $B$
decays [11, 12, 13].

Figure 1: Diagrams for the (left) CKM-favoured, colour-suppressed ${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ and (right) CKM-suppressed, colour-favoured ${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{0}}$ decays.  Table 1:  Predicted branching fractions of ${B}_{c}^{+}$ decays to two charm mesons, in units of $10^{-6}$. Channel | Ref. [14] | Ref.[15] | Ref.[16] | Ref.[17]
---|---|---|---|---
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ | 2.3 $\pm$ | 0.5 | 4.8 | 1.7 | 2.1
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{0}}$ | 3.0 $\pm$ | 0.5 | 6.6 | 2.5 | 7.4
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ | 32 $\pm$ | 7 | 53 | 32 | 33
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}}{{D}^{0}}$ | 0.10 $\pm$ | 0.02 | 0.32 | 0.11 | 0.31
${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ | 12 $\pm$ | 3 | 49 | 17 | 9
${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{D}^{0}}$ | 0.09 $\pm$ | 0.02 | 0.40 | 0.38 | 0.44

This article describes a search for fourteen
${{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{(*)0}}}$ decay channels, using proton-proton $(pp)$
collision data collected by the LHCb experiment, corresponding to an
integrated luminosity of $9\text{\,fb}^{-1}$, of which $1\text{\,fb}^{-1}$ was
recorded at a centre-of-mass energy $\sqrt{s}=7$ TeV, $2\text{\,fb}^{-1}$ at
$\sqrt{s}=8$ TeV and $6\text{\,fb}^{-1}$ at $\sqrt{s}=13$ TeV. The data taken
at 7 and $8\text{\,Te\kern-1.00006ptV}$ are referred to as Run 1, and the data
taken at $13\text{\,Te\kern-1.00006ptV}$ as Run 2. The Run 1 data has
previously been analysed and no evidence of
${{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{(*)0}}}$ decays was found [18].

Charm mesons are reconstructed in the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$,
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$,
${{D}^{+}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$, and
${{D}^{*+}}\\!\rightarrow{{D}^{0}}{{\pi}^{+}}$ decay modes. In the decay
${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}$, at least one of the neutral charm mesons is
required to decay as ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$. Partially
reconstructed ${B}_{c}^{+}$ decays, which involve one or two excited charm
mesons producing a photon or a neutral pion in their decay, are also included
in the search. These decays manifest themselves as relatively narrow
structures in the mass distributions of the reconstructed final states below
the ${B}_{c}^{+}$ mass.

The branching fractions, $\mathcal{B}$, of ${B}_{c}^{+}$ decays to fully
reconstructed final states are measured relative to high-yield
${{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ normalisation modes,

$R({{D}^{(*)+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})\equiv\frac{\raisebox{3.00003pt}{$f_{c}$}}{f_{u}}\frac{{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})}{{\mathcal{B}}({{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}=\frac{N({{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})}{\varepsilon({{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})}\frac{\varepsilon({{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}{N({{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})},$ (1)

where $f_{c}/f_{u}$ is the ratio of the ${B}_{c}^{+}$ to ${{B}^{+}}$
fragmentation fraction, $N$ denotes the measured ${B}^{+}_{({c})}$ yields, and
$\varepsilon$ represents the detection efficiencies. The value of
${f_{c}/(f_{u}+f_{d})}\cdot{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\mu^{-}}{{\overline{\nu}}_{\mu}})$
has been measured at centre-of-mass energies of 7 and
$13\text{\,Te\kern-1.00006ptV}$ [19]. Under the assumption of equal production
from hadronisation of ${{B}^{+}}$ and ${B}^{0}$, $f_{u}=f_{d}$, the value of
${f_{c}/f_{u}}$ is found to be 0.73% at
$\sqrt{s}=7\text{\,Te\kern-1.00006ptV}$ and 0.76% at
$\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$ with relative uncertainties of
approximately 25%, dominated by the uncertainty on the predicted value of
${\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\mu^{-}}{{\overline{\nu}}_{\mu}})$.
Earlier measurements of $f_{c}/f_{u}$ at 7 and $8\text{\,Te\kern-1.00006ptV}$
using fully reconstructed ${B}_{c}^{+}$ decays found compatible values [20,
21].

The invariant-mass distributions of partially reconstructed
${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}$ and
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ decays overlap, so the sum of their branching
fractions is measured as

$\begin{split}R^{\prime}({{D}^{+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})&\equiv\frac{\raisebox{3.00003pt}{$f_{c}$}}{f_{u}}\frac{{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})+{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}})}{{\mathcal{B}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}\\\
&=\left[\frac{N({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})}{\varepsilon({{B}_{c}^{+}}\\!\rightarrow({{D}^{*+}_{({s})}}\\!\rightarrow{{D}^{+}_{({s})}}{X^{0}}){\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})}+\frac{N({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}})}{\varepsilon({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}})}\right]\frac{\varepsilon({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}{N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})},\end{split}$ (2)

where $X^{0}$ represents a neutral pion or a photon.

