EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2019-013 LHCb-PAPER-2018-044 23 September 2019

Measurements of $C\\!P$ asymmetries in 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 $C\\!P$ violation in charmless four-body decays of ${\mathchar
28931\relax}^{0}_{b}$ and ${\mathchar 28932\relax}^{0}_{b}$ baryons with a
proton and three charged mesons in the final state is performed. To cancel out
production and detection charge-asymmetry effects, the search is carried out
by measuring the difference between the $C\\!P$ asymmetries in a charmless
decay and in a decay with an intermediate charmed baryon with the same
particles in the final state. The data sample used was recorded in 2011 and
2012 with the LHCb detector and corresponds to an integrated luminosity of
$3\text{\,fb}^{-1}$. A total of 18 $C\\!P$ asymmetries are considered, either
accounting for the full phase space of the decays or exploring specific
regions of the decay kinematics. No significant $C\\!P$-violation effect is
observed in any of the measurements.

Published in Eur. Phys. J. C (2019) 79: 745

© 2019 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

##  1 Introduction

All measurements of $C\\!P$ violation performed so far are consistent with the
predictions of the Standard Model (SM) [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 observed in baryon decays,
although some indications for nonvanishing $C\\!P$ asymmetries in
$b$-flavoured baryon decays have been reported by the LHCb collaboration [3,
4, 5, 6].

The abundant production of ${\mathchar 28931\relax}^{0}_{b}$ and ${\mathchar
28932\relax}^{0}_{b}$ baryons111The inclusion of charge conjugate processes is
implied throughout this paper, unless stated otherwise. in proton-proton
collisions at the Large Hadron Collider (LHC) gives the LHCb experiment the
opportunity to study multibody charmless decays of $b$-flavoured baryons. In
particular, ${\mathchar 28931\relax}^{0}_{b}$ and ${\mathchar
28932\relax}^{0}_{b}$ baryon decays to charmless four-body final states were
observed by the LHCb collaboration and their branching fractions measured [7].
Their large yields enable measurements of $C\\!P$-violating asymmetries to be
performed with a precision at the level of a few percent.

This search follows the successful path of the observation of large
$C\\!P$-violating asymmetries in multibody charmless decays of charged and
neutral $B$ mesons by LHCb [8, 9, 10, 11]. These decays proceed simultaneously
through the charged-current ${b}\rightarrow{u}$ transition and neutral-current
${b}\rightarrow{s},{d}$ transitions, and the resulting interference exhibits a
weak-phase difference. Furthermore, and analogously to the aforementioned
charmless multibody $B$-meson decays, charmless multibody decays of
$b$-flavoured baryons contain rich resonance structures, both in the two- or
three-body baryonic invariant-mass spectra (i.e. $pK^{-}$, $p\pi^{-}$,
$p\pi^{+}$, $p\pi^{+}\pi^{-}$ and $pK^{-}\pi^{+}$) and in the two- or three-
body nonbaryonic ones (i.e. the ${\pi}^{+}{\pi}^{-}$, ${K}^{\pm}$
${\pi}^{\mp}$, ${{K}^{+}}{{K}^{-}}$, $\pi^{+}\pi^{-}\pi^{\pm}$ and
$K^{\pm}\pi^{+}\pi^{-}$). Consequently, $C\\!P$ asymmetries might be enhanced
due to the strong-phase differences induced by the interference patterns
between these transitions in the mass regions around resonances. The charmless
$b$-baryon decays studied in this paper are hence well suited for a potential
first observation of $C\\!P$ violation in the baryon sector. However, the
presence of these strong phases, that are difficult to predict, would make 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 [12,
13].

This work focuses on a search for $C\\!P$ violation in
$\mbox{$X^{0}_{b}$}\rightarrow phh^{\prime}h^{\prime\prime}$ charmless decays,
where $X^{0}_{b}$ stands either for ${\mathchar 28931\relax}^{0}_{b}$ or
${\mathchar 28932\relax}^{0}_{b}$ and $h^{(\prime,\,\prime\prime)}$ stand
either for a pion or a kaon. Six decays are studied, namely ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$, ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ and ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$. The $C\\!P$ asymmetry is
defined as

$\mbox{${\cal
A}^{{C\\!P}}$}\equiv\frac{\mathrm{\Gamma}(\mbox{$X^{0}_{b}$}\rightarrow
f)-\mathrm{\Gamma}(\mbox{$\overline{X}{}^{0}_{b}$}\rightarrow\overline{f})}{\mathrm{\Gamma}(\mbox{$X^{0}_{b}$}\rightarrow
f)+\mathrm{\Gamma}(\mbox{$\overline{X}{}^{0}_{b}$}\rightarrow\overline{f})},$
(1)

where $\mathrm{\Gamma}(\mbox{$X^{0}_{b}$}\rightarrow f)$ is the partial width
of the given decay. The $C\\!P$ asymmetry measurement relies on counting the
number of reconstructed particle and antiparticle decays and includes
therefore experimental charge-asymmetric effects such as the track detection
efficiency or $b$-baryon production asymmetries. They are cancelled out to
first order by comparing the $C\\!P$ asymmetries of the signal modes to those
of charmed decays that lead to the same or very similar final states and for
which no measurable $C\\!P$ violation is expected in the SM [14]. The decays
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar
28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow
p\pi^{-}\pi^{+})\pi^{-}$ and ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow({{\mathchar 28932\relax}^{+}_{c}}\rightarrow
pK^{-}\pi^{+})\pi^{-}$ are thus reconstructed with the same selection as the
corresponding charmless signals. The $C\\!P$-violating observable considered
in this work is then referred to as $\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}\equiv\mbox{${\cal A}^{{C\\!P}}_{\rm
no\text{-}c}$}-\mbox{${\cal A}^{{C\\!P}}_{\rm c}$}$, where ${\cal
A}^{{C\\!P}}_{\rm no\text{-}c}$ (${\cal A}^{{C\\!P}}_{\rm c}$) is the
asymmetry measured in the charmless (charmed) decays. The decays of interest
are reported in Table 1.

