EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2017-316 LHCb-PAPER-2017-044

A measurement of the $C\\!P$ asymmetry difference between
$\varLambda_{c}^{+}\rightarrow pK^{-}K^{+}$ and $p\pi^{-}\pi^{+}$ decays

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

The difference between the $C\\!P$ asymmetries in the decays
$\varLambda_{c}^{+}\rightarrow pK^{-}K^{+}$ and $\varLambda_{c}^{+}\rightarrow
p\pi^{-}\pi^{+}$ is presented. Proton-proton collision data taken at centre-
of-mass energies of $7$ and $8\,\mathrm{TeV}$ collected by the LHCb detector
in 2011 and 2012 are used, corresponding to an integrated luminosity of
$3\,\mathrm{fb}^{-1}$. The $\varLambda_{c}^{+}$ candidates are reconstructed
as part of the $\varLambda_{b}^{0}\rightarrow\varLambda_{c}^{+}\mu^{-}X$ decay
chain. In order to maximize the cancellation of production and detection
asymmetries in the difference, the final-state kinematic distributions of the
two samples are aligned by applying phase-space-dependent weights to the
$\varLambda_{c}^{+}\rightarrow p\pi^{-}\pi^{+}$ sample. This alters the
definition of the integrated $C\\!P$ asymmetry to
$A_{C\\!P}^{\text{wgt}}(p\pi^{-}\pi^{+})$. Both samples are corrected for
reconstruction and selection efficiencies across the five-dimensional
$\varLambda_{c}^{+}$ decay phase space. The difference in $C\\!P$ asymmetries
is found to be

$\displaystyle\Delta{A^{\text{wgt}}_{C\\!P}}$
$\displaystyle=A_{C\\!P}(pK^{-}K^{+})-A_{C\\!P}^{\text{wgt}}(p\pi^{-}\pi^{+})$
$\displaystyle=(0.30\pm 0.91\pm 0.61)\,$\mathrm{\char 37\relax}$,$

where the first uncertainty is statistical and the second is systematic.

Published in JHEP 03 (2018) 182

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

##  1 Introduction

The Standard Model (SM) does not provide a source of charge-parity ($C\\!P$)
symmetry violation large enough to explain the matter-antimatter asymmetry
observed in the universe [1]. The ongoing experimental effort in searching for
$C\\!P$ violation in particle decays aims to find effects that are not
expected in the SM, such that new dynamics are required. Whilst the existence
of $C\\!P$ violation in kaon and beauty meson decays is well established [2,
3], no observation has been made in the analyses of beauty baryons or charm
hadrons, although evidence of $C\\!P$ violation has recently been claimed for
the former [4]. The most precise searches for $C\\!P$ violation in the charm
sector have been made using self-conjugate, singly Cabibbo-suppressed (SCS)
decays of the neutral ${D}^{0}$ meson to ${{K}^{-}}{{K}^{+}}$ and
${{\pi}^{-}}{{\pi}^{+}}$ final states [5, 6]. Such SCS decays can include
significant contributions from loop-level amplitudes, within which new
dynamics can enter.

This article reports a search for $C\\!P$ violation in the decays of the
${\mathchar 28931\relax}_{{c}}^{+}$ charm baryon to the SCS
$p{{K}^{-}}{{K}^{+}}$ and $p{{\pi}^{-}}{{\pi}^{+}}$ final states (generically
referred to as $ph^{-}h^{+}$).111 Charge conjugation is implied throughout
this article, except in the definition of asymmetry terms.  The difference in
$C\\!P$ asymmetry between the two decays, $\Delta A_{{C\\!P}}$, is measured in
a manner similar to previous measurements using ${D}^{0}$ decays [5, 6]. There
is little theoretical understanding of the dynamics of ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow ph^{-}h^{+}$ decays [7], partly due to
the unknown resonant structure of the five-dimensional (5D) phase space and
partly due to the historical lack of large experimental datasets, and so no
predictions for the magnitude of $C\\!P$ violation in ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow ph^{-}h^{+}$ decays are currently
available. As $C\\!P$ violation may be dependent on the position in phase
space, leading to locally significant effects, a multidimensional analysis
would be required to be maximally sensitive to such behaviour, requiring
assumptions on the as-yet unknown amplitude model and ${\mathchar
28931\relax}_{{c}}^{+}$ polarisation. The work presented here instead
integrates over the phase space as a search for global $C\\!P$-violating
effects.