Decays of ${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ with a fully reconstructed
${{D}^{*+}}\\!\rightarrow{{D}^{0}}{{\pi}^{+}}$ decay, and one missing neutral
pion or photon from the ${{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ meson decay, results in measurements of

$R^{\prime}({{D}^{*+}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})\equiv\frac{\raisebox{1.30005pt}{$f_{c}$}}{f_{u}}\frac{{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}))}{{\mathcal{B}}({{{B}^{+}}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}=\frac{N({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}})}{\varepsilon({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})}\frac{\varepsilon({{{B}^{+}}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}{N({{{B}^{+}}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}.$ (3)

The ${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{s}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ and
${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ decays can also be observed when both excited
charm mesons decay with either a photon or a neutral pion and neither of the
two neutral particles are reconstructed. In such cases, the ratio
$R^{\prime\prime}$ is measured:

$\begin{split}R^{\prime\prime}({{D}^{+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})&\equiv\frac{\raisebox{3.00003pt}{$f_{c}$}}{f_{u}}\frac{{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}})}{{\mathcal{B}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}\\\
&=\frac{N({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}})}{\varepsilon({{B}_{c}^{+}}\\!\rightarrow({{D}^{*+}_{({s})}}\\!\rightarrow{{D}^{+}_{({s})}}{X^{0}}){\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})}\frac{\varepsilon({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}{N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})}.\end{split}$ (4)

In total sixteen ratios are measured, corresponding to fourteen ${B}_{c}^{+}$
branching fractions, since ${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ decays are accessed in both the ${D}^{+}$ $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ and ${D}^{*+}$ $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ channels.

##  2 Detector and simulation

The LHCb detector [22, 23] 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 [24], 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 [25, 26] placed
downstream of the magnet. The tracking system provides a measurement of the
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at $200\text{\,Ge\kern-1.00006ptV\\!/}c$.
The minimum distance of a track to a primary $pp$ collision vertex (PV), the
impact parameter, is measured with a resolution of
$(15+29/p_{\mathrm{T}})\,\upmu\text{m}$, where $p_{\mathrm{T}}$ is the
component of the momentum transverse to the beam, in
$\text{\,Ge\kern-1.00006ptV\\!/}c$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
[27]. Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
and a hadronic calorimeter. Muons are identified by a system composed of
alternating layers of iron and multiwire proportional chambers [28]. The
online event selection is performed by a trigger [29], 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.

At the hardware trigger stage, events are required to have a muon with high
$p_{\mathrm{T}}$ or a hadron, photon or electron with high transverse energy
in the calorimeters. For hadrons, the transverse energy threshold is
$3.5\text{\,Ge\kern-1.00006ptV}$. The software trigger requires a two-, three-
or four-track secondary vertex with a significant displacement from any PV. At
least one track should have
$p_{\mathrm{T}}>1.7\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$\chi^{2}_{\text{IP}}$ with respect to any PV greater than 16, where
$\chi^{2}_{\text{IP}}$ is defined as the difference in the vertex-fit
$\chi^{2}$ of a given PV reconstructed with and without the considered
particle. A multivariate algorithm [30, 31] is used for the identification of
secondary vertices consistent with the decay of a $b$ hadron.

Simulation is used to model the effects of the detector acceptance and the
imposed selection requirements, as well as for the training of the
multivariate selection of the ${B}_{c}^{+}$ signals, and for establishing the
shape of the mass distributions of the signals. The Pythia [32,
*Sjostrand:2006za] package, with a specific LHCb configuration [34], is used
to simulate $pp$ collisions with ${{B}^{+}}$ production. For ${B}_{c}^{+}$
production, the Bcvegpy [35] generator is used, interfaced with the Pythia
parton shower and hadronisation model. Decays of unstable particles are
described by EvtGen [36], in which final-state radiation is generated using
Photos [37]. The interaction of the generated particles with the detector, and
its response, are implemented using the Geant4 toolkit [38,
*Agostinelli:2002hh] as described in Ref. [40]. The simulated ${{B}^{+}}$
production is corrected to match the observed spectrum of
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}$${\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$ decays in data, using a gradient
boosted reweighter (GBR) [41] technique. The weights $w(p_{\mathrm{T}},y)$ are
determined separately for Run 1 and Run 2. Simulated ${B}_{c}^{+}$ events are
corrected to match the measured linear dependence of ${f_{c}/(f_{u}+f_{d})}$
on $p_{\mathrm{T}}$ and $y$ [19]. In addition, corrections using control
samples are applied to the simulated events to improve the agreement with data
regarding particle identification (PID) variables, the momentum scale and the
momentum resolution.

##  3 Candidate selection

Charm-meson candidates are formed by combining two, three or four tracks that
are incompatible with originating from any reconstructed PV. The tracks are
required to form a high-quality vertex and the scalar sum of their
$p_{\mathrm{T}}$ must exceed $1.8\text{\,Ge\kern-1.00006ptV\\!/}c$. To reduce
background from misidentified particles, the pion and kaon candidates must
also satisfy loose criteria on $\mathrm{DLL}_{{K}{\pi}}$, the ratio of the
likelihood between the kaon and pion PID hypotheses.

The reconstructed mass of ${D}^{0}$, ${D}^{+}_{s}$ and ${D}^{+}$ candidates is
required to be within $\pm 25\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ of their
known values [42]. For channels with a fully reconstructed
${{D}^{*+}}\\!\rightarrow{{D}^{0}}{{\pi}^{+}}$ meson, the mass difference
$\Delta m$ between the ${D}^{*+}$ and the ${D}^{0}$ candidates is required to
be within $\pm 10\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ of the known value
[42]. If more than one charm-meson candidate is formed from the same track
combination, only the best according to PID information is selected.