Table 1: Four-body charmless and charmed decays considered in this analysis. The difference of $C\\!P$-asymmetries measured for the charmless modes and for the control channels results in $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ measurements. For each observable, the choice of the control channel is aiming at cancelling at first order production and detection asymmetries. Given the data samples at hand, it is not possible to meet both criteria for the signal decay ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$: the choice of the Cabibbo-favoured decay ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow({{\mathchar 28932\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ as a control channel requires in turn to correct the corresponding $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ for the kaon-detection asymmetry. Charmless mode | Control channel
---|---
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ | ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow p\pi^{-}\pi^{+})\pi^{-}$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ | ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow p\pi^{-}\pi^{+})\pi^{-}$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow({{\mathchar 28932\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ | ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow({{\mathchar 28932\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$

In addition to $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ measurements
integrated over all of the four-body phase space, specific regions of the
space are studied in order to search for local $C\\!P$ asymmetries.

The same final states have been used by the LHCb experiment to search for
$C\\!P$ violation using triple product asymmetries [5, 15]. The latter
technique and the $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$
measurements exhibit different sensitivity to $C\\!P$ violation [16], which
makes the two approaches complementary.

##  2 Detector and data set

The analysis is performed using $pp$ collision data recorded with the LHCb
detector, corresponding to an integrated luminosity of 1.0$\text{\,fb}^{-1}$
at a centre-of-mass energy of 7 TeV in 2011 and 2.0$\text{\,fb}^{-1}$ at a
centre-of-mass energy of 8 TeV in 2012. The LHCb detector [17, 18] is a
single-arm forward spectrometer covering the pseudorapidity range $2<\eta<5$,
designed for the study of particles containing $b$ or $c$ quarks. The detector
includes a high-precision tracking system consisting of a silicon-strip vertex
detector surrounding the $pp$ interaction region, a large-area silicon-strip
detector located upstream of a dipole magnet with a bending power of about
$4{\mathrm{\,Tm}}$, and three stations of silicon-strip detectors and straw
drift tubes placed downstream of the magnet. The tracking system provides a
measurement of the momentum, $p$, of charged particles with a relative
uncertainty that varies from 0.5% at low momentum to 1.0% at
200$\text{\,Ge\kern-1.00006ptV\\!/}c$. The minimum distance of a track to a
primary vertex (PV), the impact parameter (IP), is measured with a resolution
of $(15+29/p_{\mathrm{T}})\,\upmu\text{m}$, where $p_{\mathrm{T}}$ is the
component of the momentum transverse to the beam, in
$\text{\,Ge\kern-1.00006ptV\\!/}c$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
and a hadronic calorimeter. Muons are identified by a system composed of
alternating layers of iron and multiwire proportional chambers.

Simulation is 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 [19,
*Sjostrand:2007gs] with a specific LHCb configuration [21]. Decays of hadronic
particles are described by EvtGen [22] in which final-state radiation is
generated using Photos [23]. The interactions of the generated particles with
the detector, and its response, are implemented using the Geant4 toolkit [24,
*Agostinelli:2002hh] as described in Ref. [26].

##  3 Trigger and selection requirements

The selection follows most of the strategy described in Ref. [7]. The online
event selection is performed by a trigger[27] 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
$p_{\mathrm{T}}>500\,(300)\text{\,Me\kern-1.00006ptV\\!/}c$ are reconstructed
for 2011 (2012) data. At the hardware-trigger stage, events are required to
include a muon or a dimuon with high transverse momentum or a hadron, photon
or electron with high transverse energy. The software trigger reconstructs
charged particles with transverse momentum
$p_{\mathrm{T}}>500\,(300)\text{\,Me\kern-1.00006ptV\\!/}c$ for 2011 (2012)
data and requires a two-, three- or four-track secondary vertex with
significant displacement from all primary $pp$ interaction vertices. At least
one charged particle must have transverse momentum
$p_{\mathrm{T}}>1.7\,(1.6)\text{\,Ge\kern-1.00006ptV\\!/}c$ for 2011 (2012)
data and be inconsistent with originating from any PV. A multivariate
algorithm [28] is used for the identification of secondary vertices consistent
with the decay of a $b$ hadron. In the offline selection, trigger signals are
associated with reconstructed particles. Selection requirements can therefore
be made on the trigger selection itself and on whether the decision was due to
the signal candidate, other particles produced in the $pp$ collision, or a
combination of both.

The events passing the trigger requirements are filtered in two stages.
Initial requirements are applied to further reduce the size of the data sample
before a multivariate selection is applied. Selection requirements based on
topological variables, such as the flight distance of the $b$ baryon, are used
as the main discriminants. In order to preserve the phase space of the decays
of interest, only loose requirements are placed on the transverse momenta of
the decay products, $p_{\mathrm{T}}>250\text{\,Me\kern-1.00006ptV\\!/}c$.