The presented analysis uses proton-proton collision data taken at centre-of-
mass energies of $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ and
$8\text{\,}\mathrm{TeV}$, collected by the LHCb experiment at the Large Hadron
Collider (LHC) in 2011 and 2012, corresponding to an integrated luminosity of
$3\text{\,}{\mathrm{fb}}^{-1}$. To reduce the level of backgrounds, candidate
${\mathchar 28931\relax}_{{c}}^{+}\\!\rightarrow ph^{-}h^{+}$ decays are
reconstructed as part of the ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{\mathchar
28931\relax}_{{c}}^{+}{\mu^{-}}{}X$ decay chain, where $X$ represents any
number of additional, unreconstructed particles. The long lifetime of the
${\mathchar 28931\relax}^{0}_{b}$ baryon [2], in comparison with that of the
${\mathchar 28931\relax}_{{c}}^{+}$ baryon, allows for the suppression of
backgrounds through the requirement of a ${\mathchar
28931\relax}_{{c}}^{+}{\mu^{-}}$ vertex that is displaced with respect to the
primary ${p}{p}$ interaction. The total dataset contains of the order of
${10}^{4}$ and ${10}^{5}$ reconstructed $p{{K}^{-}}{{K}^{+}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}$ signal candidates, respectively.

The observed charge asymmetry $A_{\text{raw}}(f)$ for each ${\mathchar
28931\relax}_{{c}}^{+}$ final state $f$, reconstructed in association with a
muon, is measured as the difference in ${\mathchar 28931\relax}_{{c}}^{+}$ and
${\kern 1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}_{{c}}^{-}$
signal yields divided by their sum. The quantity $A_{\text{raw}}$ includes
contributions from the $C\\!P$ asymmetry in the ${\mathchar
28931\relax}_{{c}}^{+}$ decay, as well as asymmetries due to experimental
effects such as the ${\mathchar 28931\relax}^{0}_{b}$ production asymmetry and
the muon and hadron detection asymmetries. These effects have been measured at
LHCb [8, 9, 5, 10], but with large uncertainties. Using them directly, to
correct for the experimental asymmetries in $A_{\text{raw}}$, would then
result in large systematic uncertainties on the correction factors. Instead,
assuming that the asymmetries are, or can be made to be, mode independent, the
difference $\Delta
A_{{C\\!P}}=A_{\text{raw}}(p{{K}^{-}}{{K}^{+}})-A_{\text{raw}}(p{{\pi}^{-}}{{\pi}^{+}})$
is equal to the difference in the ${\mathchar 28931\relax}_{{c}}^{+}$ decay
asymmetries, as all other asymmetries cancel. A weighting technique is used to
equalise the $p{{K}^{-}}{{K}^{+}}$ and $p{{\pi}^{-}}{{\pi}^{+}}$ sample
kinematics, thereby improving the level of cancellation of the various
production, reconstruction, and selection asymmetries in $\Delta A_{{C\\!P}}$,
the formalism for which is presented in Section 2. A description of the LHCb
detector and the analysis dataset is given in Section 3, followed by a
description of the statistical models used to determine the signal yields from
the data in Section 4. The weighting method used for correcting the
measurement for experimental asymmetries and the evaluation of the efficiency
variation across the 5D $ph^{-}h^{+}$ phase space are presented in Section 5.
Systematic effects are considered and quantified in Section 6. The results of
the analysis are given in Section 7, and finally a summary is made in Section
8.

##  2 Formalism

The $C\\!P$ asymmetry in the decays of the ${\mathchar 28931\relax}_{{c}}^{+}$
baryon to a given final state $f$ is

$A_{{C\\!P}}(f)=\frac{\Gamma(f)-\Gamma(\bar{f})}{\Gamma(f)+\Gamma(\bar{f})},$
(1)

where $\Gamma(f)$ is the decay rate of the ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow f$ process, and $\Gamma(\bar{f})$ is the
decay rate of the charge conjugate decay ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}_{{c}}^{-}\\!\rightarrow\bar{f}$. Rather than measure the
individual decay rates, it is simpler to count the number of reconstructed
decays, and so the asymmetry in the yields is defined as

$A_{\text{raw}}(f)=\frac{N(f{\mu^{-}})-N(\bar{f}{\mu^{+}})}{N(f{\mu^{-}})+N(\bar{f}{\mu^{+}})},$
(2)

where $N$ is the number of signal candidates reconstructed in association with
a muon. This is labelled as the raw asymmetry of the decay because the
measurement of the physics observable of interest, $A_{{C\\!P}}$, is
contaminated by several experimental asymmetries. Assuming that each
contributing factor is small, the raw asymmetry can be expressed to first
order as the sum

$A_{\text{raw}}(f)=A_{{C\\!P}}(f)+A_{\text{P}}^{{{\mathchar
28931\relax}^{0}_{b}}}(f{\mu})+A_{\text{D}}^{{\mu}}({\mu})+A_{\text{D}}^{f}(f),$
(3)