A ${B}^{+}_{({c})}$ candidate is formed by combining a ${D}^{(*)+}_{({s})}$
candidate with a $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ candidate if the combination has a $p_{\mathrm{T}}$
greater than $4.0\text{\,Ge\kern-1.00006ptV\\!/}c$, forms a good-quality
vertex and originates from a PV. The reconstructed decay time of the charm
meson candidates with respect to the ${B}^{+}_{({c})}$ vertex divided by its
uncertainty, $t/\sigma_{t}$, is required to exceed $-3$ for ${D}^{+}_{s}$ and
${D}^{0}$ mesons. This requirement is increased to $+3$ for the longer-lived
${D}^{+}$ meson to eliminate background from ${{{B}^{+}}}\\!\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$
decays where the negatively charged pion is misidentified as a kaon. Candidate
${B}_{c}^{+}$ decays that are compatible with the combination of a fully
reconstructed
${B}^{0}_{(s)}\\!\rightarrow{{D}^{(*)-}_{({s})}}{{\pi}^{+}}({{\pi}^{-}}{{\pi}^{+}})$
decay and a charged track are rejected. To eliminate duplicate tracks, the
opening angles between any pair of final-state particles are required to be at
least 0.5  mrad. The invariant-mass resolution of ${B}^{+}_{({c})}$ decays is
significantly improved by applying a kinematic fit [43] where the invariant
masses of the ${D}^{0}$ and the ${D}^{(*)+}_{({s})}$ candidates are
constrained to their known values [42], all particles from the
${D}^{(*)+}_{({s})}$, ${D}^{0}$, and ${B}^{+}_{({c})}$ decay are constrained
to originate from their corresponding decay vertex and the ${B}^{+}_{({c})}$
candidate is constrained to originate from the PV with which it has the
smallest $\chi^{2}_{\text{IP}}$.

To reduce the combinatorial background, while maintaining high efficiency for
signal, a multivariate selection based on a boosted decision tree (BDT) [44,
45] is employed. The BDT classifier exploits kinematic and PID properties of
selected candidates, namely: the fit quality of the ${B}^{+}_{({c})}$
candidate and both charm-meson candidate vertices; the value of
$\chi^{2}_{\text{IP}}$ of the ${B}^{+}_{({c})}$ candidate; the values of
$t/\sigma_{t}$ of the ${B}^{+}_{({c})}$ and both charm-meson candidates; the
reconstructed masses of the charm-meson candidates; and the reconstructed
masses of the pairs of opposite-charge tracks from the ${D}^{+}_{({s})}$
candidate. In addition, for each charm-meson candidate, the smallest value of
$p_{\mathrm{T}}$ and the smallest value of $\chi^{2}_{\text{IP}}$ among the
decay products, and the smallest (largest) value of $\mathrm{DLL}_{{K}{\pi}}$
among all kaon (pion) candidates, are included as input variables for the BDT
classifier.

The BDT training is performed separately for the ${D}^{+}_{s}$ $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$, ${D}^{+}$ $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ and ${D}^{*+}$ $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ final states, separately for the
${{D}^{0}}\\!\rightarrow K^{-}\pi^{+}$ and ${{D}^{0}}\\!\rightarrow
K^{-}\pi^{+}\pi^{-}\pi^{+}$ decay channels, and separately for the Run 1 and
Run 2 data samples. For a given ${D}^{0}$ final state, the same classifier is
used for both ${{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ and
${{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{D}^{0}}$ decays. For signal
decays, the BDT classifier is trained using simulated ${B}_{c}^{+}$ events,
while for background, data in the range $5350<m({{D}^{(*)+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})<6200\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ are
used. For the background sample, the charm-meson mass windows are increased
from $\pm 25\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ to $\pm
75\text{\,Me\kern-1.00006ptV\\!/}c^{2}$, to increase the size of the training
sample. The $k$-fold cross-training technique [46] with $k=5$ is used to avoid
biases in the calculation of the BDT output.

The data are divided in increasing order of signal purity into three samples
having low, medium and high BDT output. Most of the sensitivity in this search
comes from the data in the high BDT sample, but including data with lower
signal purity increases the signal efficiency and constrains the shape of the
combinatorial background. A small fraction of the events ($\approx 1\%$) have
more than one ${B}^{+}_{({c})}$ candidate that satisfies the minimum BDT
requirement. In such cases, one randomly selected candidate is retained per
event. Figure 2 shows the invariant mass distributions of selected
${B}^{+}_{({c})}$ candidates in the highest BDT sample, summed over all
${D}^{0}$ final states.

Figure 2: Invariant-mass distributions for the selected ${B}^{+}_{({c})}$
candidates in the highest BDT samples for (top left) ${D}^{+}_{s}$ ${\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$, (top right) ${D}^{+}_{s}$
${D}^{0}$, (center left) ${D}^{+}$ ${\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$, (center right) ${D}^{+}$
${D}^{0}$, (bottom left) ${D}^{*+}$ ${\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$ and (bottom right) ${D}^{*+}$
${D}^{0}$, final states. The overlaid curves correspond to the sum of the
corresponding fit results.

##  4 Model of the ${B}^{+}_{({c})}$ mass distributions

To measure the signal yields, a model of the ${B}^{+}_{({c})}$ candidate mass
distribution is fitted to the data in the range $5230\leq
m({{D}^{(*)+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}})\leq 6700\text{\,Me\kern-1.00006ptV\\!/}c^{2}$. The
model consists of the following components, constrained to positive yields:
the signals for fully reconstructed ${{B}^{+}}$ and ${B}_{c}^{+}$ decays; the
signal for ${B}_{c}^{+}$ decays with one missing ${\pi}^{0}$ or photon; the
signal for ${B}_{c}^{+}$ decays with two missing ${\pi}^{0}$ or photons; the
background from ${{{B}^{+}}}\\!\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$
decays; and the combinatorial background.

