EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2020-183 LHCb-PAPER-2020-021 October 22, 2020

Measurement of the branching fraction of the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay

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

A branching fraction measurement of the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay is presented using
proton-proton collision data collected with the LHCb experiment, corresponding
to an integrated luminosity of $5.0\text{\,fb}^{-1}$. The branching fraction
is found to be
${{\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})=(19.4\pm
1.8\pm 1.3\pm 1.2)\times 10^{-6}}$, where the first uncertainty is
statistical, the second systematic and the third is due to the uncertainty on
the ${{B}^{0}}\rightarrow{{D}^{-}}{{\pi}^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ and
${{D}^{-}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$ branching fractions.
This is the most precise single measurement of this quantity to date. As this
decay proceeds through a single amplitude involving a $b\rightarrow u$
charged-current transition, the result provides information on non-
factorisable strong interaction effects and the magnitude of the Cabibbo-
Kobayashi-Maskawa matrix element $V_{ub}$. Additionally, the collision energy
dependence of the hadronisation-fraction ratio $f_{s}/f_{d}$ is measured
through ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decays.

Submitted to Eur. Phys. J. C

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

##  1 Introduction

To test the Cabibbo-Kobayashi-Maskawa (CKM) sector of the Standard Model (SM),
it is crucial to perform accurate measurements of the quark-mixing matrix
elements. Any discrepancy among the numerous measurements of CKM matrix
elements could reveal effects from new particles or forces beyond the SM. The
knowledge of the magnitude of the matrix element ${V_{{u}{b}}}$ governing the
strength of ${b}\\!\rightarrow{u}$ transitions is key in the consistency
checks of the SM and its naturally motivated extensions [1, 2].
The hadronic ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decay111Inclusion of charge-conjugate modes is implied unless explicitly
stated. proceeds in the SM through the ${b}\\!\rightarrow{u}$ transition as
shown in Fig. 1. Its branching fraction is proportional to
$|{V_{{u}{b}}}|^{2}$,

${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})=\Phi|{V_{{u}{b}}}|^{2}|V_{cs}|^{2}|F({{B}^{0}}\rightarrow{{\pi}^{-}})|^{2}f_{{{D}^{+}_{s}}}^{2}|a_{\text{NF}}|^{2},$
(1)

where $\Phi$ is a phase-space factor, $F({{B}^{0}}\rightarrow{{\pi}^{-}})$ is
a form factor, $f_{{{D}^{+}_{s}}}$ is the ${D}^{+}_{s}$ decay constant,
$V_{cs}$ is the CKM matrix element representing ${c}\rightarrow{s}$
transitions, and $|a_{\text{NF}}|$ encapsulates non-factorisable effects. The
form factor and the decay constant can be obtained from light-cone sum rules
[3, 4] and lattice QCD calculations [5, 6], and since $|V_{cs}|$ is known to
be close to unity, the ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
branching fraction can be used to probe the product
$|{V_{{u}{b}}}||a_{\text{NF}}|$. The assumption of factorisation is expected
to hold, i.e. $|a_{\text{NF}}|$ is close to unity, for $B$ meson decays into a
heavy and a light meson, where the $W$ emission of the decay corresponds to
the light meson and the spectator quark forms part of the heavy meson. This is
not the case for the ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay
and consequently $|a_{\text{NF}}|$ may be significantly different from unity
[7].

Figure 1: Tree diagram of the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay, in which a ${B}^{0}$
meson decays through the weak interaction to a ${D}^{+}_{s}$ meson and a
charged pion. This diagram represents the only (leading order) process
contributing to this decay. Strong interaction between the ${D}^{+}_{s}$ meson
and the pion lead to a non-factorisable contribution to the decay amplitude.

The measurement of the ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
branching fraction can also be used to estimate the ratio of the amplitudes of
the Cabibbo-suppressed ${{B}^{0}}\\!\rightarrow{{D}^{+}}{{\pi}^{-}}$ and the
Cabibbo-favoured ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decays,

$r_{D\pi}=\left|\frac{A({{B}^{0}}\\!\rightarrow{{D}^{+}}{{\pi}^{-}})}{A({{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}})}\right|,$
(2)

which is necessary for the measurement of charge-parity ($C\\!P$) asymmetries
in ${{B}^{0}}\\!\rightarrow{{D}^{\mp}}{{\pi}^{\pm}}$ decays [8, 9, 10, 11, 12,
13]. Assuming $\mathrm{SU}(3)$ flavour symmetry, Eq. (2) can be written as
[14, 15]

$r_{D\pi}=\tan{\theta_{c}}\frac{f_{{{D}^{+}}}}{f_{{{D}^{+}_{s}}}}\sqrt{\frac{{\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})}{{\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}})}},$
(3)

where $\theta_{c}$ is the Cabibbo angle and $f_{{{D}^{+}}}$ is the decay
constant of the ${{D}^{+}}$ meson. $\mathrm{SU}(3)$ symmetry breaking is
caused by different non-factorisable effects in in
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{+}}{{\pi}^{-}}$ decays.
This article presents measurements of
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})$ and
$r_{D\pi}$ using proton-proton ($pp$) collision data collected with the LHCb
detector at centre-of-mass energies of 7, 8 and 13  TeV corresponding to an
integrated luminosity of $5\text{\,fb}^{-1}$. The data samples recorded in the
years 2011 and 2012 (2015 and 2016) at 7 and 8 (13)  TeV will be referred to
as Run 1 (Run 2). The ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
branching ratio is measured relative to the
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ normalisation channel, which is
well measured and experimentally similar to the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay. The
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
(${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$) candidates are reconstructed
via the ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$
(${{D}^{-}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$) decay. The
branching fraction of the ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decay is determined by

${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})={\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}})\dfrac{N_{{{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}}}{N_{{{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}}}\dfrac{\epsilon_{{{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}}}{\epsilon_{{{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}}}\dfrac{{\mathcal{B}}({{D}^{-}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}})}{{\mathcal{B}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}})},$
(4)

where $N_{\rm{X}}$ denotes the selected candidate yield and
$\epsilon_{\rm{X}}$ the related efficiency for the decay mode X. In this
measurement extended maximum-likelihood fits to unbinned invariant mass
distributions are performed in order to obtain the yields, while the
efficiencies are obtained from simulated events and using calibration data
samples.
The relative production of ${B}^{0}_{s}$ and ${B}^{0}$ mesons, described by
the ratio $f_{s}/f_{d}$ where $f_{s}$ and $f_{d}$ are the ${{B}^{0}_{s}}$ and
${{B}^{0}}$ hadronisation fractions, is likely to depend on the $pp$ collision
energy [16]. The efficiency-corrected yield ratio $\cal R$,

$\mathcal{R}\equiv\dfrac{N_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}}}{N_{{{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}}}\dfrac{\epsilon_{{{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}}}{\epsilon_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}}}\propto\dfrac{f_{s}}{f_{d}},$
(5)

is proportional to the relative production ratio and its dependence on the
centre-of-mass energy is also reported here. This is measured using ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decays. Accurate knowledge
of $f_{s}/f_{d}$ is a crucial input for every ${{B}^{0}_{s}}$ branching
fraction measurement, e.g.
${\mathcal{B}}({{B}^{0}_{s}}\rightarrow\mu^{+}\mu^{-})$, since it dominates in
most cases the systematic uncertainty [17]. Following the method described in
Ref. [18], the value of $f_{s}/f_{d}$ can be calculated as

$\dfrac{f_{s}}{f_{d}}=0.982\dfrac{\tau_{B_{d}}}{\tau_{B_{s}}}\dfrac{\mathcal{R}}{\mathcal{N}_{a}\mathcal{N}_{F}\mathcal{N}_{E}}\dfrac{\mathcal{B}({{D}^{-}}\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}})}{\mathcal{B}({{D}^{+}_{s}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}})},$
(6)

where $\mathcal{R}$ is defined in Eq. (5), the numerical factor takes phase-
space effects into account, $\mathcal{N}_{a}$ describes non-factorisable SU(3)
breaking effects, $\mathcal{N}_{F}$ is the ratio of the form factors,
$\mathcal{N}_{E}$ takes into account the contribution of the $W$-exchange
diagram in the ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decay, and
$\tau_{B_{d}}\ (\tau_{B_{s}})$ is the ${B}^{0}$ (${B}^{0}_{s}$) lifetime.

