EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2017-278 LHCb-PAPER-2017-034 February 28, 2018

Measurement of branching fractions of charmless four-body ${\mathchar
28931\relax}^{0}_{b}$ and ${\mathchar 28932\relax}^{0}_{b}$ decays

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

A search for charmless four-body decays of ${\mathchar 28931\relax}^{0}_{b}$
and ${\mathchar 28932\relax}^{0}_{b}$ baryons with a proton and three charged
mesons (either kaons or pions) in the final state is performed. The data
sample used was recorded in 2011 and 2012 with the LHCb experiment and
corresponds to an integrated luminosity of 3 $\mbox{\,fb}^{-1}$. Six decay
modes are observed, among which ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-}$, ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$ and ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}K^{-}$ are established for the first time. Their branching
fractions (including the ratio of hadronisation fractions in the case of the
${\mathchar 28932\relax}^{0}_{b}$ baryon) are determined relative to the
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-}$ decay.

Published in JHEP 02 (2018) 098

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

##  1 Introduction

The abundant production of ${\mathchar 28931\relax}^{0}_{b}$ and ${\mathchar
28932\relax}^{0}_{b}$ baryons in proton-proton collisions at the Large Hadron
Collider (LHC) gives the LHCb experiment the opportunity to study multibody
charmless weak decays of $b$-flavoured baryons. The establishment of
${\mathchar 28931\relax}^{0}_{b}$ and ${\mathchar 28932\relax}^{0}_{b}$ baryon
signals will allow the measurements of their branching fractions as well as
the $C\\!P$-violating asymmetries in their decay.

The measurements of $C\\!P$-violation phenomena present, so far, a consistent
interpretation within the Standard Model paradigm [1]. Nonvanishing
$C\\!P$-violating asymmetries have been observed in the decays of both $K$ and
$B$ mesons [2]. In contrast, $C\\!P$ violation has not been clearly observed
in baryon decays although evidence for nonvanishing $C\\!P$ asymmetries in
$b$-flavoured baryon decays has been recently reported by the LHCb
collaboration [3].

A priori relevant decay modes to observe $C\\!P$ violation in $b$-baryon
decays are multibody charmless decays that can proceed simultaneously through
the charged-current ${b}\rightarrow{u}$ transition or the neutral-current
${b}\rightarrow{s},{d}$ transitions. The resulting interference exhibits a
weak-phase difference. Furthermore, the charmless multibody decays of $b$
baryons contain rich resonance structures, both in the low-mass two-body
baryon resonances (i.e. the $pK^{-}$, $p\pi^{-}$ and $p\pi^{+}$ invariant mass
spectra) and in the two-body nonbaryonic resonances (i.e. the
${\pi}^{+}{\pi}^{-}$, ${K}^{\pm}$ ${\pi}^{\mp}$ and ${{K}^{+}}{{K}^{-}}$
invariant mass spectra). Consequently, $C\\!P$ asymmetries might receive
significant enhancement from the strong-phase differences coming from the
interference of these resonances. Taken together, these factors make multibody
charmless $b$-baryon decays well suited for a potential first observation of
$C\\!P$ violation in the baryon sector. Conversely, the presence of
nonpredictible strong phases makes a potential observation of $C\\!P$
violation difficult to interpret in terms of the weak phase of the Cabibbo-
Kobayashi-Maskawa (CKM) quark-mixing matrix [4, 5].

This work focuses on a study of seven decays,111Charge conjugation is implied
throughout this document, unless stated otherwise. namely ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$, ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$, ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ and ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$, defining five exclusive
final states to study. The signal candidates are fully reconstructed and
selected by means of optimised particle identification and topological
criteria. A simultaneous fit to the invariant mass distribution of the
candidates in the five experimental spectra is performed to determine the
signal yields. The branching fractions, relative to the well-known
normalisation channel ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow
pK^{-}\pi^{+})\pi^{-}$ [6], are subsequently determined.

##  2 Detector and data set

The analysis reported here is performed using $pp$ collision data recorded
with the LHCb detector, corresponding to an integrated luminosity of
1.0$\mbox{\,fb}^{-1}$ at a centre-of-mass energy of
7$\mathrm{\,Te\kern-1.00006ptV}$ in 2011 and 2.0$\mbox{\,fb}^{-1}$ at a
centre-of-mass energy of 8$\mathrm{\,Te\kern-1.00006ptV}$ in 2012. The LHCb
detector [7, 8] 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 (PV), 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 detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.

Simulated data samples are used to investigate backgrounds from other
$b$-hadron decays and also to study the detection and reconstruction
efficiencies of the signals. In the simulation, $pp$ collisions are generated
using Pythia [9, *Sjostrand:2007gs] with a specific LHCb configuration [11].
Decays of hadronic particles are described by EvtGen [12] in which final-state
radiation is generated using Photos [13]. The interactions of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [14, *Agostinelli:2002hh] as described in Ref. [16].

##  3 Trigger and event selection

The online event selection is performed by a trigger[17] that consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, in which all charged particles with
$\mbox{$p_{\mathrm{T}}$}>500\,(300){\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ are
reconstructed for 2011 (2012) data. 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. The software trigger requires a two-,
three- or four-track secondary vertex with a significant displacement from all
primary $pp$ interaction vertices. At least one charged particle must have a
transverse momentum
$\mbox{$p_{\mathrm{T}}$}>1.7\,(1.6){\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ for
2011 (2012) data and be inconsistent with originating from any PV. A
multivariate algorithm [18] is used for the identification of secondary
vertices consistent with the decay of a $b$ hadron.

In this analysis, it is important to minimise the variation of the selection
efficiency over the phase space of the decays of interest. Trigger signals are
associated with reconstructed particles. Selection requirements can therefore
be made on whether the decision was due to the signal candidate, other
particles produced in the $pp$ collision or a combination of both. If it is
required that the hardware trigger requirements are satisfied by a high-
transverse-energy hadron belonging to the signal decay chain, a strong
variation of the efficiency over the phase space is observed. Consequently,
the strategy employed is that signal candidates are selected from events in
which the hardware trigger requirements are satisfied by other activity in the
event [17]. In that case, the variation of the efficiency over the phase space
is contained within 5%.