Neutral $b$-baryon candidates, hereafter denoted as $X^{0}_{b}$, 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 $X^{0}_{b}$ candidate is associated to the PV with the
smallest value of $\chi^{2}_{\text{IP}}$, where $\chi^{2}_{\text{IP}}$ is the
difference in $\chi^{2}$ of a given PV reconstructed with and without the
considered candidate. Each of the four tracks of the final state is required
to have $\chi^{2}_{\text{IP}}>16$ and
$3<p<100\text{\,Ge\kern-1.00006ptV\\!/}c$. Beyond 100
$\text{\,Ge\kern-1.00006ptV\\!/}c$, there is little pion/kaon/proton
discrimination. The $X^{0}_{b}$ candidates are then required to form a vertex
with a fit quality $\chi^{2}_{\text{vtx}}<20$ and to be significantly
separated from any PV with $\mbox{$\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 $X^{0}_{b}$ candidates must have a transverse momentum $p_{\rm
T}(\mbox{$X^{0}_{b}$})$ greater than $1.5\text{\,Ge\kern-1.00006ptV\\!/}c$ and
an invariant mass within the range
$5340<m(phh^{\prime}h^{\prime\prime})<6400\text{\,Me\kern-1.00006ptV\\!/}c^{2}$.
They are further required to be consistent with originating from a PV,
quantified by both $\chi^{2}_{\text{IP}}<16$ and the cosine of the angle
$\theta_{\rm DIR}$ between the reconstructed momentum of the $b$ hadron and
the vector defined by the associated PV and the decay vertex be greater than
0.999. 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 hypotheses $p\pi^{-}\pi^{+}\pi^{-}$, $pK^{-}\pi^{+}\pi^{-}$,
$pK^{-}K^{+}\pi^{-}$, $pK^{-}\pi^{+}K^{-}$ 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
background, resulting from a misidentification of one or more final-state
particles in a charmless baryon decay, which can therefore be reconstructed as
another charmless decay with a different mass hypothesis; 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 background,
which results from a random association of unrelated tracks. The pion and kaon
PID requirements, that define mutually exclusive samples, are optimised to
reduce the cross-feed background, and hence to maximise the significance of
the signal. The charmless $B$-meson decays are identified by reconstructing
the invariant-mass distributions of candidates using the pion or kaon mass
instead of the proton mass hypothesis, in the high-mass sidebands defined as
$m_{\rm
sideband}<m(phh^{\prime}h^{\prime\prime})<6400\text{\,Me\kern-1.00006ptV\\!/}c^{2}$,
where $m_{\rm sideband}=5680\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ for
$p\pi^{-}\pi^{+}\pi^{-}$ and $pK^{-}K^{+}\pi^{-}$ final states, and $m_{\rm
sideband}=5840\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ for
$pK^{-}\pi^{+}\pi^{-}$, $pK^{-}\pi^{+}K^{-}$ and $pK^{-}K^{+}K^{-}$ final
states. This background contribution is reduced by the optimisation of the
proton PID requirement.

To reject combinatorial background, multivariate discriminants based on a
boosted decision tree (BDT) [29] with the AdaBoost algorithm [30] have been
designed. Candidates from simulated ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ decays and the high-
mass sideband are used as the signal and background training samples,
respectively. This high-mass sideband region is chosen such that the sample is
free of 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. The BDT trained
on one subsample is used to select candidates from the other subsample, in
order to avoid a possible bias in the selection.

The BDTs have the following quantities as inputs: $p_{\mathrm{T}}$, $\eta$,
$\chi^{2}_{\text{IP}}$, $\chi^{2}_{\rm FD}$, $\cos\theta_{\rm DIR}$, and
$\chi^{2}_{\text{vtx}}$ of the $X^{0}_{b}$ 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

$p_{\rm T}^{\rm asym}=\frac{p_{\rm T}(\mbox{$X^{0}_{b}$})-p_{\rm T}^{\rm
cone}}{p_{\rm T}(\mbox{$X^{0}_{b}$})+p_{\rm T}^{\rm cone}}\,,$ (2)

where $p_{\rm T}^{\rm cone}$ is the transverse component of the vector sum of
all particle momenta inside a cone around the $b$-baryon candidate direction,
of radius $R\equiv\sqrt{\delta\eta^{2}+\delta\phi^{2}}=1.5$, where
$\delta\eta$ and $\delta\phi$ are the difference in pseudorapidity and
azimuthal angle (expressed in radians) around the beam direction, between the
momentum vector of the track under consideration and that of the $b$-hadron
candidate. The distribution of $p_{\rm T}^{\rm asym}$ for the signal
candidates is enhanced towards high values. The BDT output is determined to be
uncorrelated with the position in phase space of the decays of interest. The
selection requirement placed on the output of the BDTs is optimised for the
six decays of interest by minimising the uncertainties on the
$C\\!P$-asymmetry differences.

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 have similar invariant-mass distribution of the $b$-baryon candidate as
the signal along with 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 spectra: ${{\mathchar
28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+}$, ${{\mathchar
28931\relax}^{+}_{c}}\rightarrow p\pi^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{+}_{c}}\rightarrow pK^{+}K^{-}$, ${{\mathchar
28932\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+}$, ${{D}^{+}}\rightarrow
K^{-}\pi^{+}\pi^{+}$, ${{D}^{+}_{s}}\rightarrow K^{-}K^{+}\pi^{+}$,
${{D}^{0}}\rightarrow K^{-}\pi^{+}$, ${{D}^{0}}\rightarrow\pi^{+}\pi^{-}$,
${{D}^{0}}\rightarrow K^{+}K^{-}$, ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\pi^{+}\pi^{-}$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow K^{+}K^{-}$. The decays of other possible broad charmonium
resonances to $\pi^{+}\pi^{-}$ and $K^{+}K^{-}$ are retained as potential
interfering amplitudes with the charmless amplitudes under study.

The same set of trigger, $\mathrm{PID}$ and BDT requirements is applied to the
control modes ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar
28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow
p\pi^{-}\pi^{+})\pi^{-}$ and ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow({{\mathchar 28932\relax}^{+}_{c}}\rightarrow
pK^{-}\pi^{+})\pi^{-}$ to cancel out most of the systematic effects related to
the selection criteria. Candidates whose $pK^{-}\pi^{+}$ or $p\pi^{-}\pi^{+}$
invariant mass is in the range
$[2213,2313]\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ for ${{\mathchar
28931\relax}^{+}_{c}}$ and $[2437,2497]\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
for ${{\mathchar 28932\relax}^{+}_{c}}$, are retained as control channels
candidates. Events outside these intervals belong to the corresponding signal
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
invariant-mass distributions of the ${b}$-hadron candidates under each of the
mass hypotheses for the signal and control channel final-state tracks. The
data samples are split according to the charge of the proton and to the year
of data taking. Furthermore, data are split according to the hardware trigger
conditions, in order to correct raw measurements for charge-asymmetric trigger
efficiencies. The components of the model include, in addition to signal
decays, partially reconstructed five-body $X^{0}_{b}$ decays, signal and
background cross-feeds, four- and five-body decays of $B$ mesons and
combinatorial background. The independent data samples obtained for each final
state 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
$P_{j,i}$ is the probability distribution function for component $j$ evaluated
at the mass of the candidate $i$.