##  2 Detector and simulation

The LHCb detector [19, 20] 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 [21], 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 [22, 23] 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 about 0.5% below 20$\text{\,Ge\kern-1.00006ptV\\!/}c$ to 1.0% at
200$\text{\,Ge\kern-1.00006ptV\\!/}c$. The minimum distance of a track to a
primary vertex (PV), the impact parameter (IP), 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 (RICH)
detectors [24]. 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 [25].
The online event selection is performed by a trigger [26], 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.
Simulation is required to calculate geometrical, reconstruction and selection
efficiencies, and to determine shapes of invariant mass distributions. In the
simulation, $pp$ collisions are generated using Pythia [27] with a specific
LHCb configuration [28]. Decays of unstable particles are described by EvtGen
[29], in which final-state radiation is generated using Photos [30]. The
interaction of the generated particles with the detector, and its response,
are implemented using the Geant4 toolkit [31, *Agostinelli:2002hh] as
described in Ref. [33].

##  3 Selection

The ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
(${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$) decays are reconstructed by
forming a ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$
(${{D}^{-}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$) candidate and
combining it with an additional pion of opposite charge, referred to as the
companion. The same reconstruction and selection procedure is applied to the
${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decay. For the ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay, the
invariant mass of the ${{K}^{+}}{{K}^{-}}$ pair is required to be within
$20\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ of the $\phi(1020)$ mass to select
only the ${{D}^{+}_{s}}\\!\rightarrow\phi(1020){{\pi}^{+}}$ decays, which
significantly improves the signal-to-background ratio compared to other decays
with a ${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ combination in the final state.
Selecting ${{D}^{+}_{s}}\\!\rightarrow\phi(1020){{\pi}^{+}}$ decays has an
efficiency of about $40\%$.
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 varied
between 3 and 4 GeV between 2011 and 2016. The software trigger requires a
two-, three- or four-track secondary vertex with significant displacement from
any primary $pp$ interaction vertex (PV). At least one charged particle must
have transverse momentum $p_{\mathrm{T}}>1.6\text{\,Ge\kern-1.00006ptV\\!/}c$
and be inconsistent with originating from a PV. A multivariate algorithm [34]
is used for the identification of secondary vertices consistent with the decay
of a $b$ hadron.
After the trigger selection, a preselection is applied to the reconstructed
candidates to ensure good quality for the quality of the $b$-hadron and
$c$-hadron candidates comprising of tracks with large total and transverse
momentum. Combinatorial background is suppressed using a gradient boosted
decision tree (BDTG) algorithm [35, 36], trained on Run 1 ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
data. A set of 15 variables is used to train the BDTG classifier, the most
relevant ones being the transverse momentum of the companion pion, the radial
flight distance of the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}$ and of the ${{D}^{+}_{s}}$
candidates, the minimum transverse momentum of the ${{D}^{+}_{s}}$ decay
products and the minimum $\chi^{2}_{\text{IP}}$ of the companion and the
${{\kern 1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}$ candidates, 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 particle under
consideration. The BDTG classifier used in this measurement is described in
Ref. [37].
To improve the ${B}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}$ invariant mass resolutions,
the ${D}^{+}_{s}$ and ${D}^{-}$ invariant masses are constrained to their
known values [38]. All ${{D}^{+}_{s}}{{\pi}^{-}}$ (${{D}^{-}}{{\pi}^{+}}$)
candidates are required to have their invariant masses,
$m({{D}^{+}_{s}}{{\pi}^{-}})$ ($m({{D}^{-}}{{\pi}^{+}})$), within the range
$5150\text{--}5800$ $(5000\text{--}5800)\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
and the ${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ (${{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$)
invariant mass within $1930\text{--}2065$
$(1830\text{--}1920)\text{\,Me\kern-1.00006ptV\\!/}c^{2}$. The range of the
${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ invariant mass includes a large upper sideband
to model properly the combinatorial background shape, as described in Sec. 4.
To reduce the background due to misidentified final-state particles, particle
identification (PID) information from the RICH detectors is used. The
companion pion is required to pass a strict PID requirement to reduce the
number of $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993pt{{B}^{0}_{s}}$}\\!\rightarrow{{D}^{+}_{s}}{{K}^{-}}$
(${{B}^{0}}\\!\rightarrow{{D}^{-}}{{K}^{+}}$) decays where the kaon companion
is misidentified as a pion. For
${{D}^{+}_{s}}\\!\rightarrow\phi(1020){{\pi}^{+}}$ candidates, loose PID
requirements are applied to both kaons and the pion. In the case of the pion,
it is used primarily to remove protons originating from the ${{\mathchar
28931\relax}^{+}_{c}}\rightarrow\phi p$ decay. Further PID requirements are
applied to veto ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow p{{K}^{-}}{{\pi}^{+}}){{\pi}^{-}}$ and
${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}}\\!\rightarrow{{D}^{+}}(\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}){{\pi}^{-}}$
and ${{\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}{}^{0}_{b}}\\!\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}{}^{-}_{c}}(\rightarrow{\overline{p}}{{K}^{+}}{{\pi}^{-}}){{\pi}^{+}}$
and
${{B}^{0}_{s}}\\!\rightarrow{{D}^{-}_{s}}(\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{-}}){{\pi}^{+}}$
events, which are misidentified as the final-state particles of
${{D}^{+}_{s}}(\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}){{\pi}^{-}}$ and
${{D}^{-}}(\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}){{\pi}^{+}}$ decays,
respectively. These vetoes are applied if candidates are consistent with the
above mentioned decays when a mass hypothesis is changed.
The event selection efficiencies are calculated from simulation with the
exception of the efficiency of the PID requirements which is determined using
calibration data samples.