The events passing the trigger requirements are then filtered in two stages.
Initial requirements are applied to further reduce the size of the data sample
before a multivariate selection is implemented. Selection requirements based
on topological variables, such as the flight distance of the $b$-baryon
candidate, are used as the main discriminants. To reduce the variation of
selection efficiency over the phase space of the decays of interest (a
significant source of systematic uncertainty in the final result), only loose
requirements are made on the transverse momenta of the daughter particles,
$\mbox{$p_{\mathrm{T}}$}>250{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

The neutral $b$-baryon candidates, henceforth denoted $X_{b}$, are formed from
a proton candidate selected with particle identification (PID) requirements
and three additional charged tracks. When more than one PV is reconstructed,
the $X_{b}$ candidate is associated with the PV with which it forms the
smallest $\chi^{2}_{\text{IP}}$, where $\chi^{2}_{\text{IP}}$ is the
difference in $\chi^{2}$ of a given PV reconstructed with and without the
considered $X_{b}$ candidate. Each of the four tracks of the final state is
required to have $\mbox{$p$}<100{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, a value
beyond which there is little pion/kaon/proton discrimination, and
$\chi^{2}_{\text{IP}}>16$. The $X_{b}$ candidates are then required to form a
vertex with a fit quality $\chi^{2}_{\text{vtx}}<20$ with 5 degrees of freedom
and be significantly separated from any PV with $\chi^{2}_{\rm FD}>50$, where
$\chi^{2}_{\rm FD}$ is the square of the flight-distance significance. To
remove backgrounds from higher-multiplicity decays, the difference in
$\chi^{2}_{\text{vtx}}$ when adding any other track must be greater than 4.
The $X_{b}$ candidates must have
$\mbox{$p_{\mathrm{T}}$}>1.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
invariant mass within the range
$5340<m(phhh)<6400{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where $h$ stands
for either a charged pion or kaon. They are further required to be consistent
with originating from a PV, quantified by both the $\chi^{2}_{\text{IP}}$ and
the “pointing angle” between the reconstructed momentum of the $b$-hadron and
the vector defined by the associated PV and the decay vertex. Finally, PID
requirements are applied to provide discrimination between kaons and pions in
order to assign the candidates to one of the five different final-state
spectra $p\pi^{-}\pi^{+}\pi^{-}$, $pK^{-}\pi^{+}\pi^{-}$,
$pK^{-}K^{+}\pi^{-}$, $pK^{-}\pi^{+}K^{-}$ and $pK^{-}K^{+}K^{-}$.

There are three main categories of background that contribute significantly in
the selected invariant mass regions: the so-called signal “cross-feed”
backgrounds resulting from a misidentification of one or more final-state
particles; the charmless decays of neutral $B$ mesons to final states
containing four charged mesons, where a pion or a kaon is misidentified as a
proton; and the combinatorial backgrounds, which result from a random
association of unrelated tracks. The pion and kaon PID requirements that
define mutually exclusive samples are optimised to reduce the signal cross-
feed background, and hence to maximize the observation of the signal. The
charmless $B$-meson decays are identified by reconstructing the invariant mass
distributions of candidates reconstructed with a pion or kaon mass instead of
the proton mass hypothesis, in the data high-mass sidebands, defined as
$m_{\rm sideband}<m(phhh)<6400{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where
$m_{\rm sideband}$ = 5680 ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for
$p\pi^{-}\pi^{+}\pi^{-}$, $pK^{-}K^{+}\pi^{-}$ final states and $m_{\rm
sideband}$= 5840 ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for
$pK^{-}\pi^{+}\pi^{-}$, $pK^{-}\pi^{+}K^{-}$, $pK^{-}K^{+}K^{-}$ final states.
This background contribution is reduced by the optimisation of the proton PID
requirement.

In order to reject combinatorial backgrounds, multivariate discriminants based
on a boosted decision tree (BDT) [19] with the AdaBoost algorithm [20] have
been designed. Candidates from simulated ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ events and the data
high-mass sideband are used as the signal and background training samples,
respectively. This high-mass sideband region is chosen so that the sample is
free of signal cross-feed background. The samples are divided into two data-
taking periods and further subdivided into two equally sized subsamples. Each
subsample is then used to train an independent discriminant. In the subsequent
analysis the BDT trained on one subsample is used to select candidates from
the other subsample, in order to avoid bias.

The BDTs have as input discriminating quantities the $p_{\mathrm{T}}$, $\eta$,
$\chi^{2}_{\text{IP}}$, $\chi^{2}_{\rm FD}$, pointing angle and
$\chi^{2}_{\text{vtx}}$ of the $X_{b}$ candidate; the smallest change in the
$b$-baryon $\chi^{2}_{\text{vtx}}$ when adding any other track from the event;
the sum of the $\chi^{2}_{\text{IP}}$ of the four tracks of the final state;
and the $p_{\mathrm{T}}$ asymmetry

$p_{\rm T}^{\rm asym}=\frac{p_{\rm T}^{B}-p_{\rm T}^{\rm cone}}{p_{\rm
T}^{B}+p_{\rm T}^{\rm cone}}\,,$ (1)

where $p_{\rm T}^{\rm cone}$ is the transverse component of the sum of all
particle momenta inside a 1.5$\mathrm{\,rad}$ cone in $\eta$ and $\phi$ space
around the $b$-baryon candidate direction. The $p_{\rm T}^{\rm asym}$ of the
signal candidates are preferentially distributed towards high values. The BDT
output is determined to be uncorrelated with the position in the phase space
of the decay of interest.

The selection requirement placed on the output of the BDTs is independently
optimised for the seven decays of interest by maximising the figure of merit
[21]

$\mbox{FoM}=\frac{{\varepsilon}_{\rm sig}}{\frac{a}{2}+\sqrt{N_{B}}}\,,$ (2)

where the signal efficiency (${\varepsilon}_{\rm sig}$) is estimated from the
simulation and $N_{B}$ represents the number of expected background events for
a given selection, which is calculated by fitting the high-mass sideband of
the data sample, and extrapolating the yield into the signal region defined as
the invariant mass window covering $\pm$ 3 times the measured signal width.
The value $a=2$ is used in this analysis; it is found that varying this value
up to 5 does not significantly change the result. A common optimisation of the
BDT criteria is found, resulting in a signal efficiency of order 70%.