###  4.1 Fit model

The signal decays are modelled as the sum of two Crystal Ball (CB) functions
[31] that 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 is free in the fit and shared among the ${\mathchar
28931\relax}^{0}_{b}$ decays. The difference between the fitted ${\mathchar
28932\relax}^{0}_{b}$ and ${\mathchar 28931\relax}^{0}_{b}$ masses is also a
shared parameter and is constrained to the value reported in Ref. [2] by using
a Gaussian function.

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

The cross-feed backgrounds are modelled by the sum of two CB functions, whose
parameters are determined from simulated samples weighted to match the
performances of the particle identification algorithm as measured in the data.
All cases resulting from the misidentification of either one or two of the
final-state particles are considered. The yield of each misidentified decay is
constrained to the yield of the corresponding correctly identified decay and
the known misidentification probabilities. These constraints are implemented
using Gaussian prior probability distributions multiplying the likelihood
function. 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 the 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,
whose parameters are determined from simulation.

Partially reconstructed backgrounds where a neutral pion is not reconstructed,
such as ${{\mathchar 28931\relax}^{0}_{b}},{{\mathchar
28932\relax}^{0}_{b}}\rightarrow phh^{\prime}h^{\prime\prime}{{\pi}^{0}}$, are
modelled by means of generalised ARGUS functions [32] 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 $m(X_{b})-m(\pi^{0})$. Partially
reconstructed decays with a missing photon such as ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\eta^{\prime}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\eta^{\prime}$ decays, with
$\eta^{\prime}\rightarrow\pi^{+}\pi^{-}\gamma$, are modelled separately using
the same functional form but where the parameters are fixed from simulation.
The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}\pi^{0}$
decay modes where a charged 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 function determined from the partially
reconstructed background candidates in the control channel.

Finally, the combinatorial background is modelled by a linear function whose
slope is shared among the invariant-mass spectra.

###  4.2 The ensemble of measurements

The following three categories of measurements have been considered a priori
(before any evaluation of the data) to search for global and local effects of
$C\\!P$ violation.

  * •

$C\\!P$ asymmetries are measured, considering the whole selected phase space
of the decay candidates.

  * •

$C\\!P$ asymmetries are also measured in the phase-space region of low
invariant mass on the baryonic pair (i.e. $p\pi^{\pm}$ or $pK^{-}$) and low
invariant mass on the pairing of the two other tracks. The ensemble of
measurements that are performed with this phase-space selection is hereafter
referred to as LBM (Low $2\\!\times\\!2$-Body Mass) measurements. The
invariant mass of the baryonic pair is required to be lower than 2
$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ while the invariant-mass requirements
on the two remaining tracks depends on whether it is a $\pi^{+}\pi^{-}$ pair,
a $K^{\pm}\pi^{\mp}$ or a $KK$ pair. These values are chosen to include
several known resonances, in particular $f_{0}(1500)$ resonance for
$\pi^{+}\pi^{-}$, the broad scalar $K_{0}^{*}(1430)^{0}$ resonance for
$K^{+}\pi^{-}$ and the $f_{2}^{\prime}(1525)$ resonance for $K^{+}K^{-}$. Only
the modes with the largest signal yields are considered, namely ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ decays. The two-body low-
mass distributions are displayed in Fig. 1. Several resonant structures are
observed, and correspond to baryon resonances like $\Lambda(1520)$,
$\Delta(1232)^{++}$ and $N(1520)$ or meson resonances like $K^{*}(892)^{0}$,
$\rho(770)^{0}$ or $\phi(1020)$. This phase-space selection focuses therefore
on low-invariant-mass resonances (both mesonic and baryonic) as well as low-
invariant-mass nonresonant components of the amplitudes. The latter have been
shown to generate large $C\\!P$-violating asymmetries in analogous $B$-meson
decays [8].

|
---|---
(a) | (b)
|
(c) | (d)
|
(e) | (f)
Figure 1: Distributions of invariant masses of pairs of final-state particles
for the candidates selected in the mass window of $\pm 3\sigma$ around the
measured ${\mathchar 28931\relax}^{0}_{b}$ mass. Figures (a), (b) and (c) show
the two-body invariant-mass distributions of baryonic $p\pi^{-}$, $p\pi^{+}$
pairs from ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$
decays and $pK^{-}$ pairs from ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-}$ decays, respectively. Structures around known the masses of
the $N(1520)$, $\Delta(1232)^{++}$ and $\Lambda(1520)$ baryons are observed.
Figures (d), (e) and (f) show the invariant-mass distributions of
$K^{-}\pi^{+}$, $K^{-}K^{+}$ and $\pi^{+}\pi^{-}$ pairs from ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ decays, respectively.
Structures corresponding to the $K^{*}(892)^{0}$, $\phi(1020)$ and
$\rho(770)^{0}$ resonances are visible. The red lines correspond to the
invariant-mass requirements applied to the selection of the main quasi-two- or
three-body decays analysed.

  * •

$C\\!P$ asymmetries are measured for regions of the phase space that contain
specific quasi-two-body decays, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p{\mbox{$a_{1}$}}(1260)^{-}$, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
N(1520)^{0}\rho(770)^{0}$, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p{\mbox{$K_{1}$}}(1410)^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\rho(770)^{0}$,
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}{{K}^{*}(892)^{0}}$,
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar
28931\relax(1520)\phi(1020)$ or three-body decays, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar
28929\relax(1232)^{++}\pi^{-}\pi^{-}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar 28929\relax(1232)^{++}K^{-}\pi^{-}$,
and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow(pK^{-})_{\text{\tiny high-
mass}}\phi(1020)$, where in the latter only the high $pK^{-}$ mass region is
selected. Invariant-mass requirements for these measurements are reported in
Table 2. Only the narrower baryons or the well-known baryon and meson
resonances have been considered, with the noticeable exception of the
${\mbox{$a_{1}$}}(1260)$ meson. Although the ${\mbox{$a_{1}$}}(1260)$ meson is
a broad resonance, the analogous $B$-meson decay
${B}^{0}\rightarrow{\mbox{$a_{1}$}}(1260)^{\pm}\pi^{\mp}$ has been studied at
the $B$-factories [33, 34] and could serve as a benchmark comparison in the
interpretation of the results obtained for the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p{\mbox{$a_{1}$}}(1260)^{-}$ decay.

