EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2017-247 LHCb-PAPER-2017-026 January 12, 2018

Measurements of the branching fractions of ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$, ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$, and ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$

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

The ratios of the branching fractions of the decays ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$, ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$, and ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$ with respect to
the Cabibbo-favoured ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ decay are measured
using proton-proton collision data collected with the LHCb experiment at a
$7\mathrm{\,Te\kern-1.00006ptV}$ centre-of-mass energy and corresponding to an
integrated luminosity of $1.0\mbox{\,fb}^{-1}$:

$\displaystyle\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$
$\displaystyle=(7.44\pm 0.08\pm 0.18)\,\%,$
$\displaystyle\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$
$\displaystyle=(1.70\pm 0.03\pm 0.03)\,\%,$
$\displaystyle\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$
$\displaystyle=(0.165\pm 0.015\pm 0.005)\,\%,$

where the uncertainties are statistical and systematic, respectively. These
results are the most precise measurements of these quantities to date. When
multiplied by the world-average value for $\mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})$, the
corresponding branching fractions are

$\displaystyle\mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})$
$\displaystyle=(4.72\pm 0.05\pm 0.11\pm 0.25)\times 10^{-3},$
$\displaystyle\mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})$
$\displaystyle=(1.08\pm 0.02\pm 0.02\pm 0.06)\times 10^{-3},$
$\displaystyle\mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})$
$\displaystyle=(1.04\pm 0.09\pm 0.03\pm 0.05)\times 10^{-4},$

where the final uncertainty is due to $\mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})$.

Published in JHEP 03 (2018) 043

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

##  1 Introduction

Nonleptonic decays of charmed baryons are a useful environment in which to
study the interplay of the weak and strong interactions. Measurements of their
branching fractions are of great importance in understanding the internal
dynamics of the decays. The last few years have seen advances in the study of
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decays, where
$hh^{\prime}\in\\{{{K}^{-}}{{\pi}^{+}},{{K}^{-}}{{K}^{+}},{{\pi}^{-}}{{\pi}^{+}},{{\pi}^{-}}{{K}^{+}}\\}$.
Until recently, measurements of the absolute branching fraction of the
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ decay
suffered from model dependence, relying on assumptions concerning several
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}$, ${\mathchar
28931\relax}^{+}_{c}$ and ${D}^{+}$ branching fraction ratios and decay
widths. The first model-independent measurements of the absolute branching
fraction of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ decay have been
made by the Belle [1] and BESIII [2] collaborations. The precision of a number
of ${{\mathchar 28931\relax}^{+}_{c}}$ decay branching fractions has also been
improved at the $B$ factories [3, 2, 4, 5], while the first measurement of a
doubly Cabibbo-suppressed (DCS) charmed-baryon decay, ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$, has been
performed by the Belle collaboration [6].

Unlike in the charmed-meson sector, there exist a large number of favoured
internal $W$-boson exchange decays which can be readily studied. Quark-level
diagrams demonstrating external $W$-emission, internal $W$-emission, and
$W$-exchange are shown in Figure 1.

$c$$s$$\overline{d}$$u$$\overline{u}$$u$$u$$u$$d$$d$$W^{+}$$p$${\pi}^{+}$${K}^{-}$${{\mathchar
28931\relax}^{+}_{c}}$ (a)

$c$$d$$\overline{s}$$u$$\overline{u}$$u$$u$$u$$d$$d$$W^{+}$$p$${K}^{+}$${\pi}^{-}$${{\mathchar
28931\relax}^{+}_{c}}$ (b)

$c$$u$$\overline{u}$$s$$\overline{d}$$u$$u$$u$$d$$d$$W^{+}$$p$${K}^{-}$${\pi}^{+}$${{\mathchar
28931\relax}^{+}_{c}}$ (c)

$c$$u$$\overline{u}$$d$$\overline{s}$$u$$u$$u$$d$$d$$W^{+}$$p$${\pi}^{-}$${K}^{+}$${{\mathchar
28931\relax}^{+}_{c}}$ (d)

$c$$u$$\overline{u}$$s$$\overline{d}$$d$$d$$u$$u$$u$$W^{+}$$p$${K}^{-}$${\pi}^{+}$${{\mathchar
28931\relax}^{+}_{c}}$ (e)

Figure 1: Weak decays of ${{\mathchar 28931\relax}^{+}_{c}}$ to a proton and
two mesons, without hyperon mediation. Shown are external $W$-emission for (a)
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ and
(b) ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$,
internal $W$-emission for (c) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ and (d)
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$, and
$W$-exchange for (e) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$.

As can be seen, while $W$-boson exchange is not permitted in the decay
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$, it
is allowed in the decay ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$. The ratio of the
branching fractions ${{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}/{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ is a useful
variable with which to indirectly study the role of $W$-boson exchange in
hadronic decays. In the absence of flavour-SU(3) symmetry breaking, the ratio
can naively be expected to be equal to $\tan^{4}\theta_{c}$ [7], where
$\theta_{c}$ is the Cabibbo mixing angle [8]. Taking the most recent
measurements of $|{V_{{u}{d}}}|$ and $|{V_{{u}{s}}}|$ [9] yields a value
$\tan^{4}\theta_{c}\approx 0.285\,\%$. The Belle measurement for
${{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}/{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ corresponds to
$(0.82\pm 0.12)\tan^{4}\theta_{c}$.

In this paper we report measurements of the ratios of the branching fractions

$\displaystyle\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})},\
\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}\ \mathrm{and}\
\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}.$

These measurements are carried out using a data sample, corresponding to an
integrated luminosity of 1.0 $\mbox{\,fb}^{-1}$ of $p$ $p$ collision data,
collected with the LHCb detector at a centre-of-mass energy of
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$. The ${{\mathchar
28931\relax}^{+}_{c}}$ candidates are reconstructed in semileptonic (SL)
decays of ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{\mu^{-}}X$, where $X$ is any particle in this decay that
is not reconstructed. These decays have a low level of background due to the
use of high-purity muon triggers and the displacement of the ${{\mathchar
28931\relax}^{+}_{c}}$ production point from the primary $p$ $p$ collision. As
a powerful cross-check, the same measurements, although with a lower
precision, are carried out using a sample of ${{\mathchar
28931\relax}^{+}_{c}}$ produced in the primary $p$ $p$ interaction vertex
(PV), referred to as the prompt sample.

##  2 Detector and simulation

The LHCb detector [10] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5 % at low
momentum to 1.0 % at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex, the impact parameter (IP), is
measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov (RICH)
detectors [11], allowing for an effective discrimination between the different
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ final states.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.

The online event selection is performed by a trigger, which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage which is divided into two parts. The first
employs a partial reconstruction of the candidates from the hardware trigger
and a cut-based selection, while the second utilises a full event
reconstruction and further, often more complex, selection criteria on
candidates. Selection requirements can be made on whether a trigger decision
was satisfied by any given object in the event (including nonsignal objects).
In the offline selection, trigger decisions are associated with reconstructed
particles. Therefore requirements can be made on whether the signal candidate
was responsible for satisfying the trigger decision, or if another nonsignal
object in the event satisfied the trigger decision, or a combination of the
two. The detailed trigger requirements for the semileptonic and prompt samples
are described in Section 3.

In the simulation, $pp$ collisions are generated using Pythia [12,
*Sjostrand:2007gs] with a specific LHCb configuration [14]. The heavy flavour
decays are described by EvtGen [15] with the decay kinematics of the
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ generated
according to a phase-space distribution. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [16] as described in Ref. [14].