##  4 Signal and background parametrisation

After the full event selection, unbinned maximum-likelihood fits are performed
to obtain the yields of the signal
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and the normalisation
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidates. A two-dimensional
fit to the ${{D}^{+}_{s}}{{\pi}^{-}}$ and the ${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$
invariant mass distributions is performed to determine the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal yield, while the
yield of the normalisation channel is obtained from a fit to the
${{D}^{-}}{{\pi}^{+}}$ invariant mass distribution. Due to the ${{D}^{+}_{s}}$
mass constraint, the correlation between $m({{D}^{+}_{s}}{{\pi}^{-}})$ and
$m({{K}^{+}}{{K}^{-}}{{\pi}^{+}})$ is found to be small, thus the two
variables are factorised in the fit model [37]. The two-dimensional fit is
performed in order to constrain the combinatorial background (see further in
this Section for details).
The ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay is Cabibbo-
suppressed and is therefore considerably less abundant than the Cabibbo-
favoured ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decay, which produces the same final-state particles. The
$m({{D}^{+}_{s}}{{\pi}^{-}})$ and $m({{D}^{-}}{{\pi}^{+}})$ shapes for
${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidates, respectively,
are described by the sum of a double-sided Hypatia function [39] and a Johnson
$S_{U}$ function [40]. The left tail of the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
invariant mass distribution overlaps with the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal peak and therefore
special attention is given to the description of the lower mass range of the
${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
peak, shaped by the combination of detector resolution and radiative effects.
The ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal is described with
the same model as the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decay, shifted by the known ${{B}^{0}}$–${{B}^{0}_{s}}$ mass difference [38].
The left tail of this distribution is described by two parameters, $a_{1}$ and
$n_{1}$, which are found to be correlated and therefore the parameter $n_{1}$
is fixed to the value obtained from simulation, whereas $a_{1}$ is obtained
from simulated ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ events, as well as from
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ data. In the invariant mass fit
to ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidates the common mean of
the double-sided Hypatia and the Johnson $S_{U}$ functions, the widths and the
left-tail parameter $a_{1}$ are left free in the fit, while the
${{D}^{+}_{s}}{{\pi}^{-}}$ invariant mass distribution contains too much
background to determine reliably the detailed shape of the radiative tail. All
other parameters are fixed from simulation. In the
${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ invariant mass fit a sum of two Crystal Ball
functions with a common mean is used. The common mean and a scale factor for
the widths are left free, while the other shape parameters are fixed from
simulation.
The combinatorial background in
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ candidates is split in two
components, referred to as random-${D}^{+}_{s}$ and true-${D}^{+}_{s}$. The
random-${D}^{+}_{s}$ combinatorial background consists of random combinations
of tracks that do not peak in the ${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ invariant
mass, while the true-${D}^{+}_{s}$ combinatorial background consists of events
with a true ${D}^{+}_{s}$ meson, combined with a random companion track. The
upper mass range of the ${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ candidate sample is
used to account accurately for the random-${{D}^{+}_{s}}$ component, modelled
with a single exponential distribution, while the true-${{D}^{+}_{s}}$
background is described by the signal shape. In the ${D}^{+}_{s}$ ${\pi}^{-}$
invariant mass fit, the random-${{D}^{+}_{s}}$ background is described by an
exponential distribution and the true-${{D}^{+}_{s}}$ background is described
by the sum of an exponential and a constant function. The exponential
parameters are left free in both invariant mass fits.
The combinatorial background in the $m({{D}^{-}}{{\pi}^{+}})$ fit of the
normalisation channel is described by the sum of an exponential and a constant
function, with the relative weight of the two functions and exponential
parameter left free.
Decays where one or more final-state particles are not reconstructed are
referred to as partially reconstructed backgrounds. In the
${{D}^{+}_{s}}{{\pi}^{-}}$ and ${{D}^{-}}{{\pi}^{+}}$ invariant mass fits
these background contributions are described by an upward-open parabola or a
parabola exhibiting a maximum, whose ranges are defined by the kinematic
endpoints of the decay, which are convolved with Gaussian resolution
functions, and which are known to describe decays involving a missing neutral
pion or a missing photon, as defined in Ref. [41]. In the fit to the
${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ invariant mass, the partially reconstructed
background contributions are described by the signal mass shape.
The $m({{D}^{+}_{s}}{{\pi}^{-}})$ fit requires two partially reconstructed
background components from ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{*+}_{s}}(\rightarrow{{D}^{+}_{s}}\gamma/{{\pi}^{0}}){{\pi}^{-}}$
and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\rho}^{-}}(\rightarrow{{\pi}^{-}}{{\pi}^{0}})$
decays. The fit model describing the ${{D}^{-}}{{\pi}^{+}}$ invariant mass
accounts analogously for two partially reconstructed background contributions:
${{B}^{0}}\\!\rightarrow{{D}^{*-}}(\rightarrow{{D}^{-}}{{\pi}^{0}}){{\pi}^{+}}$
and
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\rho}^{+}}(\rightarrow{{\pi}^{+}}{{\pi}^{0}})$.
In the case of the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{*+}_{s}}{{\pi}^{-}}$
background the previously mentioned upward-open parabola together with a
parabola exhibiting a maximum is used to parameterise the components with
${{D}^{*+}_{s}}\rightarrow{{D}^{+}_{s}}\gamma$ and
${{D}^{*+}_{s}}\rightarrow{{D}^{+}_{s}}{{\pi}^{0}}$ decays, respectively. The
${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\rho}^{-}}$
background is described by the upward-open parabola, to take into account the
missing neutral pion. The ${{B}^{0}}\\!\rightarrow{{D}^{*-}}{{\pi}^{+}}$ decay
uses an upward-open parabola function and exhibits a double-peaked shape. Most
parameters are obtained from simulated events and fixed, aside from the
relevant invariant mass shifts and widths. For the
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\rho}^{+}}$ background a single upward-open
parabola function is taken, with a floating width and a floating mass shift
parameter that is shared with the
${{B}^{0}}\\!\rightarrow{{D}^{*-}}{{\pi}^{+}}$ contribution. The widths of the
partially reconstructed background contributions in the
$m({{D}^{+}_{s}}{{\pi}^{-}})$ fits are fixed to the values obtained from
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidates in data, corrected
for differences between the $m({{D}^{+}_{s}}{{\pi}^{-}})$ and
$m({{D}^{-}}{{\pi}^{+}})$ distributions, as obtained from simulation.
The ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidate sample is
contaminated by the ${{B}^{0}_{s}}\rightarrow{{D}^{-}_{s}}{{\pi}^{+}}$,
${{\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}{}^{0}_{b}}\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}{}^{-}_{c}}{{\pi}^{+}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{K}^{+}}$ decays, resulting from the
misidentification of one or two of the final-state particles. Analogously, the
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex] $\kern-1.79993pt{{B}^{0}_{s}}$}\\!\rightarrow{{D}^{+}_{s}}{{K}^{-}}$,
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{\pi}^{-}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}}\rightarrow{{D}^{+}}{{\pi}^{-}}$
decays are misidentified background contributions of the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ candidate sample. Their
shapes are determined from simulation using a non-parametric kernel estimation
method [42]. The yields of the misidentified background contributions are
estimated by using known branching fractions [38] and efficiencies that are
determined from simulated background decays. Each yield of a misidentified
background in the fit model is constrained to be close to its estimated value
and is allowed to vary within the corresponding uncertainty.

##  5 Signal yields

The $m({{D}^{-}}{{\pi}^{+}})$ data distributions, with overlaid fit
projections for the total, the ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$
signal and the background components, are shown in Fig. 2. The resulting
signal yields are $(4.971\pm 0.013)\times 10^{5}$ and $(6.294\pm 0.016)\times
10^{5}$ for Run 1 and Run 2 samples, respectively. The fit results are also
used to constrain the left tail of the signal shape and the widths of the
partially reconstructed backgrounds to the invariant mass distribution of
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ candidates.
The two-dimensional fit to ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
candidates is performed in the ${{D}^{+}_{s}}{{\pi}^{-}}$ and
${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ invariant mass distributions. The
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ branching fraction is
determined using the yields of the signal and normalisation modes, their
selection efficiencies and the known
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$,
${{D}^{-}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$ and
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ branching fractions
[38]. The two-dimensional fit is performed simultaneously for Run 1 and Run 2
data samples in which the
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})$ and left-tail
parameter are shared. The fit results in
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal yields of $(8.9\pm
0.8)\times 10^{2}$ and $(1.12\pm 0.11)\times 10^{3}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
yields of $(3.370\pm 0.023)\times 10^{4}$ and $(4.647\pm 0.027)\times 10^{4}$
for Run 1 and Run 2 samples, respectively. Figure 3 shows the
${{D}^{+}_{s}}{{\pi}^{-}}$ invariant mass distributions together with the fit
projections and background contributions overlaid. Additionally, the invariant
mass fits to ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ candidates are performed
simultaneously to 2011, 2012 and Run 2 data in order to study the collision
energy dependence of $f_{s}/f_{d}$, as is described in Sec. 7.