Fully reconstructed ${{B}^{+}}$ and ${B}_{c}^{+}$ signals are described by the
sum of a Gaussian function and a Crystal Ball (CB) [47] function, extended to
have power-law tails on both the low-mass and the high-mass sides. The CB and
Gaussian components share a common peak position. The tail parameters of the
CB and the ratio of the CB and Gaussian widths and integrals are determined
from simulation, accounting for a dependence of both widths on the BDT output.
The ratio of the ${B}_{c}^{+}$ and ${{B}^{+}}$ widths is determined from
simulation, while the overall width of the ${{B}^{+}}$ is a free parameter in
the fit to data. The peak position of the ${{B}^{+}}$ signal is a free
parameter in the fit to data, and the known mass difference between the
${{B}^{+}}$ and the ${B}_{c}^{+}$ meson [42] is used to constrain the peak
position of the ${B}_{c}^{+}$ signal.

Genuine ${{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{D}^{0}}$ decays are
forbidden at tree level and consequently have a negligible yield, but doubly
Cabibbo-suppressed (DCS) decays ${{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}({{\pi}^{-}}{{\pi}^{+}})$
result in crossfeed of ${{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ decays in the
${D}^{(*)+}_{({s})}$ ${D}^{0}$ final state. An additional source of crossfeed
into the ${D}^{(*)+}_{({s})}$ ${D}^{0}$ final state is double
misidentification of the pion and kaon in the Cabibbo-favoured
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}({{\pi}^{-}}{{\pi}^{+}})$ decay.
The DCS component is constrained in yield and shape by the large
${{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ signal, according to the known
${D}^{0}$ branching fractions [42]. For the shape of the misidentified
component, the width of the
${{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}_{({s})}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ peak is scaled by a factor
determined from a fit to ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{0}}$
candidates, and also used for the
${{{B}^{+}}}\\!\rightarrow{{D}^{(*)+}}{{D}^{0}}$ final states. The yield of
the misidentified component is a free parameter in all fits to data.

Models for decays with one or two missing neutral particles from
${D}^{(*)+}_{({s})}$ and/or ${D}^{(*)0}$ decays are implemented as templates,
obtained from kernel fits [48] to reconstructed mass distributions in
simulation. Both ${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}$ and
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ decays contribute according to their predicted
relative branching fractions [14]. For
${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ decays, the longitudinal and transverse
polarised contributions are weighted according to the predicted polarisation
fractions [14].

The Cabibbo-favoured ${{{B}^{+}}}\\!\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$
decay is a background to the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ channel, though its yield is
strongly reduced by the ${D}^{+}_{s}$ mass requirement. This background is
modelled by a single Gaussian function, with the width determined from a
sample of simulated decays and the normalisation determined from the peak in
the ${{B}^{+}}$ mass distribution in the ${D}^{+}_{s}$ invariant mass
sideband.

The combinatorial background is described by the sum of an exponential
function and a constant, where the parameters are allowed to differ between
different ${D}^{0}$ decay modes, but are taken to be the same for all BDT
samples of a given ${B}_{c}^{+}$ and ${D}^{0}$ decay channel. Studies of the
charm-meson invariant-mass sidebands support these assumptions.

An unbinned extended maximum-likelihood fit is used to simultaneously describe
the mass distributions of candidates in different BDT samples and different
${D}^{0}$ decay modes. In these fits the background and ${{B}^{+}}$ yields
vary independently, but the branching fraction ratios $R$, $R^{\prime}$ and
$R^{\prime\prime}$, defined in Eqs. 1–4, are constrained to be identical
between the BDT sample and ${D}^{0}$ decay modes.

##  5 Systematic uncertainties

Systematic uncertainties on the ${{B}^{+}}$ yields and the efficiencies affect
the normalisation factor relating the ${B}_{c}^{+}$ yield to the branching
fraction ratios. These uncertainties are evaluated separately for Run 1 and
Run 2, and for each ${B}_{c}^{+}$ decay, ${D}^{0}$ channel and BDT sample.
Their effective contribution in the fit, calculated as a weighted average over
BDT samples and ${D}^{0}$ decay modes, are listed in Table 2. Where no
uncertainty is given, this corresponds to either the absence of decays with
two missing neutral particles in the ${D}^{*+}$ $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ channel or the absence of the effect associated
with an uncertainty in a given data-taking period or channel.

Table 2: Effective contributions of systematic uncertainties on the normalisation factor, combined over all BDT samples and ${D}^{0}$ decay modes, given in percent. Final state | ${{D}^{+}_{s}}{\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptD$}{}^{0}}$ | ${{D}^{+}}{\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptD$}{}^{0}}$ | ${{D}^{*+}}{\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptD$}{}^{0}}$
---|---|---|---
| Run 1 | Run 2 | Run 1 | Run 2 | Run 1 | Run 2
${B}_{c}^{+}$ signal shape | $9.4$ | $3.8$ | $4.8$ | $5.3$ | $2.8$ | $3.9$
${B}_{c}^{+}$ production spectrum | $3.7$ | $2.4$ | $3.9$ | $2.4$ | $4.2$ | $2.9$
${{B}^{+}}$ production spectrum | $0.5$ | $0.9$ | $0.6$ | $1.0$ | $0.6$ | $1.1$
Hit resolution parameterisation | – | $1.5$ | – | $1.2$ | – | $2.2$
$R$ simulation sample size | $1.2$ | $1.0$ | $1.4$ | $1.1$ | $1.5$ | $1.5$
$R^{\prime}$ simulation sample size | $1.4$ | $0.9$ | $2.1$ | $1.2$ | $1.1$ | $1.1$
$R^{\prime\prime}$ simulation sample size | $1.5$ | $0.8$ | $1.7$ | $0.9$ | – | –
${B}_{c}^{+}$ lifetime | $1.3$ | $1.4$ | $1.3$ | $1.3$ | $2.1$ | $2.6$
PID efficiencies | $1.6$ | $1.2$ | $2.8$ | $0.8$ | $2.2$ | $1.4$
Multiple ${B}^{+}_{({c})}$ candidates | $0.4$ | $0.4$ | $0.6$ | $0.5$ | $1.4$ | $1.2$
Data-simulation differences | $0.1$ | $0.1$ | $0.1$ | $0.1$ | $0.1$ | $0.2$
${{{B}^{+}}}\\!\rightarrow{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ | $0.7$ | $0.5$ | – | – | – | –
${\mathcal{B}}({{D}^{*+}}\\!\rightarrow{{D}^{+}}{X^{0}})$ | – | – | $1.5$ | $1.5$ | – | –
$R$ total | $10.4$ | $5.3$ | $7.2$ | $6.6$ | $6.3$ | $6.5$
$R^{\prime}$ total | $4.6$ | $3.7$ | $5.7$ | $3.8$ | $5.5$ | $5.0$
$R^{\prime\prime}$ total | $4.6$ | $3.7$ | $5.5$ | $3.7$ | – | –