##  3 Candidate selection

The different production mechanisms in the SL and prompt processes necessitate
two distinct selections, which are verified to result in statistically
independent samples of ${{\mathchar 28931\relax}^{+}_{c}}$ candidates. The
selections are developed using a fraction of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ data corresponding
to 10 % of the integrated luminosity, chosen randomly. This sample is then
discarded from measurements of the ratios of branching fractions, with an
appropriate scaling factor applied to the final results.

###  3.1 ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}({p}hh^{{}^{\prime}}){\mu^{-}}{{\overline{\nu}}_{\mu}}$
selection

The trigger selection at the hardware stage and the first software stage is
focussed upon the muon in the ${\mathchar 28931\relax}^{0}_{b}$ decay, such
that the dependence of the selection upon the ${{\mathchar
28931\relax}^{+}_{c}}$ decay product kinematics is reduced. This results in
the ratios of trigger acceptance efficiencies between the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ modes being uniform at
these stages of the trigger. The muon candidate is required to have a
$\mbox{$p_{\mathrm{T}}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and to be
responsible for the decision of both the hardware trigger and the first stage
of the software trigger. The latter uses additional detector information to
confirm that the muon has a high $p_{\mathrm{T}}$ and is significantly
displaced from the primary vertex. In the second stage of the software
trigger, a general algorithm designed for identifying semileptonic $b$-hadron
decays selects ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}({p}hh^{{}^{\prime}}){\mu^{-}}{{\overline{\nu}}_{\mu}}$
candidates, requiring a high $p_{\mathrm{T}}$ muon that is significantly
displaced from the PV. This muon must then form a displaced secondary vertex
with between one and three other tracks. This vertex must have at least one
track with $\mbox{$p_{\mathrm{T}}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
and $\chi^{2}_{\mathrm{IP}}$ with respect to any PV greater than 16, where
$\chi^{2}_{\mathrm{IP}}$ is defined as the difference in the fit $\chi^{2}$ of
a given PV reconstructed with and without the considered particle.

The candidates selected by the trigger are then filtered to improve the signal
purity. Charged hadrons are selected with a momentum
$\mbox{$p$}>2.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and
$\mbox{$p_{\mathrm{T}}$}>0.3{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. All tracks
must have $\chi^{2}_{\mathrm{IP}}>9$ such that they are significantly
displaced from any PV in the event, and have a good fit quality. Three such
tracks must then form a high-quality vertex with a flight-distance-
significance greater than 100 (defined as the measured flight distance from
any PV divided by its uncertainty). The $p_{\mathrm{T}}$ of the three-particle
combination must also be greater than
$1.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Particle identification (PID) is applied to each charged hadron in order to
select exclusive samples of each final state, and to reject backgrounds from
other multibody charm decays. Tight PID selection criteria are enforced on the
proton and kaon candidates in order to suppress possible backgrounds from
misidentified $c$-hadron decays, with a weaker requirement placed upon the
pion candidates.

Muon candidates must have a high-quality track fit, and have
$\chi^{2}_{\mathrm{IP}}>9$, $\mbox{$p$}>3{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
and $\mbox{$p_{\mathrm{T}}$}>0.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. A
moderate PID requirement is also enforced to reduce the background from
$\pi-\mu$ misidentification. Finally, the muon and ${{\mathchar
28931\relax}^{+}_{c}}$ candidates are required to form a common vertex with a
fit $\chi^{2}$ lower than 6. The invariant mass of the three tracks in the
${{\mathchar 28931\relax}^{+}_{c}}$ combination is required to be within $\pm
40$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${{\mathchar
28931\relax}^{+}_{c}}$ mass [9]. The invariant mass of the combination of the
muon and the ${{\mathchar 28931\relax}^{+}_{c}}$ candidate must fall in the
range $2.5-6.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

###  3.2 Prompt ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ selection

To ensure that the trigger acceptance does not depend upon the ${{\mathchar
28931\relax}^{+}_{c}}$ decay channel and kinematics, all accepted candidates
must have been triggered independently of the ${{\mathchar
28931\relax}^{+}_{c}}$ decay products. If the measured branching fraction
ratios between the prompt and SL analyses are compatible, this is a strong
indication of the robustness of our method given the very different triggering
strategies.

To improve the sample purity a selection using PID and kinematic information
is employed. All charged hadrons forming the ${{\mathchar
28931\relax}^{+}_{c}}$ candidate must have a momentum greater than
$5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and a $p_{\mathrm{T}}$ greater than
$0.4{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and at least one hadron is required
to have a $p_{\mathrm{T}}$ exceeding
$1.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. All hadronic tracks should have a
$\chi^{2}_{\mathrm{IP}}$ greater than 4, with at least one greater than 8. All
tracks should have a good fit quality. The PID requirements on the protons,
kaons and pions in the selection are identical to those used in the SL
analysis.

The ${{\mathchar 28931\relax}^{+}_{c}}$ candidate formed from these tracks is
required to have a vertex-fit $\chi^{2}$ lower than 20, and a maximum
distance-of-closest-approach between any two pairings of the decay products of
$0.1\mathrm{\,mm}$. The flight-distance significance is required to be greater
than 16. The reconstructed proper time of the ${{\mathchar
28931\relax}^{+}_{c}}$ is required to be below $1.2{\mathrm{\,ps}}$ to reject
misreconstructed charmed-meson decays and ${{\mathchar 28931\relax}^{+}_{c}}$
produced in decays of $b$ hadrons (referred to as secondary ${{\mathchar
28931\relax}^{+}_{c}}$). The invariant mass of the ${{\mathchar
28931\relax}^{+}_{c}}$ candidate is required to be within $\pm
40{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${{\mathchar
28931\relax}^{+}_{c}}$ mass [9]. Finally, the angle between the line joining
the production and decay vertices and the reconstructed ${{\mathchar
28931\relax}^{+}_{c}}$ momentum vector must be small.

###  3.3 Selection efficiencies

The efficiencies for the selection of signal decays are factorised into
components which can be measured independently. These efficiencies are the
probability for the decays to occur within the detector acceptance, for the
trigger to accept the signal event, for the final-state particles to be
reconstructed, and for the decay to be selected.

The efficiency components are evaluated using simulation, with the exception
of the PID selection efficiency, where a data-driven approach is utilised.
High-purity calibration samples of kaons and pions are acquired using
${{D}^{*+}}\\!\rightarrow{{D}^{0}}{{\pi}^{+}}$ (with
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$) decays, which are identified
without the use of PID requirements, while corresponding samples of protons
are acquired using ${\mathchar 28931\relax}\\!\rightarrow{p}{{\pi}^{-}}$
decays. In the prompt analysis a small supplementary sample of ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ decays is also
used to acquire calibration protons, which are verified to be statistically
independent of the signal ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ due largely to
their different triggering and selection strategies. These calibration samples
allow for an evaluation of the PID performance as a function of a set of
variables which can fully characterise the single-track PID performance; in
this analysis the track momentum and pseudorapidity are utilised. The
distributions of these variables for the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decay product tracks are
then extracted using the sPlot technique [17], with the ${{\mathchar
28931\relax}^{+}_{c}}$ candidate invariant mass as a discriminating variable.
A weighting procedure is then used to align the signal and calibration samples
such that an average PID selection efficiency for the decay mode can be
determined entirely through the use of data.