Table 2: Invariant-mass requirements applied for the different phase-space selections for each final state considered. Decay mode | Invariant-mass requirements (in $\text{\,Me\kern-1.00006ptV\\!/}c^{2}$)
---|---
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ |
LBM |  $m(p\pi^{-})<2000$ and $m(\pi^{+}\pi^{-})<1640$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p{\mbox{$a_{1}$}}(1260)^{-}$ | $419<m(\pi^{+}\pi^{-}\pi^{+})<1500$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}\rho(770)^{0}$ |  $1078<m(p\pi^{-})<1800$ and $m(\pi^{+}\pi^{-})<1100$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28929\relax(1232)^{++}\pi^{-}\pi^{-}$ | $1078<m(p\pi^{+})<1432$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ |
LBM |  $m(pK^{-})<2000$ and $m(\pi^{+}\pi^{-})<1640$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}{{K}^{*}(892)^{0}}$ |  $1078<m(p\pi^{-})<1800$ and $750<m(\pi^{+}K^{-})<1100$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\rho(770)^{0}$ |  $1460<m(pK^{-})<1580$ and $m(\pi^{+}\pi^{-})<1100$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28929\relax(1232)^{++}K^{-}\pi^{-}$ | $1078<m(p\pi^{+})<1432$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p{\mbox{$K_{1}$}}(1410)^{-}$ | $1200<m(K^{-}\pi^{+}\pi^{-})<1600$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ |
LBM |  $m(pK^{-})<2000$ and $m(K^{+}K^{-})<1675$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\phi(1020)$ |  $1460<m(pK^{-})<1600$ and $1005<m(K^{+}K^{-})<1040$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow(pK^{-})_{\text{\tiny high-mass}}\phi(1020)$ |  $m(pK^{-})>1600$ and $1005<m(K^{+}K^{-})<1040$

##  5 Corrections for experimental detection asymmetries and related
systematic uncertainties

Tracking reconstruction, trigger selection and particle identification
requirements can generate charge-dependent selection efficiencies of the
decays of interest. Most of these charge-dependent effects are however
cancelled out in the $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$
observables, up to the kinematical differences between signal and control
channels. The remaining impact is addressed by evaluating corrections to the
$\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ observables. These
correction factors are determined from calibration samples as discussed in
this Section. Systematic uncertainties are estimated for each correction
factor and propagated to the $\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$ measurements. A summary of the systematic uncertainties is
reported in Table 3 for all modes.

Table 3: Systematic uncertainties for each decay mode. The uncertainties related to the kaon and proton detection asymmetry, the difference of triggering efficiency, the PID asymmetries and the production asymmetry are respectively reported as $\sigma_{K}$, $\sigma_{p}$, $\sigma_{\rm L0}$, $\sigma_{\rm PID}$ and $\sigma_{A_{P}}$. Decay mode | Absolute uncertainties (%) | Total (%)
---|---|---
| $\sigma_{K}$ | $\sigma_{p}$ | $\sigma_{\rm L0}$ | $\sigma_{\rm PID}$ | $\sigma_{A_{P}}$ |
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ | — | 0.20 | 0.06 | 0.42 | 0.28 | 0.54
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | 0.17 | 0.20 | 0.06 | 0.41 | 0.24 | 0.55
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ | — | 0.21 | 0.06 | 0.40 | 0.55 | 0.72
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ | 0.15 | 0.20 | 0.07 | 0.41 | 0.33 | 0.59
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ | 0.17 | 0.20 | 0.05 | 0.42 | 0.24 | 0.55
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ | 0.15 | 0.20 | 0.05 | 0.41 | 0.55 | 0.73
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ (LBM) | — | 0.16 | 0.06 | 0.36 | 0.28 | 0.49
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ (LBM) | 0.17 | 0.17 | 0.05 | 0.34 | 0.24 | 0.48
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ (LBM) | 0.16 | 0.17 | 0.05 | 0.37 | 0.33 | 0.55
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p{\mbox{$a_{1}$}}(1260)^{-}$ | — | 0.20 | 0.09 | 0.48 | 0.28 | 0.60
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}\rho(770)^{0}$ | — | 0.12 | 0.05 | 0.23 | 0.28 | 0.39
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28929\relax(1232)^{++}\pi^{-}\pi^{-}$ | — | 0.18 | 0.05 | 0.47 | 0.28 | 0.59
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p{\mbox{$K_{1}$}}(1410)^{-}$ | 0.16 | 0.14 | 0.11 | 0.58 | 0.24 | 0.74
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\rho(770)^{0}$ | 0.12 | 0.12 | 0.04 | 0.36 | 0.24 | 0.49
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}{{K}^{*}(892)^{0}}$ | 0.16 | 0.14 | 0.04 | 0.32 | 0.24 | 0.45
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28929\relax(1232)^{++}K^{-}\pi^{-}$ | 0.22 | 0.19 | 0.05 | 0.48 | 0.24 | 0.61
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\phi(1020)$ | 0.11 | 0.10 | 0.05 | 0.30 | 0.33 | 0.34
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow(pK^{-})_{\text{\tiny high-mass}}\phi(1020)$ | 0.15 | 0.14 | 0.06 | 0.58 | 0.33 | 0.64

  * •

Tracking detection efficiency: differences between the interactions of
oppositely charged pions, kaons or protons in the material of the spectrometer
induce detection charge asymmetries. The difference in $\pi^{\pm}$ and
$K^{\pm}$ tracking efficiency has been quantified with calibration samples, as
a function of the transverse momentum of the tracks [35, 36]. The simulated
signal and control channels kinematics is used to weight the simulation track
efficiency in order to match the hadron detection efficiencies as measured in
those calibration samples. The $\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$ values (as measured by the difference of signal yields) are
then corrected for these efficiencies and the uncertainty on the detection
efficiency determination itself is propagated as a systematic uncertainty to
the final $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ measurements,
taking into account the correlation between signal and control channel induced
by the use of the same calibration samples. The systematic uncertainty arises
from the size of the simulated samples used in the weighting, the statistical
and systematic uncertainties on the charge asymmetry of the data calibration
samples and the knowledge of the kinematical distributions generated in the
simulated samples. The latter is determined by taking two different kinematic
configurations of the final state (saturated by quasi two-body modes on one
hand and phase-space decay on the other hand) and using the difference as the
systematic estimate. The difference between the $p$ and $\overline{}p$
particles is not measured to date. Simulation is used to obtain the
reconstruction efficiencies as a function of the momentum of the proton or
antiproton track. An additional systematic uncertainty related to the
knowledge of the material budget in the simulation is added, as reported in
Ref. [37]. The proton detection correction follows the same procedure as
$\pi^{\pm}$ and $K^{\pm}$ detection asymmetry correction.