The uncertainty on the ${B}_{c}^{+}$ signal shape is evaluated by changing the
${B}_{c}^{+}$ signal shape to the sum of two Gaussian functions. Uncertainties
related to the ${{B}_{c}^{+}}$ production spectrum are evaluated by changing
the slope parameters from Ref. [19] by their quoted uncertainties. The
uncertainty on the $p_{\mathrm{T}}$\- and $y$-dependent weights used to
correct the ${{B}^{+}}$ production spectrum in simulation is estimated by
changing the settings of the GBR algorithm. Hit resolution parameterisation in
the silicon vertex detector affects the $\chi^{2}_{\text{IP}}$ distribution.
The uncertainty associated with the parameterisation is therefore evaluated
with simulation by varying the minimal value of the $\chi^{2}_{\text{IP}}$
applied to the final-state tracks.

The limited size of the simulation samples results in uncertainties that are
uncorrelated between the BDT samples and ${D}^{0}$ decay channels on the
efficiency ratios $\varepsilon({{B}_{c}^{+}})/\varepsilon({{{B}^{+}}})$. All
other systematic uncertainties are treated as fully correlated. A small
uncertainty on the reconstruction efficiency results from that on the
${B}_{c}^{+}$ lifetime [42]. Uncertainties on the PID efficiencies cancel to
first order in the ratio $\varepsilon({{B}_{c}^{+}})/\varepsilon({{{B}^{+}}})$
because of the identical particle content of the final state, and the
difference in relative efficiencies with and without PID corrections is used
to estimate the uncertainty from the PID correction procedure. The requirement
to select at most one ${B}^{+}_{({c})}$ candidate per event introduces an
efficiency that may not be well reproduced by simulation. Therefore, the
fraction of candidates removed by the requirement of at most one
${B}^{+}_{({c})}$ candidate per event is attributed as a systematic
uncertainty. Residual differences appear in the comparison of the
distributions of the BDT output between background-subtracted data and
simulation. The effect on the relative efficiency is evaluated by correcting
the simulation to match the distributions in data. The background from
${{{B}^{+}}}\\!\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$
decays to the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ signal is assigned an
uncertainty of 100% of its yield, resulting in a normalisation uncertainty of
less than 1%. The measurements of the branching fraction ratios according to
Eqs. 2 and 4 involve the value of
${\mathcal{B}}({{D}^{*+}}\\!\rightarrow{{D}^{+}}{X^{0}})$, the uncertainty of
which [42] is taken into account.

Other uncertainties, listed below, do not directly affect the normalisation
and are taken into account by varying the fit model. Unless specified
otherwise, these uncertainties are taken into account by replacing fixed
values of the model parameters by their Gaussian constraints.

The uncertainty on the combinatorial background shape is evaluated by
considering a single exponential function as an alternative to the exponential
plus constant model, implemented using the discrete profiling method [49]. The
${{B}^{+}}$ shape uncertainty affects the ${{B}^{+}}$ yield but, because of
its long tails, also the background shape. The effect is evaluated by
assigning an uncertainty on the tail parameters determined from a fit to
simulated events. The uncertainty on the $\alpha$ parameters of the CB
function is increased by adding in quadrature the largest observed difference
between data and simulation of this parameter in
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ decays. The fractional
uncertainty on the yield of DCS crossfeed is the sum in quadrature of the
fractional uncertainty on the normalisation yield and on the branching
fractions
${\mathcal{B}}({{D}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}({{\pi}^{+}}{{\pi}^{-}}))$
[42]. The uncertainty on the difference between the ${B}_{c}^{+}$ and
${{B}^{+}}$ peak positions, $0.5\text{\,Me\kern-1.00006ptV\\!/}c^{2}$, arises
due to uncertainty on the measured masses [42, 50] and the momentum scale
uncertainty [51]. The ratio of the ${B}_{c}^{+}$ to ${{B}^{+}}$ invariant-mass
resolution is assigned an uncertainty from the fit to simulated decays.
Candidates reconstructed as
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}$ with one missing neutral pion or photon have
contributions from ${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}}$ and
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ decays. The uncertainties on the ratios of their
relative contributions are taken from Ref. [14], to which a term is added in
quadrature that accounts for the statistical uncertainties of the templates.
The ${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{({s})}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ signals have contributions from both transverse
and longitudinal polarisations, which have differently shaped distributions of
the reconstructed mass. The uncertainties on the transverse-polarisation
fractions are taken from Ref. [14], to which a term is added in quadrature to
account for the statistical uncertainties of the templates.