For the efficiencies determined from simulation, it is necessary to consider
the unknown resonant structure of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decays. It is assumed that
the decay is characterised both by intermediate two-body resonances and a
nonresonant decay amplitude which is constant across the phase space.
According to the helicity formalism detailed in Ref. [18], the differential
decay rate as a function of the ${\mathchar 28931\relax}^{+}_{c}$
polarisation, $\mathrm{P}_{{{\mathchar 28931\relax}^{+}_{c}}}$, can be
expressed as

$\displaystyle\begin{split}\rm{d}\Gamma&\sim\frac{1+\mathrm{P}_{{{\mathchar
28931\relax}^{+}_{c}}}}{2}\left(\left|\sum_{r}BW(m_{r})\alpha_{r,\frac{1}{2},\frac{1}{2}}\right|^{2}+\left|\sum_{r}BW(m_{r})\alpha_{r,\frac{1}{2},-\frac{1}{2}}\right|^{2}\right)\\\
&+\frac{1-\mathrm{P}_{{{\mathchar
28931\relax}^{+}_{c}}}}{2}\left(\left|\sum_{r}BW(m_{r})\alpha_{r,-\frac{1}{2},\frac{1}{2}}\right|^{2}+\left|\sum_{r}BW(m_{r})\alpha_{r,-\frac{1}{2},-\frac{1}{2}}\right|^{2}\right)\end{split}$

where $\alpha_{r,m,\lambda_{\rm{p}}}$ is the complex decay amplitude for
resonance $r$ with spin $m$ (the ${\mathchar 28931\relax}^{+}_{c}$ spin
projection onto the $z$-axis), $\lambda_{\rm{p}}$ is the proton helicity in
the rest frame of the ${\mathchar 28931\relax}^{+}_{c}$, and $BW$ is the
Breit-Wigner amplitude (the form of which may be found in Ref. [19]). The
${{\mathchar 28931\relax}^{+}_{c}}$ polarisation has not yet been measured at
the LHC. For the prompt candidates, the polarisation axis is defined as the
cross product of the beam momentum and the ${{\mathchar 28931\relax}^{+}_{c}}$
momentum in the lab frame. For the SL candidates, it is defined as the cross
product of the ${\mathchar 28931\relax}^{0}_{b}$ momentum and the ${\mathchar
28931\relax}^{+}_{c}$ momentum in the lab frame. The minimum parameterisation
of this differential decay rate is represented by five kinematic variables.
These are any two of the following three invariant mass variables and each of
the three angular variables, where each angle is defined in the ${\mathchar
28931\relax}^{+}_{c}$ rest frame:

$m_{ph}$

\- the two-body invariant mass of the proton and the opposite-sign meson.

$m_{ph^{{}^{\prime}}}$

\- the two-body invariant mass of the proton and the same-sign meson.

$m_{hh^{{}^{\prime}}}$

\- the two-body invariant mass of the meson pair.

$\theta_{p}$

\- the angle between the proton momentum vector and the polarisation axis of
the ${\mathchar 28931\relax}^{+}_{c}$.

$\phi_{p}$

\- the angle between the component of the proton momentum perpendicular to the
${\mathchar 28931\relax}^{+}_{c}$ polarisation axis and the direction of the
${\mathchar 28931\relax}^{+}_{c}$ momentum vector in the laboratory frame.

$\phi_{h_{1}h_{2}}$

\- the angle between the plane containing the proton momentum vector and the
${\mathchar 28931\relax}^{+}_{c}$ polarisation vector, and the plane
containing the two meson momentum vectors.

Some of the factorisable components of the selection efficiency depend upon
combinations of these variables. For each such dependence, the variable
distributions from those listed above are obtained from the data using the
sPlot technique. The simulated data is binned in these variables, and local
efficiencies across the phase space are determined and applied to data on a
per-candidate basis. This procedure accurately describes the selection
efficiencies using the simulated data without _a priori_ knowledge of the
resonant structure of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decays. For all schemas it
is ensured that the signal yield in each bin, as determined with the sPlot
technique, is greater than three times its statistical error. Due to the
finite size of the simulated sample, two-dimensional binnings are used in the
final results, where the variables are chosen to be those with the greatest
disagreement between data and simulation, as determined with a $\chi^{2}$
compatibility test. As a cross-check, three-dimensional binning schemas are
implemented using these two primary variables in conjunction with every
possible third variable, and in all cases the reweighted efficiencies are
observed to be compatible with the two-dimensional binnings.

The full selection efficiency ratios for each measurement are summarised in
Table 1. As the number of kaons in the final state increases, the momentum
available to the final state particles decreases, and the selection removes a
higher fraction of the signal. The efficiency ratios are further from unity
for the prompt measurements than for the corresponding SL measurements due to
the tighter kinematic requirements used in the selection of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decay products. The
selection efficiencies display the same hierarchy before and after the
reweighting procedure.

Table 1: Selection efficiency ratios in the prompt and SL measurements, with their associated systematic uncertainties. $\epsilon_{\mathrm{CF}}/\epsilon_{\mathrm{CS}}$ denotes the ratio of the Cabibbo-favoured selection efficiency over that of the Cabibbo-suppressed mode.  | Measurement | $\epsilon_{\mathrm{CF}}/\epsilon_{\mathrm{CS}}$
---|---|---
Prompt | ${{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})}/{{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ | $0.67\pm 0.02$
${{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})}/{{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ | $1.42\pm 0.05$
SL | ${{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})}/{{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ | $0.96\pm 0.02$
${{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})}/{{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ | $1.25\pm 0.02$
${{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}/{{\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ | $1.06\pm 0.03$

##  4 Signal yield determination

In both the SL and prompt analyses no contamination from backgrounds due to
misidentified charm decays, such as
${{D}^{+}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$, is found in the
data. Cross-feed between the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ modes, along with any
contamination in the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$ or ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$ channels from
hyperon or ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mediation, is also found
to be negligible. It is determined that the only decays left in the retained
${\mathchar 28931\relax}^{+}_{c}$ candidates are genuine ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decays and backgrounds from
combinations of unrelated tracks.

###  4.1 ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}({p}hh^{{}^{\prime}}){\mu^{-}}{{\overline{\nu}}_{\mu}}$
yield determination

The yields of each decay mode are extracted through an extended unbinned
maximum likelihood fit to the ${\mathchar 28931\relax}^{+}_{c}$ invariant mass
distributions. The signal model for the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$ and ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$ modes is a
Gaussian function, while for the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ and ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$ modes the sum of
two Gaussian functions with a common mean is used to account for the
dependence of the reconstructed invariant mass resolution on the track
momenta, which degrades the fit quality for a single Gaussian function in
high-yield channels. In all modes, the background model is an exponential
function. All parameters are free to vary in the fit. The invariant mass
distributions for each of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ modes, with the fit results
overlaid, are shown in Figure 2, and the signal yields are given in Table 2.

(a)

(b)

(c)

(d)

Figure 2:  Invariant mass distributions of (a) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$, (b) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$, (c)
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$, and
(d) ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$
decays, with fit results superimposed. The hatched magenta region indicates
the signal, the shaded green region indicates the background from unrelated
tracks, and the solid red line indicates the full fit.