  * •

The same methodology is used to correct for the difference of triggering
efficiency between oppositely charged hadrons of the signal candidate, at the
hardware stage of the trigger system. The trigger asymmetry effects are
quantified as a function of the transverse momentum of the tracks of interest,
by studying the triggering efficiency of $K^{-}$ and $\pi^{+}$ from the decay
$D^{0}\rightarrow K^{-}\pi^{+}$ [27] and protons from ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow
pK^{-}\pi^{+})\pi^{-}$ decays.

  * •

The production asymmetry can depend on the kinematical properties of the
reconstructed $X^{0}_{b}$ candidates, though the actual dependence has not
been observed yet [38]. Differences between signal and control channel
$X^{0}_{b}$ candidates kinematics would reflect in an incomplete cancellation
of the production asymmetry in the $\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$ observable. This effect has been estimated by considering the
${\mathchar 28931\relax}^{0}_{b}$ production asymmetry measured in Ref. [38]
as a function of its $p_{\mathrm{T}}$ and pseudorapidity.

  * •

The PID requirements set on the tracks of the final state can induce
asymmetries. Efficiencies for the final-state particles are determined from
${\mathchar 28931\relax}^{+}_{c}$ decays selected in data, and are
parameterised by their momentum and electric charge. The correction factors to
apply to the value of $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ are
here again determined by performing a weighting of the simulated signal and
control channel events to match the efficiencies measured in the data. The
uncertainties coming from the finite size of the calibration samples are
propagated as a systematic uncertainty for the final $\mathchar
28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ measurements.

The first three corrections on the value of $\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$ are found to be at the few per mille level, commensurate with
their uncertainties. The lattermost source is dominating the systematic
uncertainty budget, and can reach the percent level. The correction factors
are however consistent with zero. The design of the fit model and the
simultaneous fit strategy allow the direct measurement of the combinatorial
background and the $B$-meson decay asymmetries. No significant asymmetries are
observed and the results are presented in Section 7. Systematic uncertainties
can be induced by the fit model and the fit complexity and it is evaluated by
means of pseudoexperiments reproducing the nominal fit results. No significant
biases are obtained. The normalised residuals of the signal yields are
computed and the uncertainties on their pull mean value are propagated as a
systematic uncertainty to each relevant $\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$ measurement. The largest uncertainty is determined to be at
the level of few $10^{-4}$, hence negligible in comparison to the
aforementioned systematic uncertainty estimate.

##  6 Fit results

The results of the simultaneous fits to the five experimental spectra split by
year of data taking, magnet polarity and trigger conditions are discussed in
this section. The fit results are reported for each final state in the
following subsections, and the summary of the measured yields is reported in
Table 4.

Table 4: Signal yields for each decay mode, summed over all trigger configurations and years of data taking. Decay mode | Signal yields
---|---
| $X^{0}_{b}$ | $\overline{X}{}^{0}_{b}$
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ |  02335 $\pm$ 056 |  02264 $\pm$ 055
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ |  06807 $\pm$ 092 |  06232 $\pm$ 089
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}$ |  00555 $\pm$ 038 |  00630 $\pm$ 038
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ |  02312 $\pm$ 054 |  02248 $\pm$ 054
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ |  00180 $\pm$ 028 |  00252 $\pm$ 029
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}K^{-}$ |  00265 $\pm$ 025 |  00305 $\pm$ 026
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow p\pi^{-}\pi^{+})\pi^{-}$ |  01607 $\pm$ 040 |  01586 $\pm$ 040
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ | 24687 $\pm$ 159 | 24052 $\pm$ 157
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow({{\mathchar 28932\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ |  00259 $\pm$ 018 |  00260 $\pm$ 018
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ (LBM) |  00498 $\pm$ 025 |  00455 $\pm$ 024
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}$ (LBM) |  03217 $\pm$ 061 |  02929 $\pm$ 058
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}K^{-}$ (LBM) |  01240 $\pm$ 038 |  01146 $\pm$ 036
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p{\mbox{$a_{1}$}}(1260)^{-}$ |  00422 $\pm$ 023 |  00425 $\pm$ 023
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28929\relax(1232)^{++}\pi^{-}\pi^{-}$ |  00783 $\pm$ 030 |  00771 $\pm$ 029
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}\rho(770)^{0}$ |  00241 $\pm$ 016 |  00230 $\pm$ 016
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p{\mbox{$K_{1}$}}(1410)^{-}$ |  00548 $\pm$ 026 |  00488 $\pm$ 025
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28929\relax(1232)^{++}K^{-}\pi^{-}$ |  00998 $\pm$ 037 |  00895 $\pm$ 034
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\rho(770)^{0}$ |  00167 $\pm$ 014 |  00160 $\pm$ 014
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}{{K}^{*}(892)^{0}}$ |  00977 $\pm$ 033 |  00856 $\pm$ 031
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\phi(1020)$ |  00192 $\pm$ 015 |  00172 $\pm$ 014
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow(pK^{-})_{\text{\tiny high-mass}}\phi(1020)$ |  00548 $\pm$ 025 |  00542 $\pm$ 025

  * •

$\mathbold{p\pi^{-}\pi^{+}\pi^{-}}$ final state: Figures 2 and 3 show the
results of the simultaneous fits to the invariant-mass spectra of the
$p\pi^{-}\pi^{+}\pi^{-}$ spectra for the inclusive, LBM and quasi two-body
measurements. The high-mass region of the $p\pi^{-}\pi^{+}\pi^{-}$ spectrum is
only populated by either $B$-meson decays or combinatorial background. The
good agreement between the data and the fit model, especially in this region,
validates the chosen modelling of these components. The same comment is in
order for the fit in the different phase-space regions. The combinatorial
component becomes negligible in the quasi two-body case.