##  6 Results and conclusions

To determine the ${B}_{c}^{+}$ branching fraction ratios $R$, $R^{\prime}$,
and $R^{\prime\prime}$, fits to data are performed separately for the six
${B}_{c}^{+}$ final states and for Run 1 and Run 2, while different ${D}^{0}$
decay modes and BDT samples are fit simultaneously. The results of the fits
are shown in Fig. 2, where the data of the highest BDT samples and the
corresponding fit results are summed over the ${D}^{0}$ decay channels and
over data-taking periods. Detailed views of the ${D}^{+}_{s}$ $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ final states near the ${{B}^{+}}$ mass are shown in
Fig. 3 which validate the model of the large
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ signal and its crossfeed to the
${D}^{+}_{s}$ ${D}^{0}$ final state.

Figure 3: Invariant-mass distributions for the selected ${{B}^{+}}$ candidates
in the highest BDT samples, in the region near the ${{B}^{+}}$ mass, for
(left) ${D}^{+}_{s}$ ${\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$ and
(right) ${D}^{+}_{s}$ ${D}^{0}$ final states. The overlaid curves correspond
to the sum of the corresponding fit results.

The significance of the ${B}_{c}^{+}$ signals are calculated using Wilks’
theorem [52] as $S=\sqrt{2\Delta\log\mathcal{L}}$, where
$\Delta\log\mathcal{L}$ is the difference in the logarithm of the likelihood
between the signal plus background and background-only hypotheses. Systematic
uncertainties are included in the calculation of the significance through
nuisance parameters in a minimised profile likelihood.

Evidence is found only for the decay
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ in Run 2 data, with a
significance of 3.7 standard deviations, and the measured branching fraction
ratio is $R({{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})=(3.6^{+1.5+0.3}_{-1.2-0.2})\times
10^{-4}$, where the first uncertainty is statistical and the second is
systematic. The quoted significance for this channel is compatible with
estimates from simulated pseudoexperiments.

The values of $R$, $R^{\prime}$ and $R^{\prime\prime}$ from Run 1 and Run 2
cannot be directly combined since the value of $f_{c}/f_{u}$ depends on the
$pp$ centre-of-mass energy. Therefore, a combined fit of both the Run 1 and
Run 2 data sets is made to the absolute ${B}_{c}^{+}$ branching fractions,
using external input for
${\mathcal{B}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$,
${\mathcal{B}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$,
${\mathcal{B}}({{{B}^{+}}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ [42], and $f_{c}/f_{u}$ [19].
In this combined fit the excess for
${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ has a significance of 3.4
standard deviations, or 2.5 standard deviations when considering the
probability of the excess to appear in any of the sixteen final states
considered. The corresponding value of the branching fraction is
${\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})=(3.5^{+1.5+0.3}_{-1.3-0.2}\pm
1.0)\times 10^{-4}$, where the first uncertainty is statistical, the second
systematic and the third due to external input.

Upper limits are reported on the ratio of branching fractions for all decays,
calculated at 90% and 95% confidence level (C.L.) with the frequentist CLs
method [53, 54], separately for Run 1 and Run 2. These limits are listed in
Table 3.

Table 3: Upper limits on the branching fraction ratios $R$, $R^{\prime}$ and $R^{\prime\prime}$ of ${B}_{c}^{+}$ to ${{B}^{+}}$ decays, defined in Eqs. 1–4, at the 90(95)% C.L. for Run 2 and Run 1 data, in units of $10^{-3}$. | Run 2 | Run 1
---|---|---
|  $6\text{\,fb}^{-1}$, $13\text{\,Te\kern-1.00006ptV}$ |  $3\text{\,fb}^{-1}$, 7 and $8\text{\,Te\kern-1.00006ptV}$
$R({{D}^{+}_{s}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $0.57\,(0.62)$ | $0.45\,(0.58)$
$R^{\prime}({{D}^{+}_{s}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $0.31\,(0.43)$ | $0.6\,(0.8)$
$R^{\prime\prime}({{D}^{+}_{s}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $0.9\,(1.0)$ | $0.8\,(1.1)$
$R({{D}^{+}_{s}}{{D}^{0}})$ | $0.22\,(0.25)$ | $0.51\,(0.62)$
$R^{\prime}({{D}^{+}_{s}}{{D}^{0}})$ | $0.55\,(0.62)$ | $0.8\,(1.1)$
$R^{\prime\prime}({{D}^{+}_{s}}{{D}^{0}})$ | $1.0\,(1.1)$ | $1.7\,(2.0)$
$R({{D}^{+}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $3.5\,(4.4)$ |  $8\,(11)$
$R^{\prime}({{D}^{+}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $10\,(13)$ | $17\,(19)$
$R^{\prime\prime}({{D}^{+}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $20\,(25)$ | $81\,(91)$
$R({{D}^{+}}{{D}^{0}})$ | $2.9\,(3.6)$ | $12\,(14)$
$R^{\prime}({{D}^{+}}{{D}^{0}})$ | $6.9\,(7.9)$ | $11\,(13)$
$R^{\prime\prime}({{D}^{+}}{{D}^{0}})$ | $18\,(19)$ | $82\,(93)$
$R({{D}^{*+}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $6.9\,(8.4)$ | $26\,(28)$
$R^{\prime}({{D}^{*+}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})$ | $16\,(19)$ | $36\,(48)$
$R({{D}^{*+}}{{D}^{0}})$ | $3.6\,(4.4)$ |  $8\,(13)$
$R^{\prime}({{D}^{*+}}{{D}^{0}})$ | $10\,(12)$ | $35\,(44)$