###  4.2 Prompt ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ yield determination

The yield determination procedure in the case of the prompt ${{\mathchar
28931\relax}^{+}_{c}}$ is complicated by the presence of a large secondary
${{\mathchar 28931\relax}^{+}_{c}}$ contribution. These secondary ${{\mathchar
28931\relax}^{+}_{c}}$ are statistically independent of the ${{\mathchar
28931\relax}^{+}_{c}}$ selected in the SL analysis due to the different
triggering and selection techniques employed. The secondary ${{\mathchar
28931\relax}^{+}_{c}}$ have different kinematic distributions than the prompt
${{\mathchar 28931\relax}^{+}_{c}}$. Due to the kinematic criteria employed in
the selection, the efficiency ratios between the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ modes therefore vary
between prompt and secondary ${{\mathchar 28931\relax}^{+}_{c}}$, resulting in
the need to disentangle the prompt and secondary ${{\mathchar
28931\relax}^{+}_{c}}$ candidates Such a separation is achieved through
examination of the $\chi^{2}_{\mathrm{IP}}$ of the ${{\mathchar
28931\relax}^{+}_{c}}$ candidates. The inclusion of a truly prompt
${{\mathchar 28931\relax}^{+}_{c}}$ in the PV reconstruction generally results
in a smaller increase of the PV-fit $\chi^{2}$ than in the case of an
inclusion of a truly secondary ${{\mathchar 28931\relax}^{+}_{c}}$ candidate.
To separate prompt and secondary ${{\mathchar 28931\relax}^{+}_{c}}$
candidates the natural logarithm of this quantity,
$\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$, is utilised.

The yield determination in this case follows a two-step procedure. First, the
total number of ${{\mathchar 28931\relax}^{+}_{c}}$ of each decay mode, i.e.
the sum of prompt and secondary ${{\mathchar 28931\relax}^{+}_{c}}$, is
evaluated through an extended unbinned maximum likelihood fit to the
${\mathchar 28931\relax}^{+}_{c}$ invariant mass distributions. This allows
the ${{\mathchar 28931\relax}^{+}_{c}}$ to be well separated from the
combinatoric background. The models used to describe the signal and background
components are the same as for the ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}({p}hh^{{}^{\prime}}){\mu^{-}}{{\overline{\nu}}_{\mu}}$
analysis. An unbinned extended maximum likelihood fit to the ${\mathchar
28931\relax}^{+}_{c}$ $\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$
distributions is then performed, which discriminates between the prompt and
secondary ${{\mathchar 28931\relax}^{+}_{c}}$ decays. In this fit, only
candidates in the invariant mass signal region, defined to be within three
times the fitted ${{\mathchar 28931\relax}^{+}_{c}}$ Gaussian width of the
known ${{\mathchar 28931\relax}^{+}_{c}}$ mass [9] (or where a double-Gaussian
signal model is used, three times the mean of widths of the two Gaussian
components), are considered. Information from the fit to the invariant mass is
used to constrain the total number of ${{\mathchar 28931\relax}^{+}_{c}}$ in
this fit.

The shapes of the prompt and secondary ${{\mathchar 28931\relax}^{+}_{c}}$
$\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$ distributions are described by
modified Novosibirsk functions [20] with extended tail parameters. The
functional form is

$N(x;\mu;\sigma;\xi;\rho_{\mathrm{1}};\rho_{\mathrm{2}})=\begin{cases}\exp{\left[\rho_{\mathrm{1}}\frac{(x-x_{\mathrm{1}})^{2}}{(\mu-
x_{\mathrm{1}})^{2}}+\frac{(\mu-
x_{\mathrm{1}})\xi\sqrt{\xi^{2}+1}\times\sqrt{2\log{2}}}{\sigma\left(\sqrt{\xi^{2}+1}-\xi\right)^{2}\log\left(\sqrt{\xi^{2}+1}+\xi\right)}-\log{2}\right]}&x<x_{\mathrm{1}}\\\
\exp{\left[-\log{2}\times\left[\frac{\log{\left(1+2\xi\sqrt{\xi^{2}+1}\times\frac{x-\mu}{\sigma\sqrt{2\log{2}}}\right)}}{\log{\left(1+2\xi\left(\xi-\sqrt{\xi^{2}+1}\right)\right)}}\right]^{2}\right]}&x_{\mathrm{1}}<x<x_{\mathrm{2}},\\\
\exp{\left[\rho_{\mathrm{2}}\frac{(x_{\mathrm{2}}-x)^{2}}{(x_{\mathrm{2}}-\mu)^{2}}+\frac{(x_{\mathrm{2}}-x)\xi\sqrt{\xi^{2}+1}\times\sqrt{2\log{2}}}{\sigma\left(\sqrt{\xi^{2}+1}-\xi\right)^{2}\log\left(\sqrt{\xi^{2}+1}+\xi\right)}-\log{2}\right]}&x>x_{\mathrm{2}}\end{cases}$

where $\xi$ is an asymmetry parameter, $\sigma\sqrt{2\log{2}}$ is the full-
width at half maximum, $\mu$ is the position of the mode, and
$\rho_{\mathrm{1}}$ and $\rho_{\mathrm{2}}$ are the lower and upper tail
parameters, respectively. The parameters $x_{\mathrm{1}}$ and $x_{\mathrm{2}}$
are the turnover points where the function has half of its maximum value,
defined as

$\displaystyle
x_{\mathrm{1}}\equiv\mu+\sigma\sqrt{2\log{2}}\left(\frac{\xi}{\sqrt{\xi^{2}+1}}-1\right),$
$\displaystyle
x_{\mathrm{2}}\equiv\mu+\sigma\sqrt{2\log{2}}\left(\frac{\xi}{\sqrt{\xi^{2}+1}}+1\right).$

The background component is described by a nonparametric function generated
using the data from the invariant mass sideband regions. Simulated samples of
prompt ${{\mathchar 28931\relax}^{+}_{c}}$ and of ${{\mathchar
28931\relax}^{+}_{c}}$ from a mixture of secondary $b$-hadron decays are
generated. The values of the $\xi$, $\rho_{\mathrm{1}}$, and
$\rho_{\mathrm{2}}$ parameters are fixed from fits to these prompt and
secondary simulated decays, while the means and widths of the functions are
free to vary in the fit for the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ mode.

To aid the fit convergence in the Cabibbo-suppressed modes, where the
background from unrelated tracks dominates the distribution, Gaussian
constraints on the widths and means of the shapes are applied to values taken
from fits to the simulation. The potential for bias in these shapes arising
from any poor modelling of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decay kinematics is
investigated. The selection efficiency with respect to the ${{\mathchar
28931\relax}^{+}_{c}}$ $\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$ is observed
to be independent of the kinematics of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decays. The initial
conditions of, and constraints applied to, the Novosibirsk shapes taken from
simulation are therefore shown to be reliable. The central value of each
parameter constraint is multiplied by a scaling factor, based on the
difference in the fitted value of that parameter between the data and
simulated data in the unconstrained ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ mode. The fit is
parameterised in terms of the prompt fraction and the total number of
${{\mathchar 28931\relax}^{+}_{c}}$ candidates. The latter has a Gaussian
constraint applied to the value obtained in the fit to the ${{\mathchar
28931\relax}^{+}_{c}}$ candidate invariant mass distribution.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3:  Invariant mass distributions for (a) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$, (c) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$, (e)
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$ in the
prompt analysis, with fit results superimposed. The
$\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$ distributions for (b) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$, (d) ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$, (f)
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$, with
the fit results superimposed, showing the differentiation of prompt and
secondary ${{\mathchar 28931\relax}^{+}_{c}}$.