Figure 2: Invariant $p\pi^{-}\pi^{+}\pi^{-}$ mass distributions with the
results of the fit superimposed: (first row) full phase space, (second row)
LBM and (third row) ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar
28931\relax}^{+}_{c}}\rightarrow p\pi^{-}\pi^{+})\pi^{-}$ control channel. The
two columns correspond to the charge-conjugate final states: (left) baryon,
(right) antibaryon. The different components employed in the fit model are
indicated in the legends. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$
five-body legend includes two components: the partially reconstructed
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\eta^{\prime}$ and
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}\pi^{0}$
decays where a $\gamma$ or $\pi^{0}$ is not reconstructed. The latter has a
lower-mass endpoint.

Figure 3: Invariant $p\pi^{-}\pi^{+}\pi^{-}$ mass distributions with the
results of the fit superimposed: region of the phase space containing (first
row) ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p{\mbox{$a_{1}$}}(1260)^{-}$, (second row) ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar
28929\relax(1232)^{++}\pi^{-}\pi^{-}$ and (third row) ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}\rho(770)^{0}$ quasi two-body
decays. The two columns correspond to the charge-conjugate final states:
(left) baryon, (right) antibaryon. The different components employed in the
fit model are indicated in the legends. The ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow$ five-body legend includes two components:
the partially reconstructed ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p\pi^{-}\eta^{\prime}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p\pi^{-}\pi^{+}\pi^{-}\pi^{0}$ decays where a $\gamma$ or $\pi^{0}$ is not
reconstructed. The latter has a lower-mass endpoint.

  * •

$\mathbold{pK^{-}\pi^{+}\pi^{-}}$ final state: Figures 4 and 5 show the
results of the simultaneous fits to the $pK^{-}\pi^{+}\pi^{-}$ mass spectrum
for the inclusive, LBM and quasi two-body measurements. The fit model provides
also in this case a satisfactory description of the data, despite the very
different background contributions depending on the phase-space selection. Raw
asymmetries at the level of several percent are observed.

Figure 4: Invariant $pK^{-}\pi^{+}\pi^{-}$ mass distributions with the results
of the fit superimposed: (first row) full phase space, (second row) LBM and
(third row) ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow({{\mathchar
28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ control channel. The
two columns correspond to the charge-conjugate final states: (left) baryon,
(right) antibaryon. The different components employed in the fit are indicated
in the legends. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$ five-body
legend includes two components: the partially reconstructed ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\eta^{\prime}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow pK^{-}\pi^{+}\pi^{-}\pi^{0}$ decays where a
$\gamma$ or $\pi^{0}$ is not reconstructed. The latter has a lower-mass
endpoint.

Figure 5: Invariant $pK^{-}\pi^{+}\pi^{-}$ distributions, with the results of
the fit superimposed: region of the phase space containing (first row)
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p{\mbox{$K_{1}$}}(1410)^{-}$,
(second row) ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar
28929\relax(1232)^{++}K^{-}\pi^{-}$, (third row) ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar 28931\relax(1520)\rho(770)^{0}$ and
(last row) ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
N(1520)^{0}{{K}^{*}(892)^{0}}$ quasi two-body decays. The two columns
correspond to the charge-conjugate final states: (left) baryon, (right)
antibaryon. The different components employed in the fit are indicated in the
legends.

  * •

$\mathbold{pK^{-}K^{+}K^{-}}$ final state: Figure 6 shows the results of the
simultaneous fits to the reconstructed $pK^{-}K^{+}K^{-}$ mass spectrum for
the inclusive, LBM and quasi two-body measurements. Negligible raw asymmetries
are obtained.

Figure 6: Invariant $pK^{-}K^{+}K^{-}$ mass distributions, with the results of
the fit superimposed: (first row) full phase space and (second row) LBM,
(third row) ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar
28931\relax(1520)\phi(1020)$ and (fourth row) ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow(pK^{-})_{\text{\tiny high-mass}}\phi(1020)$.
The two columns correspond to the charge-conjugate final states: (left)
baryon, (right) antibaryon. The different components employed in the fit are
indicated in the legends. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$
five-body legends 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.

  * •

$\mathbold{pK^{-}K^{+}\pi^{-}}$ and $\mathbold{pK^{-}\pi^{+}K^{-}}$ final
states: The simultaneous fit results for the two remaining final states are
shown in Fig. 7. The result of the fit for the control channel ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow({{\mathchar 28932\relax}^{+}_{c}}\rightarrow
pK^{-}\pi^{+})\pi^{-}$ is also displayed and shows a good description of the
spectrum. This control channel is used to account for the production asymmetry
of the ${\mathchar 28932\relax}^{0}_{b}$ modes.

Figure 7: Invariant (first row) $pK^{-}K^{+}\pi^{-}$ and (second row)
$pK^{-}\pi^{+}K^{-}$ mass distributions, with the results of the fit
superimposed. The two bottom plots are the results of the fit to the
${{\mathchar 28932\relax}^{0}_{b}}\rightarrow({{\mathchar
28932\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+})\pi^{-}$ control channel. The
two columns correspond to the charge-conjugate final states: (left) baryon,
(right) antibaryon. The different components employed in the fit are indicated
in the legends. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow$ five-body
legend includes 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
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow pK^{-}K^{+}\pi^{-}\pi^{0}$.

##  7 Measurements of $C\\!P$ asymmetries and concluding remarks

Five charmless final states of ${\mathchar 28931\relax}^{0}_{b}$ and
${\mathchar 28932\relax}^{0}_{b}$ four-body hadronic decays are examined in
this paper. Specific regions of their phase space have been selected to search
for local $C\\!P$ asymmetries in addition to the integrated $C\\!P$-asymmetry.
A total of eighteen measurements of $C\\!P$ asymmetries are reported in this
paper.