Figure 2: The invariant mass distributions of normalisation
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidates, for (left) Run 1 and
(right) Run 2 data samples. Overlaid are the fit projections along with the
signal and background contributions.

Figure 3: The (top) ${{D}^{+}_{s}}{{\pi}^{-}}$ and (bottom)
${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ invariant mass distributions of signal
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ candidates, for (left) Run 1
and (right) Run 2 data samples. Overlaid are the fit projections along with
the signal and background contributions.

##  6 Systematic uncertainties

Systematic uncertainties on the
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})$ measurement
arise from choices in the fit model and the determination of trigger, BDT and
PID efficiencies. Many possible sources of systematic uncertainty cancel in
the ratio of either the yields or the efficiencies of
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ events. A summary of all the
systematic uncertainties is shown in Table 1. The precision of the measurement
relies mostly on the accurate modelling of the signal shape and of the
partially reconstructed backgrounds.
A systematic uncertainty is assigned for the assumption of the signal shape.
This is done by repeating the signal fit with a different parametrisation,
i.e. the sum of a double-sided Hypatia function and a Gaussian function. This
parametrisation was found to be the only alternative parametrisation that
satisfactorily described simulated signal candidates. Furthermore, a
systematic uncertainty is assigned by fixing the mean of the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal shape to the result
of the ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ fit, rather than shifting
by the known ${{B}^{0}}$–${{B}^{0}_{s}}$ mass difference. Moreover, the width
of the ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal shape is
scaled by the ratio of the known ${{B}^{0}}$ and ${{B}^{0}_{s}}$ masses. The
widths of the partially reconstructed backgrounds is varied by $\pm
1\text{\,Me\kern-1.00006ptV\\!/}c^{2}$, in order to cover the differences
between data and simulation as well as the differences between the
${{D}^{+}_{s}}{{\pi}^{-}}$ and ${{D}^{-}}{{\pi}^{+}}$ invariant mass
distributions. The resulting difference between the signal yields is assigned
as a systematic uncertainty.
The simulated samples are corrected for an imperfect modelling of the response
of the particle identification algorithms as a function of the kinematical
properties of the particle, using samples of ${{D}^{*+}}$ calibration data. A
systematic uncertainty associated with the PID efficiency evaluation is
assigned by varying the corrections within their uncertainties. Proton
misidentification is the most difficult to control accurately from data
calibration samples. Thus a systematic uncertainty is estimated from the
difference between the nominal signal yields and a fit where the misidentified
background ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{\pi}^{-}}$ decay yield is left free to vary.
The systematic uncertainty assigned to the hardware trigger efficiency takes
into account a difference in detection efficiency between kaons and pions.
This mostly cancels in the ratio of
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ efficiencies, but the
difference of one final-state particle is sensitive to this detection
asymmetry. Moreover, an uncertainty related to the reconstruction efficiency
of charged particles is taken into account, which mainly arises from the
uncertainty on the LHCb material and the different interaction cross-section
of pions and kaons with the material [43]. Additionally, a systematic
uncertainty is determined on the BDT efficiency due to the difference between
simulation and data. This is determined by weighting all the BDT input
variables in the simulated signal sample to the signal distributions in data,
which are obtained using signal weights for each candidate using the sPlot
technique [44].

Table 1: Relative systematic uncertainty $\sigma$ on the ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ branching fraction measurement. Source |  $\sigma({\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})$) [%]
---|---
Fit model |
Signal shape parametrisation | $5.1$
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal width | $1.5$
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ mean | $0.2$
Partially reconstructed backgrounds | $4.2$
Misidentified backgrounds | $0.6$
Efficiencies |
Hardware trigger efficiency | $0.3$
Reconstruction efficiency | $0.5$
BDT efficiency | $0.7$
PID efficiency | $1.1$
Total | $6.9$

The systematic uncertainties on the collision energy dependence of the
efficiency-corrected ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ yield ratios are shown in
Table 2. The sources of these systematic uncertainties are the same as for the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ branching fraction.
Exceptions are the uncertainties on the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ signal and the partially
reconstructed backgrounds, which are found to be negligible, and the
uncertainty on the charged-particle reconstruction efficiency, which cancels
out in the double ratio of efficiencies.

Table 2: Relative systematic uncertainty $\sigma$ on the ratio of the efficiency-corrected ${{\kern 1.61993pt\overline{\kern-1.61993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ yield ratios. The ratios $\mathcal{R}_{13\text{\,Te\kern-0.63004ptV}}/\mathcal{R}_{7\text{\,Te\kern-0.63004ptV}}$ and $\mathcal{R}_{13\text{\,Te\kern-0.63004ptV}}/\mathcal{R}_{8\text{\,Te\kern-0.63004ptV}}$ are reported together as the difference of the systematic uncertainty for 7 and 8  TeV is negligible. Source |  $\sigma\left(\dfrac{\mathcal{R}_{13\text{\,Te\kern-0.70004ptV}}}{{\mathcal{R}_{7,8\text{\,Te\kern-0.70004ptV}}}}\right)$ [%] |  $\sigma\left(\dfrac{\mathcal{R}_{8\text{\,Te\kern-0.70004ptV}}}{\mathcal{R}_{7\text{\,Te\kern-0.70004ptV}}}\right)$ [%]
---|---|---
Fit model |  |
Signal shape parametrisation | $0.2$ | –
Misidentified backgrounds | $0.2$ | –
Efficiencies |  |
Hardware trigger efficiency | $0.4$ | $0.4$
BDT efficiency | $1.1$ | $1.3$
PID efficiency | $1.4$ | $1.4$
Total | $1.9$ | $2.0$

##  7 Results

Table 3 gathers all measurements and inputs to determine the branching
fraction according to Eq. (4).

Table 3: Results of ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ signal efficiencies and yields, as well as the branching fractions used as input for this measurement [38]. | Run 1 | Run 2
---|---|---
$\epsilon_{{{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}}$ ($\%$) | $0.1412\pm 0.0010$ | $0.1922\pm 0.0012$
$\epsilon_{{{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}}$ ($\%$) | $0.3485\pm 0.0016$ | $0.4536\pm 0.0016$
$N_{{{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}}$ |  $(4.971\pm 0.013)\times 10^{5}$ |  $(6.294\pm 0.016)\times 10^{5}$
$N_{{{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}}$ |  $(8.9\pm 0.8)\times 10^{2}$ |  $(1.12\pm 0.11)\times 10^{3}$
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}})$ | $(2.52\pm 0.13)\times 10^{-3}$
${\mathcal{B}}({{D}^{-}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}})$ | $(9.38\pm 0.16)\times 10^{-2}$
${\mathcal{B}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}})$ | $(5.39\pm 0.15)\times 10^{-2}$

The branching fraction ratio of
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decays is found to be

$\frac{{\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})}{{\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}})}=(7.7\pm
0.7\pm 0.5\pm 0.3)\times 10^{-3},$

where the first uncertainty is statistical, the second systematic and the
third stems from knowledge of the
${{D}^{-}}\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$ and
${{D}^{-}_{s}}\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{-}}$ branching fractions.
Using the known value of
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}})$ [38], the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ branching fraction is found
to be

${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})=(19.4\pm
1.8\pm 1.3\pm 1.2)\times 10^{-6},$

where the first uncertainty is statistical, the second systematic and the
third refers to the uncertainty due to the branching fractions listed in Table
3. This result represents the most precise single measurement of
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})$ to date.
The ${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ branching fraction
depends on both $|a_{\text{NF}}|$ and $|{V_{{u}{b}}}|$. Using the measurement
of ${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})$, the
product