The invariant mass distributions for each of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ modes, with the associated
fit results overlaid, are shown in the left of Figure 3, while the
$\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$ distributions and associated fit
are shown on the right. The yields in both the SL and prompt measurements are
summarised in Table 2.

The fitting procedure for each decay mode is validated with a study of 1000
generated pseudoexperiments. In each case, candidates are generated from
probability density functions according to the fitted values for each decay
mode, with each candidate assigned an invariant mass and a
$\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$. The number of candidates
generated per species is the number found in the nominal fit to the data. The
fit procedure is repeated for each generated data sample as in the nominal
fit. The extracted prompt yield is shown to be unbiased, and the standard
deviation on the distribution of the prompt yields verifies the reported
uncertainty in the nominal fit.

Table 2:  Signal yields in both the SL and prompt measurements.  | Mode | Yield
---|---|---
SL | ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ |  $226{,}851$$\,\pm\,$ | $522$
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$ |  $19{,}584$$\,\pm\,$ | $207$
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$ |  $3{,}420$$\,\pm\,$ | $62$
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$ |  $392$$\,\pm\,$ | $35$
Prompt | ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ |  $58{,}115$$\,\pm\,$ | $1{,}561$
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$ |  $7{,}480$$\,\pm\,$ | $328$
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$ |  $766$$\,\pm\,$ | $61$

##  5 Systematic uncertainties

Several sources of systematic uncertainty are considered in the evaluation of
the selection efficiencies and in the yield determinations. The uncertainties
are summarised for the SL measurements in Table 3, and for the prompt
measurements in Table 4. The systematics for the SL and prompt analyses are
described together.

The uncertainties on the PID efficiencies are determined in bins of track
momentum and pseudorapidity and propagated to determine the systematic
uncertainties on the ratios of branching fractions. It is assumed that the
efficiency for each candidate track in a given kinematic bin is single-valued,
while the finite bin size results in a kinematic distribution within each bin.
As such, small differences in the kinematic distributions of calibration and
signal tracks within each bin can result in systematic errors in the assigned
efficiencies. The effect of this variation in kinematics is tested by
repeating the calibration procedure with a variety of binning schemes, such
that the kinematic distributions of calibration and signal tracks within each
bin are altered. After the calibration procedure has been carried out for each
binning scheme and a PID selection efficiency ratio determined for each, the
maximum deviation from the nominal efficiency ratio is assigned as a
systematic uncertainty. For the SL measurements this is the dominant source of
systematic uncertainty, ranging from 1.4 to 2.0 %.

Table 3:  Relative systematic uncertainties in each ratio of branching fractions, for the SL analysis.  SL analysis systematic [%] | ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$ | ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$ | ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}}$
---|---|---|---
PID selection efficiency ratio | 2.0 | 1.4 | 2.0
Unknown ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decay structure | 1.1 | 0.7 | 1.7
Size of simulation sample | 0.3 | 0.3 | 0.3
Trigger efficiency ratio | 0.6 | 0.8 | 0.3
Total | 2.4 | 1.8 | 2.7
Table 4:  Relative systematic uncertainties in each ratio of branching fractions, for the prompt analysis.  Prompt analysis systematic [%] | ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}}$ | ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}}$
---|---|---
PID selection efficiency ratio | 1.2 | 1.2
Unknown ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decay structure | 2.7 | 3.3
Yield determination uncertainty | 3.5 | 5.7
Size of simulation sample | 0.5 | 0.5
Total | 4.6 | 6.7

The weighting procedure to align the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ data and simulation relies
upon dividing the simulation into bins of the kinematic variables describing
the resonant character of the decay to evaluate the efficiency as a function
of these variables. The limited size of the simulation sample limits the
precision of the description of the acceptance variation across the phase
space, and therefore affects the evaluation of the selection efficiency with
the weighted simulation. Any systematic uncertainty arising from this source
is evaluated through the use of generated pseudoexperiments whereby the
weights assigned to the simulation in each region of the phase space are
randomly resampled to determine the effect on the evaluation of selection
efficiencies. Uncertainties arising from the limited size of the simulation
sample in the evaluation of the geometrical acceptance of the detector and the
trigger efficiency are also assigned.

In the SL analysis imperfect modelling of variables upon which the trigger
acceptance depends can lead to differences between the simulation and data
which can affect the determination of the trigger acceptances. A set of
variables used in the software trigger was investigated to examine the
compatibility of the data and simulation. Where any differences were found,
the simulation was reweighted individually for each variable to match the data
distributions and the trigger acceptance ratios reevaluated. A systematic
uncertainty was assigned as the maximum difference between the reweighted and
nominal efficiency ratios for any reweighted variable.

The systematic uncertainty on the signal yield determination is evaluated in
the SL analysis by varying the choice of the fit model. As an alternative for
the signal model, a Crystal Ball function [21] and a Crystal Ball function
summed with a Gaussian function with a common mean are used. The background
model is modified to be a first-order or second-order polynomial. Variations
of the fit model do not result in significant changes in the signal yields and
no systematic uncertainty is assigned.

For the prompt analysis the uncertainty on the determined signal yield may
arise from the shape parameters that are fixed or constrained with fits to the
simulated samples, and also from the limited size of the sample in the
background region of the ${{\mathchar 28931\relax}^{+}_{c}}$ invariant mass
used to populate the background nonparametric distribution. These are both
evaluated through the use of pseudoexperiments. The parameters governing the
$\ln\\!\left(\chi^{2}_{\mathrm{IP}}\right)$ shapes are generated successively
with values differing by $10\,\%$ from their fixed or constrained values in
the fit; this is the maximum difference in any Novosibirsk width or mean
parameter between the data and simulation fits for the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ mode, where no
constraints are applied. The background population in each bin of the template
is fluctuated randomly according to a Gaussian distribution, and the fit
procedure repeated. Pseudoexperiments are also utilised to verify the
statistical precision of the reported prompt ${{\mathchar
28931\relax}^{+}_{c}}$ yield, and that the yields are unaffected by any bias.

The dominant systematics in the SL analysis are found to be those associated
with the determination of the PID selection efficiency. In the prompt analysis
the contribution from the background template and from the constrained shape
parameters are found to be the dominant uncertainties.

##  6 Results

The ratios of the branching fractions of each suppressed ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ mode relative to the
${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ mode
are given by

$\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}=\frac{N({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime})\times
s_{\mathrm{scale}}}{N({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}\times\frac{\epsilon({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}{\epsilon({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime})},$

where $N$ represents the measured yield in each case, $\epsilon$ is the full
selection efficiency for the mode, and $s_{\mathrm{scale}}=0.9$ is a scaling
factor to account for the discarded ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ data that is
utilised in the selection training. The results of the SL analysis are

$\begin{split}\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}&=(7.44\pm 0.08\pm
0.18)\,\%,\\\ \frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}&=(1.70\pm 0.03\pm
0.03)\,\%,\\\ \frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}&=(0.165\pm
0.015\pm 0.005)\,\%,\end{split}$

where the first uncertainties are statistical and the second are systematic.
Each of the measurements in the SL analysis are the most precise of these
quantities to date. In the prompt analysis the results are

$\begin{split}\frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}&=(7.86\pm 0.40\pm
0.36)\,\%,\\\ \frac{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})}{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}&=(1.68\pm 0.14\pm
0.11)\,\%,\\\ \end{split}$

where the first uncertainties are statistical and the second are systematic.
The results in the prompt analysis are of comparable precision to the recent
measurements at Belle [3] and at BESIII [5].