A number of background contributions consisting of fully reconstructed
$b$-baryon decays into the two-body ${{\mathchar 28931\relax}^{+}_{c}}h$,
${{\mathchar 28932\relax}^{+}_{c}}h$, three-body ${D}ph$ or
$({c}{\overline{c}})ph$ combinations, where $({c}{\overline{c}})$ represents a
charmonium resonance, may produce the same final state as the signal. Hence,
they will have the same $b$-baryon candidate invariant mass distribution as
the signal candidates, as well as a similar selection efficiency. The presence
of a misidentified hadron in the $D$, ${\mathchar 28931\relax}^{+}_{c}$ and
${\mathchar 28932\relax}^{+}_{c}$ decay also produces peaking background under
the signal. Therefore, the following decay channels are explicitly
reconstructed under the relevant particle hypotheses and vetoed by means of a
requirement on the resulting invariant mass, in all experimental spectra:
${\mathchar 28931\relax}^{+}_{c}$ ($\rightarrow
pK^{-}\pi^{+},p\pi^{+}\pi^{-},pK^{+}K^{-}$), ${\mathchar 28932\relax}^{+}_{c}$
($\rightarrow pK^{-}\pi^{+}$), ${D}^{+}$ ($\rightarrow K^{-}\pi^{+}\pi^{+}$),
${D}^{+}_{s}$ ($\rightarrow K^{-}K^{+}\pi^{+}$), ${D}^{0}$ ($\rightarrow
K^{\mp}\pi^{\pm},\pi^{+}\pi^{-},K^{+}K^{-}$), $\chi_{{c}0}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
($\rightarrow\pi^{+}\pi^{-},K^{+}K^{-}$).

The same set of trigger, $\mathrm{PID}$ and BDT requirements is applied to the
normalisation mode ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar
28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ to cancel out most of
the systematics effects related to the selection criteria. Candidates whose
$pK^{-}\pi^{+}$ invariant mass is in the range $2213<m(pK^{-}\pi^{+})<2313$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are retained as normalisation-mode
candidates. Conversely, events outside this interval belong to the signal
$pK^{-}\pi^{+}\pi^{-}$ spectrum, again ensuring statistically independent
samples for the simultaneous fit.

The fraction of events containing more than one candidate is below the percent
level. The candidate to be retained in each event is chosen randomly and
reproducibly.

##  4 Simultaneous fit

A simultaneous unbinned extended maximum likelihood fit is performed to the
${b}$-hadron candidate invariant mass distributions under each of the five
sets of mass hypotheses for the final-state tracks and the normalisation
channel candidates. The data samples are further split according to the year
of data taking. The components of the model include, in addition to the signal
decays, the partially reconstructed five-body $X^{0}_{b}$ decays, the signal
and background cross-feeds, the four- and the five-body decays of $B$-mesons
and the combinatorial background. The independent data samples constructed for
each experimental reconstructed spectrum are fitted simultaneously. For each
sample, the likelihood is expressed as

$\displaystyle\ln{\cal
L}=\sum_{i}\ln\left({\sum_{j}N_{j}P_{j,i}}\right)-\sum_{j}N_{j}$ (3)

where $N_{j}$ is the number of events related to the component $j$ and $P_{i}$
the probability of the candidate $i$.

###  4.1 Fit model

The signal decays are modelled as the sum of two Crystal Ball (CB) functions
[22]. These two CB functions share peak positions and widths but have
independent power-law tails on opposite sides of the peak. The ${\mathchar
28931\relax}^{0}_{b}$ mass parameter, corresponding to the most probable value
of the double-CB function, is free in the fit and is shared among all
invariant mass spectra. The difference between the ${\mathchar
28932\relax}^{0}_{b}$ and ${\mathchar 28931\relax}^{0}_{b}$ masses is also a
shared parameter and is constrained to the measured value in Ref. [2].

The ratio of the experimental widths of the signal decay functions is
constrained using Gaussian prior probability distributions included in the
likelihood, with parameters obtained from the fit to simulated events. The
measured ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$
width in the 2012 data-taking sample is chosen as the reference (measured to
be $\sigma=16.47\pm 0.22$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$). The
other parameters of the CB components are obtained by a simultaneous fit to
simulated samples, and are fixed to those values in the nominal fits to the
data.

The cross-feed backgrounds are modelled by the sum of two CB functions, the
parameters of which are determined from simulated samples. All cases resulting
from the misidentification of either one or two of the final-state particles
are considered. The relative yield of each misidentified decay is constrained
with respect to the yield of the corresponding correctly identified decay and
the known misidentification probabilities. The constraints are implemented
using Gaussian prior probability distributions included in the likelihood.
Their mean values are obtained from the ratio of selection efficiencies and
their widths include uncertainties originating from the finite size of the
simulated events samples as well as the systematic uncertainties related to
the determination of the PID efficiencies.

The backgrounds resulting from four- or five-body decays of $B$ mesons are
identified in each spectrum by a dedicated fit to the candidates in the high-
mass sideband, reconstructed under the hypothesis of a kaon mass for the
proton candidates. The relative yield of each decay is then constrained in the
simultaneous fit from its observed abundance in the high-mass sidebands. The
invariant mass distributions are modelled by the sum of two CB functions, the
parameters of which are determined from simulated events.

Partially reconstructed backgrounds where a neutral pion is not reconstructed,
such as ${\mathchar 28931\relax}^{0}_{b}$, ${\mathchar 28932\relax}^{0}_{b}$
$\rightarrow$ $phhh\pi^{0}$, are modelled by means of generalised ARGUS
functions [23] convolved with a Gaussian resolution function. The Gaussian
width is taken as the signal ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$ width parameter. The parameters of the ARGUS function
are shared among all invariant mass spectra and are determined directly from
the fit, except for the threshold, which is given by $m(X_{b})-m(\pi^{0})$.
Radiative decays such as ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p\pi^{-}\eta^{\prime}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}\eta^{\prime}$ ($\eta^{\prime}\rightarrow\pi^{+}\pi^{-}\gamma$) are
modelled separately using the same functional form but where the parameters
are determined using simulated events. The decay modes ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}\pi^{0}$ where a pion is
misidentified as a kaon can significantly contribute to the
$pK^{-}K^{+}\pi^{-}$ and $pK^{-}\pi^{+}K^{-}$ spectra. They are modelled with
an empirical (histogrammed) function determined from the partially
reconstructed background candidates in the normalisation channel.