Upper limits on the absolute ${B}_{c}^{+}$ branching fractions are based on
the Run 2 dataset alone, which has nearly four times the sensitivity of the
Run 1 dataset. The upper limits at 90(95%) C.L. are

$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})<7.2\,(8.4)\times 10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{0}})<3.0\,(3.7)\times
10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})<1.9\,(2.5)\times 10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}}{{D}^{0}})<1.4\,(1.8)\times
10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})<3.8\,(4.8)\times 10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{D}^{0}})<2.0\,(2.4)\times
10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})+{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{*0}})<4.1\,(4.9)\times 10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{s}}{{D}^{0}})+{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{*0}})<7.0\,(8.5)\times
10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}})+{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{*0}})<5.8\,(6.9)\times 10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{D}^{0}})+{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{+}}{{D}^{*0}})<3.6\,(4.5)\times
10^{-4};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{*0}})<1.1\,(1.4)\times 10^{-3};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}_{s}}{{D}^{*0}})<1.2\,(1.4)\times
10^{-3};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{*0}})<0.9\,(1.1)\times 10^{-3};$
$\displaystyle{\mathcal{B}}({{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{D}^{*0}})<5.2\,(6.7)\times
10^{-4}.$

The reported upper limits on ${{B}_{c}^{+}}\\!\rightarrow{{D}^{*+}}{{\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{*0}}}$ decays are based on the analyses of fully
reconstructed ${{D}^{*+}}\\!\rightarrow{{D}^{0}}{{\pi}^{+}}$ decays, which
have a higher sensitivity than the channels with partially reconstructed
${{D}^{*+}}\\!\rightarrow{{D}^{+}}{X^{0}}$ decays.

In conclusion, this article reports the results of a search for
${{B}_{c}^{+}}\\!\rightarrow{{D}^{(*)+}_{({s})}}$$\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptD$}{}^{0}$ decays, covering fourteen ${B}_{c}^{+}$ decay
channels in sixteen final states, which include partially reconstructed decays
where one or two neutral pions or photons from the decay of an excited charm
meson are not reconstructed. The results, based on $pp$ collision data
corresponding to $9\text{\,fb}^{-1}$ of integrated luminosity, supersede an
earlier LHCb measurement [18] on Run 1 data only. No signal is observed in any
of the channels investigated, consistent with the Standard Model expectation.
An excess with a significance of 3.4 standard deviations is found for the
decay ${{B}_{c}^{+}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$, which is in tension with the
theoretical expectation [14, 15, 16, 17].

## 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); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MICINN (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and NERSC (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 ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, IPhU and Labex P2IO, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