The measurements of the ratios of the Cabibbo-suppressed branching fractions
to the Cabibbo-favoured branching fraction are in agreement between the SL and
prompt analyses, demonstrating that the methods employed in their
determination are robust. The efficiency correction to the ratio
${{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}/{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ is small, with
the ratio of corrected and uncorrected yields differing by 3 %, which is
comparable to the systematic uncertainty on the measurement. The SL and prompt
measurements are not combined, because the precision of such a combination
would not offer a significant improvement over the precision of the SL result
alone.

The measurements of the ratios of the branching fractions in the SL analysis
are combined with the world-average value of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ branching
fraction, $\mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})=(6.35\pm
0.33)\,\%$ [9], to compute the branching fractions of the suppressed modes

$\displaystyle\begin{split}\mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{\pi}^{+}})&=(4.72\pm
0.05\pm 0.11\pm 0.25)\times 10^{-3},\\\ \mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{K}^{+}})&=(1.08\pm 0.02\pm
0.02\pm 0.06)\times 10^{-3},\\\ \mathcal{B}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})&=(1.04\pm 0.09\pm
0.03\pm 0.05)\times 10^{-4},\end{split}$

where the uncertainties are statistical, systematic and due to the uncertainty
of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ branching
fraction, respectively.

The measurement presented in this paper of ${{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{\pi}^{-}}{{K}^{+}})}/{{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}$ is lower than
the value of $(0.235\pm 0.027\pm 0.021)\,\%$ found by Belle, at the
$2.0\sigma$ level, and corresponds to $(0.58\pm 0.06)\tan^{4}\theta_{c}$. To
account for the known flavour-SU(3) symmetry breaking that occurs due to the
presence of different resonant contributions in the two modes, the fraction of
the favoured decay proceeding via the ${\mathchar 28931\relax}(1520)$ and
${\mathchar 28929\relax}^{++}$ states111Some contribution from the
$W$-emission decay of ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{\mathchar 28929\relax}^{0}{{K}^{+}}$ is
expected in the doubly-suppressed mode, but as argued in Ref. [22] the
favoured decay ${{\mathchar 28931\relax}^{+}_{c}}\\!\rightarrow{\mathchar
28929\relax}^{++}{{K}^{-}}$ is expected to be dominated by the $W$-exchange
contribution, which cannot happen in the doubly suppressed mode. The relative
$W$-exchange and $W$-emission contributions are unknown, and the mode
proceeding via a ${\mathchar 28929\relax}^{++}$ is neglected entirely., which
cannot proceed through a doubly-suppressed transition and make up $(25\pm
4)\,\%$ of the favoured decay, is discounted. This yields a value of $(0.77\pm
0.08)\tan^{4}\theta_{c}$. The deviation from the naive expectation is
indicative that either $W$-exchange contributions to the favoured mode are
more significant than previously believed, or that some flavour-SU(3) symmetry
breaking effect not present in the charmed-meson sector is present in the
charmed-baryon sector, or some combination of the two.

Future analysis of the resonant character of the ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}hh^{\prime}$ decays, through which such
symmetry breaking effects occur will be important in establishing the nature
of this effect. In particular the comparison of individual resonant
contributions which can proceed through $W$-exchange in the favoured mode but
not the doubly suppressed mode, such as ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{\mathchar 28929\relax}^{++}{{K}^{-}}$,
${\mathchar 28929\relax}^{++}\\!\rightarrow{p}{{\pi}^{+}}$ and ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{\mathchar 28929\relax}^{0}{{K}^{+}}$,
${\mathchar 28929\relax}^{0}\\!\rightarrow{p}{{\pi}^{-}}$, will provide a
stronger statement about the prominence of $W$-exchange diagrams in the
charmed-baryon sector.

## 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 (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing
resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany),
INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom),
RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF
(Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities
behind the multiple open-source software packages on which we depend.
Individual groups or members have received support from AvH Foundation
(Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union),
ANR, Labex P2IO, ENIGMASS and OCEVU, and Région Auvergne-Rhône-Alpes (France),
RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith
Fund, the Royal Society, the English-Speaking Union and the Leverhulme Trust
(United Kingdom).