Finally, the combinatorial background is modelled by a linear function whose
slope is shared among the invariant mass spectra. An exponential function is
used as an alternative model in order to estimate any systematic effect
related to this choice of modelling.

###  4.2 Fit results

Figures 1 to 5 display the fit results of the simultaneous fit to the
invariant mass spectra of the five final states using the whole data sample.
Figure 6 displays the result of the fit to the normalisation channel. The
signal yields for each decay channel are shown in Table 1. The fit model
provides an overall satisfactory description of the data. However, differences
between the data and the fit model can be noted in the high-mass sidebands of
Figs. 2, 4 and 5. The significance of the disagreement is not larger than two
standard deviations. Those discrepancies are covered within the size of the
variations considered in the evaluation of the systematic uncertainties.

Figure 1: Results of the fit to the $p\pi^{-}\pi^{+}\pi^{-}$ candidate mass spectrum with (top) linear and (bottom) logarithmic scales. The different components employed in the fit are indicated in the legend. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$ 5-body legend describes two components, the radiative partially reconstructed background ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\eta^{\prime}$ and the partially reconstructed background ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}\pi^{0}$ where a $\pi^{0}$ is not reconstructed. The latter has a lower-mass endpoint. Figure 2: Results of the fit to the $pK^{-}\pi^{+}\pi^{-}$ candidate mass spectrum with (top) linear and (bottom) logarithmic scales. The different components employed in the fit are indicated in the legend. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$ 5-body legend describes two components, the radiative partially reconstructed background ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\eta^{\prime}$ and the partially reconstructed background ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}\pi^{0}$ where a $\pi^{0}$ is not reconstructed. The latter has a lower-mass endpoint. Figure 3: Results of the fit to the $pK^{-}K^{+}\pi^{-}$ candidate mass spectrum with (top) linear and (bottom) logarithmic scales. The different components employed in the fit are indicated in the legend. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$ 5-body legend describes two components where a $\pi^{0}$ is not reconstructed, the partially reconstructed background ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}\pi^{0}$ where a pion is misidentified as a kaon and the partially reconstructed background ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}\pi^{0}$. Figure 4: Results of the fit to the $pK^{-}\pi^{+}K^{-}$ candidate mass spectrum with (top) linear and (bottom) logarithmic scales. The different components employed in the fit are indicated in the legend. Figure 5: Results of the fit to the $pK^{-}K^{+}K^{-}$ candidate mass spectrum with (top) linear and (bottom) logarithmic scales. The different components employed in the fit are indicated in the legend. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$ 5-body legend includes two decays, partially reconstructed ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}{\gamma}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}\pi^{0}$, where the $\gamma$ and $\pi^{0}$ are not reconstructed. Figure 6: Results of the fit to the ${{\mathchar 28931\relax}^{+}_{c}}\pi^{-}$ candidate mass spectrum on linear scale. The different components employed in the fit are indicated in the legend. Table 1: Signal yields for each decay mode, determined by summing the fitted yields in each year of data taking. The signal ($S$) to background ($B$, adding all sources) ratios in an invariant mass window, covering $\pm$ 3 times the measured signal widths, are provided. The corresponding invariant mass ranges are reported in the fourth column. Decay mode | Signal yield | $S/B$ |  $\pm 3\sigma$ range (${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$)
---|---|---|---
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ | $1809\,\pm\,{\color[rgb]{1,1,1}0}48$ | $4.9{\color[rgb]{1,1,1}0}\,\pm\,0.3$ | [5573.9, 5674.6]
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | $5193\,\pm\,{\color[rgb]{1,1,1}0}76$ | $7.7{\color[rgb]{1,1,1}0}\,\pm\,0.4$ | [5574.4, 5674.2]
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ | $444\,\pm\,{\color[rgb]{1,1,1}0}30$ | $0.71\,\pm\,0.06$ | [5577.4, 5671.1]
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | $1706\,\pm\,{\color[rgb]{1,1,1}0}46$ | $8.1{\color[rgb]{1,1,1}0}\,\pm\,0.7$ | [5579.0, 5674.6]
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | $183\,\pm\,{\color[rgb]{1,1,1}0}22$ | $0.59\,\pm\,0.09$ | [5747.9, 5846.2]
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ | $199\,\pm\,{\color[rgb]{1,1,1}0}21$ | $0.81\,\pm\,0.10$ | [5747.4, 5846.2]
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | $27\,\pm\,{\color[rgb]{1,1,1}0}14$ | $0.14\,\pm\,0.08$ | [5752.7, 5840.8]
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ | $16518\,\pm\,133$ | — | [5573.7, 5674.8]

All signals that were searched for are established unambiguously with the
exception of the ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-}$ decay. The signal-to-background ratios vary from mode to
mode following the hierarchy of the branching fractions and are summarized in
Table 1.

##  5 Determination of the signal efficiencies

The experimentally determined result for each four-body signal decay is the
quantity $R$, defined as