A simple counting experiment allows the measurement of a $C\\!P$ asymmetry up
to the corrections due to instrumental and $b$-baryon production asymmetries.
These corrections are mitigated by establishing the differences (denoted
$\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$) between the raw ${\cal
A}^{{C\\!P}}$ values of the signals and those of the decay modes with
intermediate charmed baryons comprising the same final-state particles. The
asymmetries $\mathchar 28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ are further
corrected for residual experimental charge asymmetries due to kinematic
differences between signal and control modes. The integrated $\mathchar
28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ asymmetry differences are measured to
be

$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p\pi^{-}\pi^{+}\pi^{-}$})$ $\displaystyle=(+1.1\pm 2.5\pm 0.6)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$})$ $\displaystyle=(+3.2\pm 1.1\pm 0.6)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}\pi^{-}$})$ $\displaystyle=(-6.9\pm 4.9\pm 0.8)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-}$})$ $\displaystyle=(+0.2\pm 1.8\pm 0.6)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$})$
$\displaystyle=(-17\phantom{.}\pm\phantom{.}11\pm\phantom{.6}1)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28932\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}K^{-}$})$ $\displaystyle=(-6.8\pm 8.0\pm 0.8)\,\%.$ The
measurements for the two-body low invariant-mass regions are
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p\pi^{-}\pi^{+}\pi^{-}$})$ $\displaystyle=(+3.7\pm 4.1\pm 0.5)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}\pi^{+}\pi^{-}$})$ $\displaystyle=(+3.5\pm 1.5\pm 0.5)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
pK^{-}K^{+}K^{-}$})$ $\displaystyle=(+2.7\pm 2.3\pm 0.6)\,\%.$ Finally, the
measurements for the quasi two-body decays are $\displaystyle\mbox{$\mathchar
28929\relax\mbox{${\cal A}^{{C\\!P}}$}$}(\mbox{${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p{\mbox{$a_{1}$}}(1260)^{-}$})$
$\displaystyle=(-1.5\pm 4.2\pm 0.6)\,\%\,,$ $\displaystyle\mbox{$\mathchar
28929\relax\mbox{${\cal A}^{{C\\!P}}$}$}(\mbox{${{\mathchar
28931\relax}^{0}_{b}}\rightarrow N(1520)^{0}\rho(770)^{0}$})$
$\displaystyle=(+2.0\pm 4.9\pm 0.4)\,\%,$ $\displaystyle\mbox{$\mathchar
28929\relax\mbox{${\cal A}^{{C\\!P}}$}$}(\mbox{${{\mathchar
28931\relax}^{0}_{b}}\rightarrow\mathchar
28929\relax(1232)^{++}\pi^{-}\pi^{-}$})$ $\displaystyle=(+0.1\pm 3.2\pm
0.6)\,\%,$ $\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p{\mbox{$K_{1}$}}(1410)^{-}$})$ $\displaystyle=(+4.7\pm 3.5\pm 0.8)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar
28931\relax(1520)\rho(770)^{0}$})$ $\displaystyle=(+0.6\pm 6.0\pm 0.5)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
N(1520)^{0}{{K}^{*}(892)^{0}}$})$ $\displaystyle=(+5.5\pm 2.5\pm 0.5)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar
28929\relax(1232)^{++}K^{-}\pi^{-}$})$ $\displaystyle=(+4.4\pm 2.6\pm
0.6)\,\%,$ $\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\mathchar
28931\relax(1520)\phi(1020)$})$ $\displaystyle=(+4.3\pm 5.6\pm 0.4)\,\%,$
$\displaystyle\mbox{$\mathchar 28929\relax\mbox{${\cal
A}^{{C\\!P}}$}$}(\mbox{${{\mathchar
28931\relax}^{0}_{b}}\rightarrow(pK^{-})_{\text{\tiny high-
mass}}\phi(1020)$})$ $\displaystyle=(-0.7\pm 3.3\pm 0.7)\,\%.$

In all cases the first uncertainties are statistical and the second
systematic. No significant $C\\!P$ violation is observed. The $\mathchar
28929\relax\mbox{${\cal A}^{{C\\!P}}$}$ measurements for the independent
samples of the two magnet polarities, the two categories of trigger
requirements and the two distinct data-taking samples are found to be
consistent. In addition, the measured asymmetries for the combinatorial
background in all spectra are consistent with zero. The background
contributions coming from $B$-meson decays (that could potentially exhibit
nonzero $C\\!P$ violation) are also consistent with null asymmetries.

In a previous analysis, the LHCb collaboration reported evidence for $C\\!P$
violation in a specific region of the phase space of the decay ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$, by measuring triple-
product asymmetries [5]. By contrast, in the present analysis, no indication
of a significant $C\\!P$-violating asymmetry is obtained with the same data
sample, providing complementary insights about the origin of this potential
$C\\!P$-symmetry breaking effect. The quest for the first observation of
$C\\!P$ violation in baryon decays continues. LHCb Run 2 data provides about
five times larger yields allowing for a more sensitive search of smaller
$C\\!P$-violating effects.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); 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
(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 and OCEVU,
and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier
Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF
and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal Society
and the Leverhulme Trust (United Kingdom); Laboratory Directed Research and
Development program of LANL (USA).

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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
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Derkach35, O. Deschamps5, F. Dettori54, B. Dey65, A. Di Canto40, P. Di
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Douglas53, A. Dovbnya45, K. Dreimanis54, L. Dufour43, G. Dujany8, P.
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Ghez4, S. Gianì41, V. Gibson49, O.G. Girard41, L. Giubega30, K. Gizdov52, V.V.
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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.
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H. Luo52, A. Lupato23, E. Luppi17,g, O. Lupton40, A. Lusiani24, X. Lyu63, F.
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Benito38, M. Marinangeli41, P. Marino41, J. Marks12, G. Martellotti26, M.
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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.
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, T.
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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, 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