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LHCb collaboration

R. Aaij40, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, J. Albrecht10,
F. Alessio40, M. Alexander53, A. Alfonso Albero38, S. Ali43, G. Alkhazov31, P.
Alvarez Cartelle55, A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L.
An3, L. Anderlini18, G. Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B.
Appleby56, F. Archilli43, P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M.
Artuso61, E. Aslanides6, G. Auriemma26, M. Baalouch5, I. Babuschkin56, S.
Bachmann12, J.J. Back50, A. Badalov38,m, C. Baesso62, S. Baker55, V.
Balagura7,b, W. Baldini17, A. Baranov35, R.J. Barlow56, C. Barschel40, S.
Barsuk7, W. Barter56, F. Baryshnikov32, V. Batozskaya29, V. Battista41, A.
Bay41, L. Beaucourt4, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61,
L.J. Bel43, N. Beliy63, V. Bellee41, N. Belloli21,i, K. Belous37, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson43, S. Beranek9, A.
Berezhnoy33, R. Bernet42, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt42, F. Betti15, M.-O. Bettler40, M. van Beuzekom43, Ia. Bezshyiko42,
S. Bifani47, P. Billoir8, A. Birnkraut10, A. Bitadze56, A. Bizzeti18,u, M.
Bjørn57, T. Blake50, F. Blanc41, J. Blouw11,†, S. Blusk61, V. Bocci26, T.
Boettcher58, A. Bondar36,w, N. Bondar31, W. Bonivento16, I. Bordyuzhin32, A.
Borgheresi21,i, S. Borghi56, M. Borisyak35, M. Borsato39, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, E. Bowen42, C. Bozzi17,40, S. Braun12, T.
Britton61, J. Brodzicka27, D. Brundu16, E. Buchanan48, C. Burr56, A.
Bursche16,f, J. Buytaert40, W. Byczynski40, S. Cadeddu16, H. Cai64, R.
Calabrese17,g, R. Calladine47, M. Calvi21,i, M. Calvo Gomez38,m, A.
Camboni38,m, P. Campana19, D.H. Campora Perez40, L. Capriotti56, A.
Carbone15,e, G. Carboni25,j, R. Cardinale20,h, A. Cardini16, P. Carniti21,i,
L. Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina21, L. Castillo
Garcia41, M. Cattaneo40, G. Cavallero20,40,h, R. Cenci24,t, D. Chamont7, M.G.
Chapman48, M. Charles8, Ph. Charpentier40, G. Chatzikonstantinidis47, M.
Chefdeville4, S. Chen56, S.F. Cheung57, S.-G. Chitic40, V. Chobanova39, M.
Chrzaszcz42,27, A. Chubykin31, P. Ciambrone19, X. Cid Vidal39, G. Ciezarek43,
P.E.L. Clarke52, M. Clemencic40, H.V. Cliff49, J. Closier40, J. Cogan6, E.
Cogneras5, V. Cogoni16,f, L. Cojocariu30, P. Collins40, T. Colombo40, A.
Comerma-Montells12, A. Contu40, A. Cook48, G. Coombs40, S. Coquereau38, G.
Corti40, M. Corvo17,g, C.M. Costa Sobral50, B. Couturier40, G.A. Cowan52, D.C.
Craik58, A. Crocombe50, M. Cruz Torres1, R. Currie52, C. D’Ambrosio40, F. Da
Cunha Marinho2, E. Dall’Occo43, J. Dalseno48, A. Davis3, O. De Aguiar
Francisco54, S. De Capua56, M. De Cian12, J.M. De Miranda1, L. De Paula2, M.
De Serio14,d, P. De Simone19, C.T. Dean53, D. Decamp4, L. Del Buono8, H.-P.
Dembinski11, M. Demmer10, A. Dendek28, D. Derkach35, O. Deschamps5, F.
Dettori54, B. Dey65, A. Di Canto40, P. Di Nezza19, H. Dijkstra40, F. Dordei40,
M. Dorigo40, A. Dosil Suárez39, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L.
Dufour43, G. Dujany8, P. Durante40, R. Dzhelyadin37, M. Dziewiecki12, A.
Dziurda40, A. Dzyuba31, S. Easo51, M. Ebert52, U. Egede55, V. Egorychev32, S.
Eidelman36,w, S. Eisenhardt52, U. Eitschberger10, R. Ekelhof10, L. Eklund53,
S. Ely61, S. Esen12, H.M. Evans49, T. Evans57, A. Falabella15, N. Farley47, S.
Farry54, D. Fazzini21,i, L. Federici25, D. Ferguson52, G. Fernandez38, P.
Fernandez Declara40, A. Fernandez Prieto39, F. Ferrari15, F. Ferreira
Rodrigues2, M. Ferro-Luzzi40, S. Filippov34, R.A. Fini14, M. Fiore17,g, M.
Fiorini17,g, M. Firlej28, C. Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, K.
Fohl40, M. Fontana16,40, F. Fontanelli20,h, D.C. Forshaw61, R. Forty40, V.
Franco Lima54, M. Frank40, C. Frei40, J. Fu22,q, W. Funk40, E. Furfaro25,j, C.
Färber40, E. Gabriel52, A. Gallas Torreira39, D. Galli15,e, S. Gallorini23, S.
Gambetta52, M. Gandelman2, P. Gandini57, Y. Gao3, L.M. Garcia Martin70, J.
García Pardiñas39, J. Garra Tico49, L. Garrido38, P.J. Garsed49, D. Gascon38,
C. Gaspar40, L. Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck12, M.
Gersabeck56, T. Gershon50, Ph. Ghez4, S. Gianì41, V. Gibson49, O.G. Girard41,
L. Giubega30, K. Gizdov52, V.V. Gligorov8, D. Golubkov32, A. Golutvin55,40, A.
Gomes1,a, I.V. Gorelov33, C. Gotti21,i, E. Govorkova43, J.P. Grabowski12, R.
Graciani Diaz38, L.A. Granado Cardoso40, E. Graugés38, E. Graverini42, G.
Graziani18, A. Grecu30, R. Greim9, P. Griffith16, L. Grillo21,40,i, L.
Gruber40, B.R. Gruberg Cazon57, O. Grünberg67, E. Gushchin34, Yu. Guz37, T.
Gys40, C. Göbel62, T. Hadavizadeh57, C. Hadjivasiliou5, G. Haefeli41, C.
Haen40, S.C. Haines49, B. Hamilton60, X. Han12, T.H. Hancock57, S. Hansmann-
Menzemer12, N. Harnew57, S.T. Harnew48, J. Harrison56, C. Hasse40, M. Hatch40,
J. He63, M. Hecker55, K. Heinicke10, A. Heister9, K. Hennessy54, P. Henrard5,
L. Henry70, E. van Herwijnen40, M. Heß67, A. Hicheur2, D. Hill57, C.
Hombach56, P.H. Hopchev41, Z.C. Huard59, W. Hulsbergen43, T. Humair55, M.
Hushchyn35, D. Hutchcroft54, P. Ibis10, M. Idzik28, P. Ilten58, R.
Jacobsson40, J. Jalocha57, E. Jans43, A. Jawahery60, F. Jiang3, M. John57, D.
Johnson40, C.R. Jones49, C. Joram40, B. Jost40, N. Jurik57, S. Kandybei45, M.
Karacson40, J.M. Kariuki48, S. Karodia53, N. Kazeev35, M. Kecke12, M.
Kelsey61, M. Kenzie49, T. Ketel44, E. Khairullin35, B. Khanji12, C.
Khurewathanakul41, T. Kirn9, S. Klaver56, K. Klimaszewski29, T. Klimkovich11,
S. Koliiev46, M. Kolpin12, I. Komarov41, R. Kopecna12, P. Koppenburg43, A.
Kosmyntseva32, S. Kotriakhova31, M. Kozeiha5, L. Kravchuk34, M. Kreps50, P.
Krokovny36,w, F. Kruse10, W. Krzemien29, W. Kucewicz27,l, M. Kucharczyk27, V.
Kudryavtsev36,w, A.K. Kuonen41, K. Kurek29, T. Kvaratskheliya32,40, D.
Lacarrere40, G. Lafferty56, A. Lai16, G. Lanfranchi19, C. Langenbruch9, T.
Latham50, C. Lazzeroni47, R. Le Gac6, A. Leflat33,40, J. Lefrançois7, R.
Lefèvre5, F. Lemaitre40, E. Lemos Cid39, O. Leroy6, T. Lesiak27, B.
Leverington12, P.-R. Li63, T. Li3, Y. Li7, Z. Li61, T. Likhomanenko68, R.
Lindner40, F. Lionetto42, V. Lisovskyi7, X. Liu3, D. Loh50, A. Loi16, I.
Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M. Lucio Martinez39, H. Luo52, A.
Lupato23, E. Luppi17,g, O. Lupton40, A. Lusiani24, X. Lyu63, F. Machefert7, F.