$\displaystyle R(X_{b}\rightarrow phh^{\prime}h^{\prime\prime})$
$\displaystyle\equiv$ $\displaystyle\frac{{\mathcal{B}}(X_{b}\rightarrow
phh^{\prime}h^{\prime\prime})}{{\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-})}\cdot\frac{f_{X_{b}}}{f_{{{\mathchar
28931\relax}^{0}_{b}}}},$ $\displaystyle=$
$\displaystyle\frac{\epsilon_{{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-}}^{\mbox{\small{geo.}
}}}{\epsilon_{X_{b}\rightarrow
phh^{\prime}h^{\prime\prime}}^{\mbox{\small{geo.}}}}\cdot\frac{\epsilon_{{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-}}^{\mbox{\small{sel.}
}}}{\epsilon_{X_{b}\rightarrow
phh^{\prime}h^{\prime\prime}}^{\mbox{\small{sel.}}}}\cdot\frac{\epsilon_{{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-}}^{\mbox{\scriptsize{PID}
}}}{\epsilon_{X_{b}\rightarrow
phh^{\prime}h^{\prime\prime}}^{\mbox{\scriptsize{PID}}}}\cdot\frac{1}{\epsilon_{X_{b}\rightarrow
phh^{\prime}h^{\prime\prime}}^{\mbox{\scriptsize{veto}}}}\cdot\frac{\mathcal{N}_{X_{b}\rightarrow
phh^{\prime}h^{\prime\prime}}}{\mathcal{N}_{{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi^{-}}},$

where $\mathcal{B}$ represents the relevant branching fraction and
$f_{X_{b}}/{f_{{{\mathchar 28931\relax}^{0}_{b}}}}$ is the relative
hadronisation fraction of ${b}\rightarrow X_{b}$ with respect to
${b}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}$. From left to right, the
ratios of efficiencies are related to the geometrical acceptance, the
selection criteria, the PID requirements and the veto of charm and charmonium
backgrounds. The measured signal and normalisation channel yields are
represented by $\mathcal{N}_{X_{b}\rightarrow phh^{\prime}h^{\prime\prime}}$
and $\mathcal{N}_{{{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-}}$.

The efficiencies are determined from simulated signal events that have been
generated with an arbitrary mixture of phase-space decays and quasi-two-body
amplitudes, which feature the production of intermediate resonances close to
their kinematic threshold. For instance, the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ decay proceeds in the
simulation of quasi-two-body amplitudes via the decays ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar
28931\relax^{*}(1520)^{0}\rho(770)^{0}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar
28931\relax^{*}(1520)^{0}f_{2}(1270)$ or ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow N^{*}(1520)^{0}K^{*}(892)$. In principle, the
selection efficiency of each decay mode depends on the phase-space
coordinates, but the actual dynamics of the decays is a priori unknown and a
data-driven correction of the efficiency determination with simulated events
would be required as was done in Ref. [24]. However, the candidate selection
has been designed without relying on the kinematics of the daughter particles
in the decay. The candidates selected such that the hardware trigger is
satisfied independently of the signal particles, provide a sample with an
efficiency that is, to a very good approximation, constant over the phase
space of the decays. The residual variation of the efficiency over the phase
space is consequently addressed as a systematic uncertainty.

The imperfections of the simulation are corrected for in several respects.
Inaccuracies of the tracking simulation and the PID simulation are mitigated
by a weighting of the simulation to match the efficiencies measured in the
data calibration samples [25]. The uncertainties related to these corrections
are propagated to the branching fraction measurements as systematic
uncertainties. Other inaccuracies in the simulation are addressed as
systematic uncertainties and discussed in Section 6. A number of two- or
three-body invariant mass criteria have been used to veto charm and charmonium
resonances. The efficiency of these vetoes is determined a posteriori on the
data samples by inferring the number of signal candidates vetoed by each mass
criterion from a linear interpolation of the invariant mass distribution
reconstructed under the relevant mass hypotheses of the final-state particles.

Table 2 shows the ratios of efficiencies for the 2011 and 2012 data-taking
periods, necessary to derive the branching fraction values relative to the
normalisation channel ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-}$. The associated uncertainties are propagated as
systematic uncertainties in the derivation of the branching fractions.

Table 2: Ratios of the normalisation decay mode efficiencies, relative to the signal decay mode as used in Eq. (5), for (first row) 2011 and (second row) 2012. The last column shows the efficiency of the veto of charm and charmonium backgrounds (applied to the signal mode only), as discussed in the text. Since the ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ decay mode is not observed, the veto efficiency is determined with the simulated data sample. The difference between the simulation value and the average veto efficiency measured on other ${\mathchar 28932\relax}^{0}_{b}$ modes is reported in the table as the uncertainty. Decay mode | Ratios of efficiencies
---|---
| Acceptance | Selection | $\mathrm{PID}$ | Vetoes
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ | 1.070 $\pm$ 0.003 | 0.433 $\pm$ 0.011 | 1.018 $\pm$ 0.013 | 0.693 $\pm$ 0.028
1.050 $\pm$ 0.004 | 0.425 $\pm$ 0.009 | 1.046 $\pm$ 0.010 | 0.712 $\pm$ 0.017
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | 1.020 $\pm$ 0.003 | 0.438 $\pm$ 0.011 | 0.922 $\pm$ 0.012 | 0.758 $\pm$ 0.032
1.004 $\pm$ 0.004 | 0.432 $\pm$ 0.009 | 0.958 $\pm$ 0.009 | 0.744 $\pm$ 0.016
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ | 0.978 $\pm$ 0.003 | 0.462 $\pm$ 0.012 | 0.846 $\pm$ 0.011 | 0.742 $\pm$ 0.099
0.970 $\pm$ 0.004 | 0.468 $\pm$ 0.010 | 0.874 $\pm$ 0.008 | 0.765 $\pm$ 0.050
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | 0.928 $\pm$ 0.003 | 0.445 $\pm$ 0.012 | 0.783 $\pm$ 0.010 | 0.751 $\pm$ 0.036
0.916 $\pm$ 0.003 | 0.452 $\pm$ 0.010 | 0.801 $\pm$ 0.007 | 0.787 $\pm$ 0.026
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | 1.019 $\pm$ 0.003 | 0.431 $\pm$ 0.011 | 0.902 $\pm$ 0.011 | 0.652 $\pm$ 0.082
1.009 $\pm$ 0.004 | 0.424 $\pm$ 0.009 | 0.917 $\pm$ 0.008 | 0.659 $\pm$ 0.109
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ | 0.979 $\pm$ 0.003 | 0.434 $\pm$ 0.011 | 0.829 $\pm$ 0.010 | 0.689 $\pm$ 0.074
0.969 $\pm$ 0.004 | 0.450 $\pm$ 0.010 | 0.847 $\pm$ 0.008 | 0.752 $\pm$ 0.081
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | 0.929 $\pm$ 0.003 | 0.425 $\pm$ 0.011 | 0.764 $\pm$ 0.009 | 0.819 $\pm$ 0.123
0.922 $\pm$ 0.003 | 0.429 $\pm$ 0.009 | 0.771 $\pm$ 0.007

##  6 Systematic uncertainties

The systematic uncertainties are largely reduced by normalising the branching
fraction measurements with respect to that of the decay channel ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow
pK^{-}\pi^{+})\pi^{-}$. The remaining sources of systematic uncertainties and
the methods used to estimate them are described in this section. Tables 3 and
4 provide the yields measured by the fit, the related statistical
uncertainties, the overall efficiency, as well as the systematic uncertainty
for each decay, for 2011 and 2012 data, respectively. The other sources of
systematic uncertainty, which are not reported here, have negligible impact on
the measurements.