$|V_{ub}||a_{\text{NF}}|=(3.14\pm 0.20\pm 0.25)\times 10^{-3}$

is obtained, where the first uncertainty is from the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ branching fraction
measurement and the second from the CKM and QCD parameters. The form factor
$F({{B}^{0}}\rightarrow{{\pi}^{-}})|_{q^{2}=m^{2}_{{{D}^{+}_{s}}}}=0.327\pm
0.025$ is obtained using light-cone sum rules [3, 4] and lattice QCD
calculations are used for the decay constant $f_{{{D}^{+}_{s}}}=0.2499\pm
0.0005\text{\,Ge\kern-1.00006ptV}$ [5, 6]. A phase-space factor $\Phi=296.2\pm
0.8\text{\,Ge\kern-1.00006ptV}^{-2}$ is used in order to relate the branching
fraction to $|{V_{{u}{b}}}||a_{\text{NF}}|$. Additionally, the CKM matrix
element $|V_{cs}|$ is well measured and used as an input [38]. The
determination of $|{V_{{u}{b}}}||a_{\text{NF}}|$ can be compared to the known
inclusive and exclusive determinations of $|{V_{{u}{b}}}|$ to provide a
constraint on the $|a_{\text{NF}}|$ parameter as displayed in Fig. 4.

Figure 4: Result of the determination of $|V_{ub}||a_{\text{NF}}|$. The blue
line represents the result of this measurement, the vertical bands are the
known exclusive and inclusive measurements of $|V_{ub}|$, which are $(3.70\pm
0.16)\times 10^{-3}$ and $(4.49\pm 0.28)\times 10^{-3}$, respectively [38].
The horizontal dashed line at $|a_{\text{NF}}|=1.0$ represents exact
factorisation. The error bands represent an uncertainty of one standard
deviation.

The branching fraction ratio of
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decays can be used to determine
the parameter $r_{D\pi}$, as shown in Eq. (3). Inserting the measured
branching fraction ratio
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})/{\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}})$,
the tangent of $\theta_{c}$ [38] and the fraction between the decay constants
$f_{{{D}^{+}_{s}}}$ and $f_{{{D}^{+}}}$ [5, 6] into Eq. (3) gives

$r_{D\pi}=0.0163\pm 0.0011\pm 0.0033,$

where the first uncertainty arises from the uncertainties propagated from Eq.
(3) and the second from possible non-factorisable $\mathrm{SU}(3)$-breaking
effects, estimated to be $20\%$ according to Ref. [12].
$\mathrm{SU}(3)$-breaking effects of about $20\%$ are consistent with the
measured $|a_{\text{NF}}|$ in this analysis, see Fig. 4.
Finally, the potential dependence of the hadronisation fraction $f_{s}/f_{d}$
on collision energy is probed using the
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
signal yields obtained in the invariant mass fits, using Eq. (5). To determine
these, the fit to Run 1 data is split based on collision energy into 2011
($7\text{\,Te\kern-1.00006ptV}$) and 2012 ($8\text{\,Te\kern-1.00006ptV}$),
sharing the shape parameters. The measured double ratios for the different
collision energies are

$\displaystyle\mathcal{R}_{13\text{\,Te\kern-0.70004ptV}}/\mathcal{R}_{7\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=1.020\pm 0.013\pm 0.021,$
$\displaystyle\mathcal{R}_{13\text{\,Te\kern-0.70004ptV}}/\mathcal{R}_{8\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=1.035\pm 0.011\pm 0.021,$
$\displaystyle\mathcal{R}_{8\text{\,Te\kern-0.70004ptV}}/\mathcal{R}_{7\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=0.986\pm 0.013\pm 0.021,$

where the first uncertainty is statistical and the second systematic. The
average transverse momentum of the $B$ meson after full event selection is
found to be $10.4$, $10.6$ and $10.9\text{\,Ge\kern-1.00006ptV\\!/}c$ for $pp$
collision centre-of-mass energies of $7\text{\,Te\kern-1.00006ptV}$,
$8\text{\,Te\kern-1.00006ptV}$ and $13\text{\,Te\kern-1.00006ptV}$,
respectively. The separate values of $\mathcal{R}$ at the three collision
energies are

$\displaystyle\mathcal{R}_{7\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=0.1631\pm 0.0018\pm 0.0025\pm 0.0014,$
$\displaystyle\mathcal{R}_{8\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=0.1609\pm 0.0013\pm 0.0024\pm 0.0014,$
$\displaystyle\mathcal{R}_{13\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=0.1665\pm 0.0011\pm 0.0023\pm 0.0012,$

where the first uncertainty is statistical and the following are the
uncorrelated and correlated systematic uncertainties, respectively. The value
of $\mathcal{R}$ at $7\text{\,Te\kern-1.00006ptV}$ shows good agreement with
the previous hadronic $f_{s}/f_{d}$ measurement at
$7\text{\,Te\kern-1.00006ptV}$, which was performed using ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$,
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{K}^{+}}$ decays [45]. A visualisation of
the dependence of $\mathcal{R}$ on the centre-of-mass energy is given in Fig.
5. The resulting centre-of-mass energy dependence is obtained from a linear
fit using the statistical and uncorrelated systematic uncertainties and is
found to be $\mathcal{R}=0.156(6)+0.0008(6)\sqrt{s}$, where $\sqrt{s}$ is in
TeV. The observed trend is in agreement with the LHCb measurement of the
$f_{s}/f_{u}$ dependence upon the $pp$ collision energy [16].

Figure 5: Visualisation of the $pp$ collision energy dependence of the
efficiency-corrected yield ratio of ${{\kern
1.61993pt\overline{\kern-1.61993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decays, which scales with
$f_{s}/f_{d}$. The inner error bars indicate the statistical uncertainty only,
whereas the outer indicate the uncorrelated, including statistical,
uncertainties. The correlated systematic uncertainty is not shown. The red
dotted line represents a linear fit through the three values of $\mathcal{R}$
with uncorrelated, including statistical, uncertainties.

The values for $\mathcal{R}$ will be used in a future work and can be used to
obtain $f_{s}/f_{d}$ by correcting $\mathcal{R}$ for the relative $D$
branching fractions, the ratio of $B$ lifetimes, the form factor ratio, the
contribution from non-factorisable SU(3)-breaking effects and the contribution
from the exchange diagram, as given by Eq. (6).

##  8 Summary

A branching fraction measurement of the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decay is performed using
$pp$ collision data taken between 2011 and 2016, leading to

${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})=(19.4\pm
1.8\pm 1.3\pm 1.2)\times 10^{-6},$

where the first uncertainty is statistical, the second systematic and the
third is due the branching fractions used as normalisation inputs. This is the
most precise single measurement of
${\mathcal{B}}({{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})$ to date, and
is in agreement with the current world average [38]. Using this branching
fraction, the product of $|{V_{{u}{b}}}|$ and the non-factorisation constant
$|a_{\text{NF}}|$ is determined to be

$|{V_{{u}{b}}}||a_{\text{NF}}|=(3.14\pm 0.32)\times 10^{-3}.$

Comparison with independently measured values of ${V_{{u}{b}}}$ [38] indicate
that $|a_{\text{NF}}|$ may deviate from unity by around $20\%$, indicating
significant non-factorisable corrections.
The measurement of the ratio of the
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ branching fractions is used to
determine the $r_{D\pi}$ parameter,

$r_{D\pi}=0.0163\pm 0.0011\pm 0.0033,$

where the first uncertainty comes from the uncertainties propagated from Eq.
(3) and the second comes from possible non-factorisable
$\mathrm{SU}(3)$-breaking effects, estimated to be $20\%$ [12]. Knowledge of
this parameter is essential to interpret the $C\\!P$ asymmetries in
${{B}^{0}}\\!\rightarrow{{D}^{\mp}}{{\pi}^{\pm}}$ decays.
Finally, the efficiency-corrected yield ratio of ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
and ${{B}^{0}}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ decays, $\mathcal{R}$, is
used to probe the collision energy dependence of the hadronisation fraction
$f_{s}/f_{d}$.