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LHCb collaboration

R. Aaij32, A.S.W. Abdelmotteleb56, C. Abellán Beteta50, T. Ackernley60, B.
Adeva46, M. Adinolfi54, H. Afsharnia9, C. Agapopoulou13, C.A. Aidala86, S.
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Cartelle55, S. Amato2, J.L. Amey54, Y. Amhis11, L. An48, L. Anderlini22, A.
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Bachmayer49, J.J. Back56, P. Baladron Rodriguez46, V. Balagura12, W.
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Blake56, F. Blanc49, S. Blusk68, D. Bobulska59, J.A. Boelhauve15, O. Boente
Garcia46, T. Boettcher65, A. Boldyrev82, A. Bondar43, N. Bondar38,48, S.
Borghi62, M. Borisyak42, M. Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V.
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Madejczyk34, L.R. Madhan Mohan54, O. Maev38, A. Maevskiy82, D. Maisuzenko38,
M.W. Majewski34, J.J. Malczewski35, S. Malde63, B. Malecki48, A. Malinin81, T.
Maltsev43,v, H. Malygina17, G. Manca27,e, G. Mancinelli10, D. Manuzzi20,d, D.
Marangotto25,i, J. Maratas9,s, J.F. Marchand8, U. Marconi20, S. Mariani22,g,
C. Marin Benito48, M. Marinangeli49, J. Marks17, A.M. Marshall54, P.J.
Marshall60, G. Martelli78, G. Martellotti30, L. Martinazzoli48,j, M.
Martinelli26,j, D. Martinez Santos46, F. Martinez Vidal47, A. Massafferri1, M.
Materok14, R. Matev48, A. Mathad50, Z. Mathe48, V. Matiunin41, C. Matteuzzi26,
K.R. Mattioli86, A. Mauri32, E. Maurice12, J. Mauricio45, M. Mazurek48, M.
McCann61, L. Mcconnell18, T.H. Mcgrath62, N.T. Mchugh59, A. McNab62, R.
McNulty18, J.V. Mead60, B. Meadows65, G. Meier15, N. Meinert76, D.
Melnychuk36, S. Meloni26,j, M. Merk32,80, A. Merli25,i, L. Meyer Garcia2, M.
Mikhasenko48, D.A. Milanes74, E. Millard56, M. Milovanovic48, M.-N. Minard8,
A. Minotti26,j, L. Minzoni21,f, S.E. Mitchell58, B. Mitreska62, D.S. Mitzel48,
A. Mödden 15, R.A. Mohammed63, R.D. Moise61, T. Mombächer46, I.A. Monroy74, S.
Monteil9, M. Morandin28, G. Morello23, M.J. Morello29,m, J. Moron34, A.B.
Morris75, A.G. Morris56, R. Mountain68, H. Mu3, F. Muheim58,48, M. Mulder48,
D. Müller48, K. Müller50, C.H. Murphy63, D. Murray62, P. Muzzetto27,48, P.
Naik54, T. Nakada49, R. Nandakumar57, T. Nanut49, I. Nasteva2, M. Needham58,
I. Neri21, N. Neri25,i, S. Neubert75, N. Neufeld48, R. Newcombe61, T.D.
Nguyen49, C. Nguyen-Mau49,x, E.M. Niel11, S. Nieswand14, N. Nikitin40, N.S.
Nolte64, C. Normand8, C. Nunez86, A. Oblakowska-Mucha34, V. Obraztsov44, T.
Oeser14, D.P. O’Hanlon54, S. Okamura21, R. Oldeman27,e, M.E. Olivares68,
C.J.G. Onderwater79, R.H. O’Neil58, A. Ossowska35, J.M. Otalora Goicochea2, T.
Ovsiannikova41, P. Owen50, A. Oyanguren47, K.O. Padeken75, B. Pagare56, P.R.
Pais48, T. Pajero63, A. Palano19, M. Palutan23, Y. Pan62, G. Panshin84, A.
Papanestis57, M. Pappagallo19,c, L.L. Pappalardo21,f, C. Pappenheimer65, W.
Parker66, C. Parkes62, B. Passalacqua21, G. Passaleva22, A. Pastore19, M.
Patel61, C. Patrignani20,d, C.J. Pawley80, A. Pearce48, A. Pellegrino32, M.
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Piccini78, B. Pietrzyk8, G. Pietrzyk49, M. Pili63, D. Pinci30, F. Pisani48, M.
Pizzichemi26,48,j, Resmi P.K10, V. Placinta37, J. Plews53, M. Plo Casasus46,
F. Polci13, M. Poli Lener23, M. Poliakova68, A. Poluektov10, N. Polukhina83,u,
I. Polyakov68, E. Polycarpo2, S. Ponce48, D. Popov6,48, S. Popov42, S.
Poslavskii44, K. Prasanth35, L. Promberger48, C. Prouve46, V. Pugatch52, V.
Puill11, H. Pullen63, G. Punzi29,n, H. Qi3, W. Qian6, J. Qin6, N. Qin3, R.
Quagliani13, B. Quintana8, N.V. Raab18, R.I. Rabadan Trejo6, B. Rachwal34,
J.H. Rademacker54, M. Rama29, M. Ramos Pernas56, M.S. Rangel2, F.
Ratnikov42,82, G. Raven33, M. Reboud8, F. Redi49, F. Reiss62, C. Remon
Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, S. Ricciardi57, K. Rinnert60,
P. Robbe11, G. Robertson58, A.B. Rodrigues49, E. Rodrigues60, J.A. Rodriguez
Lopez74, E.R.R. Rodriguez Rodriguez46, A. Rollings63, P. Roloff48, V.
Romanovskiy44, M. Romero Lamas46, A. Romero Vidal46, J.D. Roth86, M.
Rotondo23, M.S. Rudolph68, T. Ruf48, R.A. Ruiz Fernandez46, J. Ruiz Vidal47,
A. Ryzhikov82, J. Ryzka34, J.J. Saborido Silva46, N. Sagidova38, N. Sahoo56,
B. Saitta27,e, M. Salomoni48, C. Sanchez Gras32, R. Santacesaria30, C.
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Savrina41,40, H. Sazak9, L.G. Scantlebury Smead63, A. Scarabotto13, S.
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Schulte49, M.H. Schune11, R. Schwemmer48, B. Sciascia23, S. Sellam46, A.
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Shields26,j, Y. Shimizu11, E. Shmanin83, J.D. Shupperd68, B.G. Siddi21, R.
Silva Coutinho50, G. Simi28, S. Simone19,c, N. Skidmore62, T. Skwarnicki68,
M.W. Slater53, I. Slazyk21,f, J.C. Smallwood63, J.G. Smeaton55, A. Smetkina41,
E. Smith50, M. Smith61, A. Snoch32, M. Soares20, L. Soares Lavra9, M.D.
Sokoloff65, F.J.P. Soler59, A. Solovev38, I. Solovyev38, F.L. Souza De
Almeida2, B. Souza De Paula2, B. Spaan15, E. Spadaro Norella25,i, P.
Spradlin59, F. Stagni48, M. Stahl65, S. Stahl48, S. Stanislaus63, O.
Steinkamp50,83, O. Stenyakin44, H. Stevens15, S. Stone68, M.E. Stramaglia49,
M. Straticiuc37, D. Strekalina83, F. Suljik63, J. Sun27, L. Sun73, Y. Sun66,
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Zunica62.

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
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provincial Key Laboratory of Nuclear Science, Guangdong-Hong Kong
Joint Laboratory of Quantum Matter, Institute of Quantum Matter, South China
Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Institut für Physik, Universität Rostock, Rostock, Germany, associated to 17
77Eotvos Lorand University, Budapest, Hungary, associated to 48
78INFN Sezione di Perugia, Perugia, Italy, associated to 21
79Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
80Universiteit Maastricht, Maastricht, Netherlands, associated to 32
81National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
82National Research University Higher School of Economics, Moscow, Russia,
associated to 42
83National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
84National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
85DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
86University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
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 Genova, Genova, Italy
iUniversità degli Studi di Milano, Milano, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Modena e Reggio Emilia, Modena, Italy
lUniversità di Padova, Padova, Italy
mScuola Normale Superiore, Pisa, Italy
nUniversità di Pisa, Pisa, Italy
oUniversità della Basilicata, Potenza, Italy
pUniversità di Roma Tor Vergata, Roma, Italy
qUniversità di Siena, Siena, Italy
rUniversità di Urbino, Urbino, Italy
sMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
tAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
uP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
vNovosibirsk State University, Novosibirsk, Russia
wDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden
xHanoi University of Science, Hanoi, Vietnam