###  6.1 Fit model uncertainties

Uncertainties related to the fit model result from uncertainties in the values
of the parameters taken from the simulation as well as from the choice of the
functional forms used to describe the various components of the model.

The systematic uncertainties related to the parameters fixed to values
determined from simulated events are obtained by repeating the fit with the
parameters allowed to vary according to their uncertainties using
pseudoexperiments. The fixed parameters that are driving the shape of the
tails of the functional forms describing signal channels, cross-feeds and $B$
backgrounds distributions are estimated from a simultaneous fit of the
simulated events of these categories. The parameters are then varied according
to the covariance matrix obtained from simulated events. The nominal fit is
then performed on this ensemble of pseudoexperiments and the distribution of
the difference between the yield determined in each of these fits and that of
the nominal fit is in turn fitted with a Gaussian function. The systematic
uncertainty associated with the choice of the value of each signal parameter
from simulated events is then assigned as the linear sum of the absolute value
of the mean of the Gaussian and its width. The variation of the fixed
parameters of a functional form covers any reasonable variation of that shape.

The combinatorial background is modelled by a linear function. This model is
substituted by an exponential form in the fit to the data. Pseudoexperiments
based on the latter model are fit with the nominal model. The value of the
uncertainty is computed as the linear sum of the mean of the resulting
distribution and its RMS.

The mixture of quasi-two-body and phase-space decays that has been used to
generate the simulation samples is a source of systematic uncertainty. The
true signal dynamics (a priori unknown) lies between two extreme cases: the
decays are saturated by quasi-two-body amplitudes or are fully described by a
uniform amplitude over phase space. The shapes used to model all signal modes
and cross-feeds are weighted according to these two extreme cases and the
range of variation of the fit results obtained under the two conditions is
taken as the corresponding systematic uncertainty estimate. In addition, the
data-driven kinematics-dependent $\mathrm{PID}$ corrections, applied to the
$\mathrm{PID}$ efficiencies, obtained in the simulation to match the data, are
also used to weight the functional forms of all the components of the fit
model derived from simulated events.

The total systematic uncertainty of the fit model is given by the sum in
quadrature of all the contributions. It is mostly dominated by the shape
parameters fixed to values determined from simulated events.

###  6.2 Selection efficiency uncertainties

The most significant source of systematic uncertainty is related to the
control of the variation of the candidate selection efficiency over the phase
space of the decays of interest. The systematic uncertainties coming from the
determination of the efficiencies are larger than the statistical
uncertainties for a few modes. Their estimation relies on the simulation of
the two extreme dynamics of each decay, namely intermediate resonances close
to the kinematic threshold (e.g. $\mathchar
28931\relax^{*}(1520)^{0}\rho(770)^{0}$, $\mathchar
28931\relax^{*}(1520)^{0}f_{2}(1270)$ or $N^{*}(1520)^{0}K^{*}(892)$ for
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ simulated
signal events) or uniformly populated phase-space decays. The difference in
efficiency measured between these two cases is examined for all elements of
the signal candidate selection procedure: geometrical acceptance,
reconstruction and selection, trigger, $\mathrm{PID}$ and BDT criteria. The
individual ranges of variation are summed in quadrature to provide the total
systematic uncertainty estimate, which is found to be the dominant source for
most of the modes. The correlation between the determinations for 2011 and
2012 data samples is taken into account in the combined measurement.

The training of the BDT relies on simulated signal events. Potential
inaccuracies in the simulation of the variables used in the BDT produce
suboptimal discrimination of the multivariate tool. In addition, the
$b$-hadron kinematics is a known source of differences between simulated
events and data, and can further induce a bias in the signal efficiency
determination. The systematic uncertainty due to this effect is estimated by
weighting the simulated distributions of the $p_{\mathrm{T}}$ and $\eta$ of
the $X_{b}$ candidates to match the distributions of the selected data for the
normalisation channel. The observed differences with the nominal selection
efficiency are taken as the uncertainty estimates.

Uncertainties related to the efficiencies of the charm and charmonium
resonance vetoes (discussed in Section 5) are dominated by the statistical
uncertainties on the counting of the candidates in the two- or three-body
invariant mass distributions before and after the veto criteria. It is
analytically propagated to the branching fraction measurements and is a major
source in the systematic uncertainty budget.

Table 3: Yields and efficiencies of each signal decay with the statistical uncertainty, and systematic uncertainties related to the fit model and the efficiency determination, for the 2011 data samples. Decay mode | Yield | Eff.($10^{-3}$) | Stat.(%) | Fit Model(%) | Eff. Syst.(%)
---|---|---|---|---|---
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ | $533$ | 0.51 | $\pm 4.8$ | $\pm 1.4$ | $\pm 5.2$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | $1679$ | 0.64 | $\pm 2.6$ | $\pm 1.1$ | $\pm 5.5$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ | $120$ | 0.68 | $\pm 14$ | $\pm 8.5$ | $\pm 14$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | $565$ | 0.81 | $\pm 4.7$ | $\pm 1.8$ | $\pm 6.4$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | $65$ | 0.57 | $\pm 19$ | $\pm 3.5$ | $\pm 14$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ | $68$ | 0.68 | $\pm 17$ | $\pm 5.2$ | $\pm 12$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | $9$ | 0.95 | $\pm 83$ | $\pm 12.8$ | $\pm 16$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ | $5427$ | 0.35 | $\pm 1.4$ | $\pm 0.8$ | —
Table 4: Yields and efficiencies of each signal decay with the statistical uncertainty, and systematic uncertainties related to the fit model and the efficiency determination, for the 2012 data samples. Decay mode | Yield | Eff.($10^{-3}$) | Stat.(%) | Fit Model(%) | Eff. Syst.(%)
---|---|---|---|---|---
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ | $1277$ | 0.45 | $\pm 3.2$ | $\pm 1.2$ | $\pm 4.8$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | $3515$ | 0.53 | $\pm 1.9$ | $\pm 1.3$ | $\pm 3.7$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ | $324$ | 0.57 | $\pm 7.9$ | $\pm 5.9$ | $\pm 7.3$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | $1141$ | 0.70 | $\pm 3.3$ | $\pm 1.4$ | $\pm 5.1$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | $118$ | 0.49 | $\pm 16$ | $\pm 3.1$ | $\pm 18$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ | $131$ | 0.60 | $\pm 13$ | $\pm 5.8$ | $\pm 13$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | $19$ | 0.79 | $\pm 60$ | $\pm 10$ | $\pm 16$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ | $12226$ | 0.29 | $\pm 1.0$ | $\pm 0.8$ | —