Maciuc30, V. Macko41, P. Mackowiak10, S. Maddrell-Mander48, O. Maev31,40, K.
Maguire56, D. Maisuzenko31, M.W. Majewski28, S. Malde57, A. Malinin68, T.
Maltsev36,w, G. Manca16,f, G. Mancinelli6, P. Manning61, D. Marangotto22,q, J.
Maratas5,v, J.F. Marchand4, U. Marconi15, C. Marin Benito38, M. Marinangeli41,
P. Marino41, J. Marks12, G. Martellotti26, M. Martin6, M. Martinelli41, D.
Martinez Santos39, F. Martinez Vidal70, D. Martins Tostes2, L.M. Massacrier7,
A. Massafferri1, R. Matev40, A. Mathad50, Z. Mathe40, C. Matteuzzi21, A.
Mauri42, E. Maurice7,b, B. Maurin41, A. Mazurov47, M. McCann55,40, A. McNab56,
R. McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N. Meinert67,
D. Melnychuk29, M. Merk43, A. Merli22,40,q, E. Michielin23, D.A. Milanes66, E.
Millard50, M.-N. Minard4, L. Minzoni17, D.S. Mitzel12, A. Mogini8, J. Molina
Rodriguez1, T. Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, M.J.
Morello24,t, O. Morgunova68, J. Moron28, A.B. Morris52, R. Mountain61, F.
Muheim52, M. Mulder43, D. Müller56, J. Müller10, K. Müller42, V. Müller10, P.
Naik48, T. Nakada41, R. Nandakumar51, A. Nandi57, I. Nasteva2, M. Needham52,
N. Neri22,40, S. Neubert12, N. Neufeld40, M. Neuner12, T.D. Nguyen41, C.
Nguyen-Mau41,n, S. Nieswand9, R. Niet10, N. Nikitin33, T. Nikodem12, A.
Nogay68, D.P. O’Hanlon50, A. Oblakowska-Mucha28, V. Obraztsov37, S. Ogilvy19,
R. Oldeman16,f, C.J.G. Onderwater71, A. Ossowska27, J.M. Otalora Goicochea2,
P. Owen42, A. Oyanguren70, P.R. Pais41, A. Palano14,d, M. Palutan19,40, A.
Papanestis51, M. Pappagallo14,d, L.L. Pappalardo17,g, W. Parker60, C.
Parkes56, G. Passaleva18, A. Pastore14,d, M. Patel55, C. Patrignani15,e, A.
Pearce40, A. Pellegrino43, G. Penso26, M. Pepe Altarelli40, S. Perazzini40, P.
Perret5, L. Pescatore41, K. Petridis48, A. Petrolini20,h, A. Petrov68, M.
Petruzzo22,q, E. Picatoste Olloqui38, B. Pietrzyk4, M. Pikies27, D. Pinci26,
F. Pisani40, A. Pistone20,h, A. Piucci12, V. Placinta30, S. Playfer52, M. Plo
Casasus39, F. Polci8, M. Poli Lener19, A. Poluektov50,36, I. Polyakov61, E.
Polycarpo2, G.J. Pomery48, S. Ponce40, A. Popov37, D. Popov11,40, S.
Poslavskii37, C. Potterat2, E. Price48, J. Prisciandaro39, C. Prouve48, V.
Pugatch46, A. Puig Navarro42, H. Pullen57, G. Punzi24,p, W. Qian50, R.
Quagliani7,48, B. Quintana5, B. Rachwal28, J.H. Rademacker48, M. Rama24, M.
Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†, F. Ratnikov35, G. Raven44, M.
Ravonel Salzgeber40, M. Reboud4, F. Redi55, S. Reichert10, A.C. dos Reis1, C.
Remon Alepuz70, V. Renaudin7, S. Ricciardi51, S. Richards48, M. Rihl40, K.
Rinnert54, V. Rives Molina38, P. Robbe7, A. Robert8, A.B. Rodrigues1, E.
Rodrigues59, J.A. Rodriguez Lopez66, P. Rodriguez Perez56,†, A. Rogozhnikov35,
S. Roiser40, A. Rollings57, V. Romanovskiy37, A. Romero Vidal39, J.W.
Ronayne13, M. Rotondo19, M.S. Rudolph61, T. Ruf40, P. Ruiz Valls70, J. Ruiz
Vidal70, J.J. Saborido Silva39, E. Sadykhov32, N. Sagidova31, B. Saitta16,f,
V. Salustino Guimaraes1, C. Sanchez Mayordomo70, B. Sanmartin Sedes39, R.
Santacesaria26, C. Santamarina Rios39, M. Santimaria19, E. Santovetti25,j, G.
Sarpis56, A. Sarti26, C. Satriano26,s, A. Satta25, D.M. Saunders48, D.
Savrina32,33, S. Schael9, M. Schellenberg10, M. Schiller53, H. Schindler40, M.
Schlupp10, M. Schmelling11, T. Schmelzer10, B. Schmidt40, O. Schneider41, A.
Schopper40, H.F. Schreiner59, K. Schubert10, M. Schubiger41, M.-H. Schune7, R.
Schwemmer40, B. Sciascia19, A. Sciubba26,k, A. Semennikov32, E.S. Sepulveda8,
A. Sergi47, N. Serra42, J. Serrano6, L. Sestini23, P. Seyfert40, M. Shapkin37,
I. Shapoval45, Y. Shcheglov31, T. Shears54, L. Shekhtman36,w, V. Shevchenko68,
B.G. Siddi17,40, R. Silva Coutinho42, L. Silva de Oliveira2, G. Simi23,o, S.
Simone14,d, M. Sirendi49, N. Skidmore48, T. Skwarnicki61, E. Smith55, I.T.
Smith52, J. Smith49, M. Smith55, l. Soares Lavra1, M.D. Sokoloff59, F.J.P.
Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, S. Sridharan40, F.
Stagni40, M. Stahl12, S. Stahl40, P. Stefko41, S. Stefkova55, O. Steinkamp42,
S. Stemmle12, O. Stenyakin37, M. Stepanova31, H. Stevens10, S. Stone61, B.
Storaci42, S. Stracka24,p, M.E. Stramaglia41, M. Straticiuc30, U. Straumann42,
J. Sun3, L. Sun64, W. Sutcliffe55, K. Swientek28, V. Syropoulos44, M.
Szczekowski29, T. Szumlak28, M. Szymanski63, S. T’Jampens4, A. Tayduganov6, T.
Tekampe10, G. Tellarini17,g, F. Teubert40, E. Thomas40, J. van Tilburg43, M.J.
Tilley55, V. Tisserand4, M. Tobin41, S. Tolk49, L. Tomassetti17,g, D.
Tonelli24, F. Toriello61, R. Tourinho Jadallah Aoude1, E. Tournefier4, M.
Traill53, M.T. Tran41, M. Tresch42, A. Trisovic40, A. Tsaregorodtsev6, P.
Tsopelas43, A. Tully49, N. Tuning43,40, A. Ukleja29, A. Usachov7, A.
Ustyuzhanin35, U. Uwer12, C. Vacca16,f, A. Vagner69, V. Vagnoni15,40, A.
Valassi40, S. Valat40, G. Valenti15, R. Vazquez Gomez19, P. Vazquez
Regueiro39, S. Vecchi17, M. van Veghel43, J.J. Velthuis48, M. Veltri18,r, G.
Veneziano57, A. Venkateswaran61, T.A. Verlage9, M. Vernet5, M. Vesterinen57,
J.V. Viana Barbosa40, B. Viaud7, D. Vieira63, M. Vieites Diaz39, H. Viemann67,
X. Vilasis-Cardona38,m, M. Vitti49, V. Volkov33, A. Vollhardt42, B. Voneki40,
A. Vorobyev31, V. Vorobyev36,w, C. Voß9, J.A. de Vries43, C. Vázquez Sierra39,
R. Waldi67, C. Wallace50, R. Wallace13, J. Walsh24, J. Wang61, D.R. Ward49,
H.M. Wark54, N.K. Watson47, D. Websdale55, A. Weiden42, M. Whitehead40, J.
Wicht50, G. Wilkinson57,40, M. Wilkinson61, M. Williams56, M.P. Williams47, M.
Williams58, T. Williams47, F.F. Wilson51, J. Wimberley60, M. Winn7, J.
Wishahi10, W. Wislicki29, M. Witek27, G. Wormser7, S.A. Wotton49, K.
Wraight53, K. Wyllie40, Y. Xie65, Z. Xu4, Z. Yang3, Z. Yang60, Y. Yao61, H.
Yin65, J. Yu65, X. Yuan61, O. Yushchenko37, K.A. Zarebski47, M.
Zavertyaev11,c, L. Zhang3, Y. Zhang7, A. Zhelezov12, Y. Zheng63, X. Zhu3, V.
Zhukov33, J.B. Zonneveld52, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Universita e INFN, Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Universita & INFN, Milano-Bicocca, Milano, Italy
22Sezione di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Universidad de Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
70Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
71Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43

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