## 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 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); A*MIDEX, ANR, Labex P2IO
and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Program of
Frontier Sciences of CAS, CAS PIFI, Thousand Talents Program, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Royal Society and the Leverhulme Trust (United
Kingdom).

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LHCb collaboration

R. Aaij32, C. Abellán Beteta50, T. Ackernley60, B. Adeva46, M. Adinolfi54, H.
Afsharnia9, C.A. Aidala85, S. Aiola25, Z. Ajaltouni9, S. Akar65, J.
Albrecht15, F. Alessio48, M. Alexander59, A. Alfonso Albero45, Z. Aliouche62,
G. Alkhazov38, P. Alvarez Cartelle55, S. Amato2, Y. Amhis11, L. An48, L.
Anderlini22, A. Andreianov38, M. Andreotti21, F. Archilli17, A. Artamonov44,
M. Artuso68, K. Arzymatov42, E. Aslanides10, M. Atzeni50, B. Audurier12, S.
Bachmann17, M. Bachmayer49, J.J. Back56, S. Baker61, P. Baladron Rodriguez46,
V. Balagura12, W. Baldini21, J. Baptista Leite1, R.J. Barlow62, S. Barsuk11,
W. Barter61, M. Bartolini24,g, F. Baryshnikov82, J.M. Basels14, G. Bassi29, B.
Batsukh68, A. Battig15, A. Bay49, M. Becker15, F. Bedeschi29, I. Bediaga1, A.
Beiter68, V. Belavin42, S. Belin27, V. Bellee49, K. Belous44, I. Belov40, I.
Belyaev41, G. Bencivenni23, E. Ben-Haim13, A. Berezhnoy40, R. Bernet50, D.
Berninghoff17, H.C. Bernstein68, C. Bertella48, A. Bertolin28, C.
Betancourt50, F. Betti20,c, Ia. Bezshyiko50, S. Bhasin54, J. Bhom35, L.
Bian73, M.S. Bieker15, S. Bifani53, P. Billoir13, M. Birch61, F.C.R. Bishop55,
A. Bizzeti22,j, M. Bjørn63, M.P. Blago48, T. Blake56, F. Blanc49, S. Blusk68,
D. Bobulska59, J.A. Boelhauve15, O. Boente Garcia46, T. Boettcher64, A.
Boldyrev81, A. Bondar43, N. Bondar38, S. Borghi62, M. Borisyak42, M.
Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V. Bowcock60, A. Boyer48, C.
Bozzi21, M.J. Bradley61, S. Braun66, A. Brea Rodriguez46, M. Brodski48, J.
Brodzicka35, A. Brossa Gonzalo56, D. Brundu27, A. Buonaura50, C. Burr48, A.
Bursche27, A. Butkevich39, J.S. Butter32, J. Buytaert48, W. Byczynski48, S.
Cadeddu27, H. Cai73, R. Calabrese21,e, L. Calefice15,13, L. Calero Diaz23, S.
Cali23, R. Calladine53, M. Calvi26,i, M. Calvo Gomez84, P. Camargo
Magalhaes54, A. Camboni45,84, P. Campana23, A.F. Campoverde Quezada6, S.
Capelli26,i, L. Capriotti20,c, A. Carbone20,c, G. Carboni31, R. Cardinale24,g,
A. Cardini27, I. Carli4, P. Carniti26,i, K. Carvalho Akiba32, A. Casais
Vidal46, G. Casse60, M. Cattaneo48, G. Cavallero48, S. Celani49, J.
Cerasoli10, A.J. Chadwick60, M.G. Chapman54, M. Charles13, Ph. Charpentier48,
G. Chatzikonstantinidis53, C.A. Chavez Barajas60, M. Chefdeville8, C. Chen3,
S. Chen27, A. Chernov35, S.-G. Chitic48, V. Chobanova46, S. Cholak49, M.
Chrzaszcz35, A. Chubykin38, V. Chulikov38, P. Ciambrone23, M.F. Cicala56, X.
Cid Vidal46, G. Ciezarek48, P.E.L. Clarke58, M. Clemencic48, H.V. Cliff55, J.
Closier48, J.L. Cobbledick62, V. Coco48, J.A.B. Coelho11, J. Cogan10, E.
Cogneras9, L. Cojocariu37, P. Collins48, T. Colombo48, L. Congedo19,b, A.
Contu27, N. Cooke53, G. Coombs59, G. Corti48, C.M. Costa Sobral56, B.
Couturier48, D.C. Craik64, J. Crkovská67, M. Cruz Torres1, R. Currie58, C.L.
Da Silva67, E. Dall’Occo15, J. Dalseno46, C. D’Ambrosio48, A. Danilina41, P.
d’Argent48, A. Davis62, O. De Aguiar Francisco62, K. De Bruyn78, S. De
Capua62, M. De Cian49, J.M. De Miranda1, L. De Paula2, M. De Serio19,b, D. De
Simone50, P. De Simone23, J.A. de Vries79, C.T. Dean67, D. Decamp8, L. Del
Buono13, B. Delaney55, H.-P. Dembinski15, A. Dendek34, V. Denysenko50, D.
Derkach81, O. Deschamps9, F. Desse11, F. Dettori27,d, B. Dey73, P. Di Nezza23,
S. Didenko82, L. Dieste Maronas46, H. Dijkstra48, V. Dobishuk52, A.M.
Donohoe18, F. Dordei27, A.C. dos Reis1, L. Douglas59, A. Dovbnya51, A.G.
Downes8, K. Dreimanis60, M.W. Dudek35, L. Dufour48, V. Duk77, P. Durante48,
J.M. Durham67, D. Dutta62, M. Dziewiecki17, A. Dziurda35, A. Dzyuba38, S.
Easo57, U. Egede69, V. Egorychev41, S. Eidelman43,u, S. Eisenhardt58, S. Ek-
In49, L. Eklund59,v, S. Ely68, A. Ene37, E. Epple67, S. Escher14, J. Eschle50,
S. Esen32, T. Evans48, A. Falabella20, J. Fan3, Y. Fan6, B. Fang73, N.
Farley53, S. Farry60, D. Fazzini26,i, P. Fedin41, M. Féo48, P. Fernandez
Declara48, A. Fernandez Prieto46, J.M. Fernandez-tenllado Arribas45, F.
Ferrari20,c, L. Ferreira Lopes49, F. Ferreira Rodrigues2, S. Ferreres Sole32,
M. Ferrillo50, M. Ferro-Luzzi48, S. Filippov39, R.A. Fini19, M. Fiorini21,e,
M. Firlej34, K.M. Fischer63, C. Fitzpatrick62, T. Fiutowski34, F. Fleuret12,
M. Fontana13, F. Fontanelli24,g, R. Forty48, V. Franco Lima60, M. Franco
Sevilla66, M. Frank48, E. Franzoso21, G. Frau17, C. Frei48, D.A. Friday59, J.
Fu25, Q. Fuehring15, W. Funk48, E. Gabriel32, T. Gaintseva42, A. Gallas
Torreira46, D. Galli20,c, S. Gambetta58,48, Y. Gan3, M. Gandelman2, P.
Gandini25, Y. Gao5, M. Garau27, L.M. Garcia Martin56, P. Garcia Moreno45, J.
García Pardiñas26, B. Garcia Plana46, F.A. Garcia Rosales12, L. Garrido45, C.
Gaspar48, R.E. Geertsema32, D. Gerick17, L.L. Gerken15, E. Gersabeck62, M.
Gersabeck62, T. Gershon56, D. Gerstel10, Ph. Ghez8, V. Gibson55, M.
Giovannetti23,o, A. Gioventù46, P. Gironella Gironell45, L. Giubega37, C.
Giugliano21,e,48, K. Gizdov58, E.L. Gkougkousis48, V.V. Gligorov13, C.