##  7 Branching fraction measurements and concluding remarks

Six decays are unambiguously observed. The ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ decay mode is measured with
a significance of $2.3\sigma$. Tables 5 and 6 summarise the relative branching
fraction measurements determined from Eq. (5), separately for the 2011 and
2012 data samples. The consistency of the two determinations of each decay
mode for each year is quantified as the ratio of the signed difference of the
central values over the quadratic sum of the related uncertainties. The two
measurements are in fair agreement, namely better that $2.1$ statistical
standard deviations in all cases.

Table 5: Measurements of the $R$ ratio from the (first row) 2011 and the (second row) 2012 data samples for ${\mathchar 28931\relax}^{0}_{b}$ decay modes expressed in percent as well as their combination. The three uncertainties are statistical, systematic related to the fit model and systematic related to the efficiency, respectively. The consistency of the two determinations for each year, denoted $\Delta$, is quantified as the ratio of the signed difference of the central values over the quadratic sum of the related uncertainties. $R$ (per decay) | Value ($\%$) | $\Delta$ | Combination ($\%$)
---|---|---|---
$R$(${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$) |  06.69 $\pm$ 0.33 $\pm$ 0.09 $\pm$ 0.37 | $-0.6\sigma$ | ${\color[rgb]{1,1,1}0}6.85\pm 0.19\pm 0.08\pm 0.32$
06.91 $\pm$ 0.23 $\pm$ 0.08 $\pm$ 0.35
$R($${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$) | 16.83 $\pm$ 0.49 $\pm$ 0.19 $\pm$ 1.00 | ${\color[rgb]{1,1,1}+}1.2\sigma$ | $16.4{\color[rgb]{1,1,1}0}\pm 0.3{\color[rgb]{1,1,1}0}\pm 0.2{\color[rgb]{1,1,1}0}\pm 0.7{\color[rgb]{1,1,1}0}$
16.18 $\pm$ 0.33 $\pm$ 0.20 $\pm$ 0.66
$R($${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$) |  01.14 $\pm$ 0.15 $\pm$ 0.10 $\pm$ 0.16 | $-1.4\sigma$ | ${\color[rgb]{1,1,1}0}1.32\pm 0.09\pm 0.09\pm 0.10$
01.39 $\pm$ 0.11 $\pm$ 0.08 $\pm$ 0.10
$R($${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$) |  04.49 $\pm$ 0.22 $\pm$ 0.08 $\pm$ 0.29 | ${\color[rgb]{1,1,1}+}2.1\sigma$ | ${\color[rgb]{1,1,1}0}4.11\pm 0.12\pm 0.06\pm 0.19$
03.97 $\pm$ 0.14 $\pm$ 0.05 $\pm$ 0.20
Table 6: Measurements of the $R$ ratio from the (first row) 2011 and the (second row) 2012 data samples for ${\mathchar 28932\relax}^{0}_{b}$ decay modes expressed in per mil as well as their combination. The three uncertainties are statistical, systematic related to the fit model and systematic related to the efficiency, respectively. The consistency of the two determinations for each year, denoted $\Delta$, is quantified as the ratio of the signed difference of the central values over the quadratic sum of the related uncertainties. $R$ (per decay) | Value $(10^{-3})$ | $\Delta$ | Combination $(10^{-3})$
---|---|---|---
$R$(${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$) | $7.2{\color[rgb]{1,1,1}0}\,\pm\,1.4{\color[rgb]{1,1,1}0}\pm 0.2{\color[rgb]{1,1,1}0}\pm 0.9$ | 0.9$\sigma$ | 6.20 $\pm$ 0.80 $\pm$ 0.20 $\pm$ 0.80
$5.8{\color[rgb]{1,1,1}0}\,\pm\,0.9{\color[rgb]{1,1,1}0}\pm
0.2{\color[rgb]{1,1,1}0}\pm 1.0$
$R$(${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$) | $6.4{\color[rgb]{1,1,1}0}\,\pm\,1.1{\color[rgb]{1,1,1}0}\pm 0.4{\color[rgb]{1,1,1}0}\pm 0.7$ | 0.9$\sigma$ | 5.60 $\pm$ 0.60 $\pm$ 0.40 $\pm$ 0.50
$5.3{\color[rgb]{1,1,1}0}\,\pm\,0.7{\color[rgb]{1,1,1}0}\pm
0.4{\color[rgb]{1,1,1}0}\pm 0.6$
$R$(${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$) | $0.59\,\pm\,0.49\pm 0.12\pm 0.10$ | 0.1$\sigma$ | 0.57 $\pm$ 0.28 $\pm$ 0.08 $\pm$ 0.10
$0.56\,\pm\,0.34\pm 0.07\pm 0.09$

As the decay mode ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-}$ is not observed, 90% and 95% confidence level (C.L.)
intervals, based on the Feldman-Cousins confidence belt inference described in
Ref. [26], are placed on the branching fraction for this decay mode relative
to ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar
28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$

$R({{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-})\in[4.05\mathrm{-}8.86]\cdot 10^{-4}$ at 90$\%$ C.L.,

$R({{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-})\in[3.82\mathrm{-}9.81]\cdot 10^{-4}$ at 95$\%$ C.L..