Göbel70, E. Golobardes84, D. Golubkov41, A. Golutvin61,82, A. Gomes1,a, S.
Gomez Fernandez45, F. Goncalves Abrantes70, M. Goncerz35, G. Gong3, P.
Gorbounov41, I.V. Gorelov40, C. Gotti26,i, E. Govorkova48, J.P. Grabowski17,
R. Graciani Diaz45, T. Grammatico13, L.A. Granado Cardoso48, E. Graugés45, E.
Graverini49, G. Graziani22, A. Grecu37, L.M. Greeven32, P. Griffith21,e, L.
Grillo62, S. Gromov82, B.R. Gruberg Cazon63, C. Gu3, M. Guarise21, P. A.
Günther17, E. Gushchin39, A. Guth14, Y. Guz44,48, T. Gys48, T. Hadavizadeh69,
G. Haefeli49, C. Haen48, J. Haimberger48, T. Halewood-leagas60, P.M.
Hamilton66, Q. Han7, X. Han17, T.H. Hancock63, S. Hansmann-Menzemer17, N.
Harnew63, T. Harrison60, C. Hasse48, M. Hatch48, J. He6, M. Hecker61, K.
Heijhoff32, K. Heinicke15, A.M. Hennequin48, K. Hennessy60, L. Henry25,47, J.
Heuel14, A. Hicheur2, D. Hill49, M. Hilton62, S.E. Hollitt15, J. Hu72, J.
Hu17, W. Hu7, W. Huang6, X. Huang73, W. Hulsbergen32, R.J. Hunter56, M.
Hushchyn81, D. Hutchcroft60, D. Hynds32, P. Ibis15, M. Idzik34, D. Ilin38, P.
Ilten65, A. Inglessi38, A. Ishteev82, K. Ivshin38, R. Jacobsson48, S.
Jakobsen48, E. Jans32, B.K. Jashal47, A. Jawahery66, V. Jevtic15, M.
Jezabek35, F. Jiang3, M. John63, D. Johnson48, C.R. Jones55, T.P. Jones56, B.
Jost48, N. Jurik48, S. Kandybei51, Y. Kang3, M. Karacson48, N. Kazeev81, F.
Keizer55,48, M. Kenzie56, T. Ketel33, B. Khanji15, A. Kharisova83, S.
Kholodenko44, K.E. Kim68, T. Kirn14, V.S. Kirsebom49, O. Kitouni64, S.
Klaver32, K. Klimaszewski36, S. Koliiev52, A. Kondybayeva82, A.
Konoplyannikov41, P. Kopciewicz34, R. Kopecna17, P. Koppenburg32, M.
Korolev40, I. Kostiuk32,52, O. Kot52, S. Kotriakhova38,30, P. Kravchenko38, L.
Kravchuk39, R.D. Krawczyk48, M. Kreps56, F. Kress61, S. Kretzschmar14, P.
Krokovny43,u, W. Krupa34, W. Krzemien36, W. Kucewicz35,s, M. Kucharczyk35, V.
Kudryavtsev43,u, H.S. Kuindersma32, G.J. Kunde67, T. Kvaratskheliya41, D.
Lacarrere48, G. Lafferty62, A. Lai27, A. Lampis27, D. Lancierini50, J.J.
Lane62, R. Lane54, G. Lanfranchi23, C. Langenbruch14, J. Langer15, O.
Lantwin50,82, T. Latham56, F. Lazzari29,p, R. Le Gac10, S.H. Lee85, R.
Lefèvre9, A. Leflat40, S. Legotin82, O. Leroy10, T. Lesiak35, B.
Leverington17, H. Li72, L. Li63, P. Li17, Y. Li4, Y. Li4, Z. Li68, X. Liang68,
T. Lin61, R. Lindner48, V. Lisovskyi15, R. Litvinov27, G. Liu72, H. Liu6, S.
Liu4, X. Liu3, A. Loi27, J. Lomba Castro46, I. Longstaff59, J.H. Lopes2, G.
Loustau50, G.H. Lovell55, Y. Lu4, D. Lucchesi28,k, S. Luchuk39, M. Lucio
Martinez32, V. Lukashenko32, Y. Luo3, A. Lupato62, E. Luppi21,e, O. Lupton56,
A. Lusiani29,l, X. Lyu6, L. Ma4, S. Maccolini20,c, F. Machefert11, F.
Maciuc37, V. Macko49, P. Mackowiak15, S. Maddrell-Mander54, O. Madejczyk34,
L.R. Madhan Mohan54, O. Maev38, A. Maevskiy81, D. Maisuzenko38, M.W.
Majewski34, S. Malde63, B. Malecki48, A. Malinin80, T. Maltsev43,u, H.
Malygina17, G. Manca27,d, G. Mancinelli10, R. Manera Escalero45, D.
Manuzzi20,c, D. Marangotto25,h, J. Maratas9,r, J.F. Marchand8, U. Marconi20,
S. Mariani22,f,48, C. Marin Benito11, M. Marinangeli49, P. Marino49,l, J.
Marks17, P.J. Marshall60, G. Martellotti30, L. Martinazzoli48,i, M.
Martinelli26,i, D. Martinez Santos46, F. Martinez Vidal47, A. Massafferri1, M.
Materok14, R. Matev48, A. Mathad50, Z. Mathe48, V. Matiunin41, C. Matteuzzi26,
K.R. Mattioli85, A. Mauri32, E. Maurice12, J. Mauricio45, M. Mazurek36, M.
McCann61, L. Mcconnell18, T.H. Mcgrath62, A. McNab62, R. McNulty18, J.V.
Mead60, B. Meadows65, C. Meaux10, G. Meier15, N. Meinert76, D. Melnychuk36, S.
Meloni26,i, M. Merk32,79, A. Merli25, L. Meyer Garcia2, M. Mikhasenko48, D.A.
Milanes74, E. Millard56, M. Milovanovic48, M.-N. Minard8, L. Minzoni21,e, S.E.
Mitchell58, B. Mitreska62, D.S. Mitzel48, A. Mödden 15, R.A. Mohammed63, R.D.
Moise61, T. Mombächer15, I.A. Monroy74, S. Monteil9, M. Morandin28, G.
Morello23, M.J. Morello29,l, J. Moron34, A.B. Morris75, A.G. Morris56, R.
Mountain68, H. Mu3, F. Muheim58, M. Mukherjee7, 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,e,
N. Neri25,h, S. Neubert75, N. Neufeld48, R. Newcombe61, T.D. Nguyen49, C.
Nguyen-Mau49,w, E.M. Niel11, S. Nieswand14, N. Nikitin40, N.S. Nolte48, C.
Nunez85, A. Oblakowska-Mucha34, V. Obraztsov44, D.P. O’Hanlon54, R.
Oldeman27,d, M.E. Olivares68, C.J.G. Onderwater78, A. Ossowska35, J.M. Otalora
Goicochea2, T. Ovsiannikova41, P. Owen50, A. Oyanguren47, B. Pagare56, P.R.
Pais48, T. Pajero29,l,48, A. Palano19, M. Palutan23, Y. Pan62, G. Panshin83,
A. Papanestis57, M. Pappagallo19,b, L.L. Pappalardo21,e, C. Pappenheimer65, W.
Parker66, C. Parkes62, C.J. Parkinson46, B. Passalacqua21, G. Passaleva22, A.
Pastore19, M. Patel61, C. Patrignani20,c, C.J. Pawley79, A. Pearce48, A.
Pellegrino32, M. Pepe Altarelli48, S. Perazzini20, D. Pereima41, P. Perret9,
K. Petridis54, A. Petrolini24,g, A. Petrov80, S. Petrucci58, M. Petruzzo25, A.
Philippov42, L. Pica29, M. Piccini77, B. Pietrzyk8, G. Pietrzyk49, M. Pili63,
D. Pinci30, F. Pisani48, A. Piucci17, Resmi P.K10, V. Placinta37, J. Plews53,
M. Plo Casasus46, F. Polci13, M. Poli Lener23, M. Poliakova68, A. Poluektov10,
N. Polukhina82,t, I. Polyakov68, E. Polycarpo2, G.J. Pomery54, S. Ponce48, D.
Popov6,48, S. Popov42, S. Poslavskii44, K. Prasanth35, L. Promberger48, C.
Prouve46, V. Pugatch52, H. Pullen63, G. Punzi29,m, W. Qian6, J. Qin6, R.
Quagliani13, B. Quintana8, N.V. Raab18, R.I. Rabadan Trejo10, B. Rachwal34,
J.H. Rademacker54, M. Rama29, M. Ramos Pernas56, M.S. Rangel2, F.
Ratnikov42,81, G. Raven33, M. Reboud8, F. Redi49, F. Reiss13, C. Remon
Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, S. Ricciardi57, D.S.
Richards57, K. Rinnert60, P. Robbe11, A. Robert13, G. Robertson58, A.B.
Rodrigues49, E. Rodrigues60, J.A. Rodriguez Lopez74, A. Rollings63, P.
Roloff48, V. Romanovskiy44, M. Romero Lamas46, A. Romero Vidal46, J.D. Roth85,
M. Rotondo23, M.S. Rudolph68, T. Ruf48, J. Ruiz Vidal47, A. Ryzhikov81, J.
Ryzka34, J.J. Saborido Silva46, N. Sagidova38, N. Sahoo56, B. Saitta27,d, D.
Sanchez Gonzalo45, C. Sanchez Gras32, R. Santacesaria30, C. Santamarina
Rios46, M. Santimaria23, E. Santovetti31,o, D. Saranin82, G. Sarpis59, M.
Sarpis75, A. Sarti30, C. Satriano30,n, A. Satta31, M. Saur15, D. Savrina41,40,
H. Sazak9, L.G. Scantlebury Smead63, S. Schael14, M. Schellenberg15, M.
Schiller59, H. Schindler48, M. Schmelling16, B. Schmidt48, O. Schneider49, A.
Schopper48, M. Schubiger32, S. Schulte49, M.H. Schune11, R. Schwemmer48, B.
Sciascia23, A. Sciubba23, S. Sellam46, A. Semennikov41, M. Senghi Soares33, A.
Sergi53,48, N. Serra50, L. Sestini28, A. Seuthe15, P. Seyfert48, D.M.
Shangase85, M. Shapkin44, I. Shchemerov82, L. Shchutska49, T. Shears60, L.
Shekhtman43,u, Z. Shen5, V. Shevchenko80, E.B. Shields26,i, E. Shmanin82, J.D.
Shupperd68, B.G. Siddi21, R. Silva Coutinho50, G. Simi28, S. Simone19,b, I.
Skiba21,e, N. Skidmore62, T. Skwarnicki68, M.W. Slater53, J.C. Smallwood63,
J.G. Smeaton55, A. Smetkina41, E. Smith14, 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,h, P. Spradlin59, F. Stagni48, M. Stahl65, S. Stahl48, P. Stefko49,
O. Steinkamp50,82, S. Stemmle17, O. Stenyakin44, H. Stevens15, S. Stone68,
M.E. Stramaglia49, M. Straticiuc37, D. Strekalina82, S. Strokov83, F.
Suljik63, J. Sun27, L. Sun73, Y. Sun66, P. Svihra62, P.N. Swallow53, K.
Swientek34, A. Szabelski36, T. Szumlak34, M. Szymanski48, S. Taneja62, F.
Teubert48, E. Thomas48, K.A. Thomson60, M.J. Tilley61, V. Tisserand9, S.
T’Jampens8, M. Tobin4, S. Tolk48, L. Tomassetti21,e, D. Torres Machado1, D.Y.
Tou13, M. Traill59, M.T. Tran49, E. Trifonova82, C. Trippl49, G. Tuci29,m, A.
Tully49, N. Tuning32, A. Ukleja36, D.J. Unverzagt17, A. Usachov32, A.
Ustyuzhanin42,81, U. Uwer17, A. Vagner83, V. Vagnoni20, A. Valassi48, G.
Valenti20, N. Valls Canudas45, M. van Beuzekom32, E. van Herwijnen82, C.B. Van
Hulse18, M. van Veghel78, R. Vazquez Gomez46, P. Vazquez Regueiro46, C.
Vázquez Sierra48, S. Vecchi21, J.J. Velthuis54, M. Veltri22,q, A.
Venkateswaran68, M. Veronesi32, M. Vesterinen56, D. Vieira65, M. Vieites
Diaz49, H. Viemann76, X. Vilasis-Cardona84, E. Vilella Figueras60, P.
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Vorobyev43,u, N. Voropaev38, R. Waldi76, J. Walsh29, C. Wang17, J. Wang73, J.
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Wark60, N.K. Watson53, S.G. Weber13, D. Websdale61, C. Weisser64, B.D.C.
Westhenry54, D.J. White62, M. Whitehead54, D. Wiedner15, G. Wilkinson63, M.
Wilkinson68, I. Williams55, M. Williams64,69, M.R.J. Williams58, F.F.
Wilson57, W. Wislicki36, M. Witek35, L. Witola17, G. Wormser11, S.A. Wotton55,
H. Wu68, K. Wyllie48, Z. Xiang6, D. Xiao7, Y. Xie7, A. Xu5, J. Xu6, L. Xu3, M.
Xu7, Q. Xu6, Z. Xu6, Z. Xu5, D. Yang3, Y. Yang6, Z. Yang3, Z. Yang66, Y.
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Zarebski53, M. Zavertyaev16,t, M. Zdybal35, O. Zenaiev48, M. Zeng3, D. Zhang7,
L. Zhang3, S. Zhang5, Y. Zhang5, Y. Zhang63, A. Zhelezov17, Y. Zheng6, X.
Zhou6, Y. Zhou6, X. Zhu3, V. Zhukov14,40, J.B. Zonneveld58, S. Zucchelli20,c,
D. Zuliani28, G. 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. Grenoble Alpes, Univ. 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 (llr), 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 Provencial Key Laboratory of Nuclear Science, 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
77INFN Sezione di Perugia, Perugia, Italy, associated to 21
78Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
79Universiteit Maastricht, Maastricht, Netherlands, associated to 32
80National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
81National Research University Higher School of Economics, Moscow, Russia,
associated to 42
82National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
83National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
84DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
85University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Genova, Genova, Italy
hUniversità degli Studi di Milano, Milano, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Modena e Reggio Emilia, Modena, Italy
kUniversità di Padova, Padova, Italy
lScuola Normale Superiore, Pisa, Italy
mUniversità di Pisa, Pisa, Italy
nUniversità della Basilicata, Potenza, Italy
oUniversità di Roma Tor Vergata, Roma, Italy
pUniversità di Siena, Siena, Italy
qUniversità di Urbino, Urbino, Italy
rMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
sAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
tP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
uNovosibirsk State University, Novosibirsk, Russia
vDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden
wHanoi University of Science, Hanoi, Vietnam