Using the world-average values ${\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-})=(0.430\pm 0.036)\%$ and
${\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\rightarrow
pK^{-}\pi^{+})=(6.46\pm 0.24)\%$ [27], the branching fractions of the
${\mathchar 28931\relax}^{0}_{b}$ decay modes are

$\displaystyle{\mathcal{B}}({{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p\pi^{-}\pi^{+}\pi^{-})$ $\displaystyle=(1.90\pm 0.06\pm 0.10\pm 0.16\pm
0.07)\cdot 10^{-5}$ , $\displaystyle{\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-})$
$\displaystyle=(4.55\pm 0.08\pm 0.20\pm 0.39\pm 0.17)\cdot 10^{-5}$ ,
$\displaystyle{\mathcal{B}}({{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}\pi^{-})$ $\displaystyle=(0.37\pm 0.03\pm 0.04\pm 0.03\pm
0.01)\cdot 10^{-5}$ , $\displaystyle{\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-})$ $\displaystyle=(1.14\pm
0.03\pm 0.07\pm 0.10\pm 0.05)\cdot 10^{-5}$ ,

where the first uncertainty is statistical and the second comes from
experimental systematic sources. The two last uncertainties are due to the
knowledge of the branching fractions ${\mathcal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi^{-})$ and
${\mathcal{B}}({{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})$ in
that order.
The product of the branching fractions of the ${\mathchar
28932\relax}^{0}_{b}$ decay modes with the hadronisation fraction of
${\mathchar 28932\relax}^{0}_{b}$ relative to ${\mathchar
28931\relax}^{0}_{b}$ are accordingly obtained

$\displaystyle{\mathcal{B}}({{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-})\cdot f_{{{\mathchar
28932\relax}^{0}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$
$\displaystyle=(1.72\pm 0.21\pm 0.25\pm 0.15\pm 0.07)\cdot 10^{-6}$ ,
$\displaystyle{\mathcal{B}}({{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}K^{-})\cdot f_{{{\mathchar 28932\relax}^{0}_{b}}}/f_{{{\mathchar
28931\relax}^{0}_{b}}}$ $\displaystyle=(1.56\pm 0.16\pm 0.19\pm 0.13\pm
0.06)\cdot 10^{-6}$ , $\displaystyle{\mathcal{B}}({{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-})\cdot f_{{{\mathchar
28932\relax}^{0}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$
$\displaystyle\in[0.11\mathrm{-}0.25]\cdot 10^{-6}\mbox{ at 90\% C.L.}$

In summary, the four decay modes ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-}$, ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$ and ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}K^{-}$ are observed for the first time. Branching fractions
(including the ratio of hadronisation fractions in the case of the ${\mathchar
28932\relax}^{0}_{b}$ baryon) of these decay modes and the branching fractions
of the two already observed decay modes ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ [3] are determined
relative to the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\pi^{-}$ decay. The ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ decay mode is measured with
a significance of $2.3\sigma$ and 90% and 95% confidence level intervals are
set on its branching fraction relative to ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi^{-}$. The
establishment of these signals opens new channels in which to search for
$C\\!P$-violating asymmetries in these fully charged four-body decays of
${\mathchar 28931\relax}^{0}_{b}$ and ${\mathchar 28932\relax}^{0}_{b}$
baryons.

## 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, M. Atzeni42, 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. Belyaev32,40, 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. Bizzeti18,u, M. Bjørn57, T.
Blake50, F. Blanc41, S. Blusk61, V. Bocci26, T. Boettcher58, A. Bondar36,w, N.
Bondar31, I. Bordyuzhin32, 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, M. Cattaneo40, G.
Cavallero20,40,h, R. Cenci24,t, D. Chamont7, M. Charles8, Ph. Charpentier40,
G. Chatzikonstantinidis47, M. Chefdeville4, S. Chen16, S.F. Cheung57, S.-G.
Chitic40, V. Chobanova39,40, 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 Francisco40, 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. 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. Gandini22, 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. Gersabeck56, M. Gersabeck56, T. Gershon50, Ph.
Ghez4, S. Gianì41, V. Gibson49, O.G. Girard41, L. Giubega30, K. Gizdov52, V.V.
Gligorov8, D. Golubkov32, A. Golutvin55, 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, 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, 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, W. Hu65, 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, F. Keizer49, M. Kelsey61, M. Kenzie49, T. Ketel44, E.
Khairullin35, B. Khanji12, C. Khurewathanakul41, T. Kirn9, S. Klaver56, K.
Klimaszewski29, T. Klimkovich11, S. Koliiev46, M. Kolpin12, R. Kopecna12, P.
Koppenburg43, A. Kosmyntseva32, S. Kotriakhova31, M. Kozeiha5, L. Kravchuk34,
M. Kreps50, F. Kress55, P. Krokovny36,w, F. Kruse10, W. Krzemien29, W.
Kucewicz27,l, M. Kucharczyk27, V. Kudryavtsev36,w, A.K. Kuonen41, 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, B.
Malecki27, A. Malinin68, T. Maltsev36,w, G. Manca16,f, G. Mancinelli6, 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, 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. Mombacher10, 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, M. Palutan19,40, A. Papanestis51, M. Pappagallo14,d, L.L.
Pappalardo17,g, W. Parker60, C. Parkes56, G. Passaleva18,40, 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, A. Pistone20,h, A. Piucci12, V.
Placinta30, S. Playfer52, M. Plo Casasus39, F. Polci8, M. Poli Lener19, A.
Poluektov50, 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, 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. Sarti19,k, C. Satriano26,s, A. Satta25, D.M.
Saunders48, D. Savrina32,33, S. Schael9, M. Schellenberg10, M. Schiller53, H.
Schindler40, M. Schmelling11, T. Schmelzer10, B. Schmidt40, O. Schneider41, A.
Schopper40, H.F. Schreiner59, 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, 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.
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S. Stemmle12, O. Stenyakin37, M. Stepanova31, H. Stevens10, S. Stone61, B.
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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, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
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