where $A_{\text{P}}^{{{\mathchar 28931\relax}^{0}_{b}}}$,
$A_{\text{D}}^{{\mu}}$, and $A_{\text{D}}^{f}$ are the ${\mathchar
28931\relax}^{0}_{b}$ production asymmetry, muon detection asymmetry, and
${\mathchar 28931\relax}_{{c}}^{+}$ final-state detection asymmetry,
respectively. A nonzero ${\mathchar 28931\relax}^{0}_{b}$ production asymmetry
may arise for several reasons, such as the relative abundance of matter quarks
in the ${p}{p}$ collision region. A dependence on the reconstructed
${\mathchar 28931\relax}^{0}_{b}$ final state is introduced by the detector
acceptance and the reconstruction and selection applied to that state, which
alters the observed ${\mathchar 28931\relax}^{0}_{b}$ production phase space.
The two detection asymmetries may be nonzero due to the different interaction
cross-sections of the matter and antimatter states with the LHCb detector.
There may also be charge-dependent reconstruction and selection effects. In
all cases, an experimental asymmetry is assumed to be fully parameterised by
the kinematics of the objects involved. The asymmetry of interest,
$A_{{C\\!P}}$, is assumed to be dependent on $f$ but independent of
${\mathchar 28931\relax}_{{c}}^{+}$ kinematics. This motivates a measurement
of the difference between raw asymmetries of two distinct ${\mathchar
28931\relax}_{{c}}^{+}$ decay modes, chosen to be $p{{K}^{-}}{{K}^{+}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}$ in this analysis,

$\displaystyle\Delta A_{{C\\!P}}$
$\displaystyle=A_{{C\\!P}}(p{{K}^{-}}{{K}^{+}})-A_{{C\\!P}}(p{{\pi}^{-}}{{\pi}^{+}})$
(4) $\displaystyle\approx
A_{\text{raw}}(p{{K}^{-}}{{K}^{+}})-A_{\text{raw}}(p{{\pi}^{-}}{{\pi}^{+}}),$
(5)

where the approximation tends to an equality as the kinematics between the
final states become indistinguishable.

The observed kinematics of the $p{{K}^{-}}{{K}^{+}}{\mu^{-}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}{\mu^{-}}$ final states are not expected to be equal
given the different energy release and resonant structure of the two
${\mathchar 28931\relax}_{{c}}^{+}$ decays. To ensure similarity, the
kinematic spectra of one state can be matched to that of another. As around
six times as many $p{{\pi}^{-}}{{\pi}^{+}}$ signal candidates are found than
$p{{K}^{-}}{{K}^{+}}$ signal candidates, as described in Section 4, the
$p{{\pi}^{-}}{{\pi}^{+}}{\mu^{-}}$ data are weighted to match the
$p{{K}^{-}}{{K}^{+}}{\mu^{-}}$ data, given that the statistical uncertainty on
the $A_{\text{raw}}(p{{K}^{-}}{{K}^{+}})$ measurement will be the dominant
contribution to that on $\Delta A_{{C\\!P}}^{\text{wgt}}$. Details of the
weighting procedure are given in Section 5. The kinematic weighting may alter
the physics asymmetry, as the $p{{\pi}^{-}}{{\pi}^{+}}$ phase space can be
distorted, and so it is a weighted asymmetry, $A_{{C\\!P}}^{\text{wgt}}$, that
enters the measurement

$\displaystyle\Delta A_{{C\\!P}}^{\text{wgt}}$
$\displaystyle=A_{{C\\!P}}(p{{K}^{-}}{{K}^{+}})-A_{{C\\!P}}^{\text{wgt}}(p{{\pi}^{-}}{{\pi}^{+}})$
(6) $\displaystyle\approx
A_{\text{raw}}(p{{K}^{-}}{{K}^{+}})-A_{\text{raw}}^{\text{wgt}}(p{{\pi}^{-}}{{\pi}^{+}}).$
(7)

To allow for comparisons with theoretical models, a weighting function is
provided in the supplementary material of this article which provides a weight
for a given coordinate in the five-dimensional ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow p{{\pi}^{-}}{{\pi}^{+}}$ phase space and
mimics the transformation imposed by the kinematic weighting applied here. The
five dimensions are defined similarly to those in Ref. [11], with the only
difference being that the ‘beam axis’ is replaced by the displacement vector
pointing from the ${p}{p}$ collision vertex, the primary vertex (PV), to the
${\mathchar 28931\relax}_{{c}}^{+}{\mu^{-}}$ vertex.

##  3 Detector and dataset

The LHCb detector [12, 13] 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 ${p}{p}$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about
$4\text{\,}\mathrm{T}\text{\,}\mathrm{m}$, 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 of charged particles with a
relative uncertainty that varies from $0.5\text{\,}\mathrm{\char 37\relax}$ at
low momentum to $1.5\text{\,}\mathrm{\char 37\relax}$ at
$200\text{\,}\mathrm{\\!\per}$. The minimum distance of a track to a PV, the
impact parameter, is measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$})\,$\mathrm{\SIUnitSymbolMicro m}$$, where
$p_{\mathrm{T}}$ is the component of the momentum transverse to the beam, in
$\mathrm{\\!\per}$. 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. To control possible left-right
interaction asymmetries, the polarity of the dipole magnet is reversed
periodically throughout data-taking. The configuration with the magnetic field
vertically upwards (downwards) bends positively (negatively) charged particles
in the horizontal plane towards the centre of the LHC.

The online event selection is performed by a trigger, which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a two-stage software trigger, which applies first a simplified and
then a full event reconstruction. For the dataset used for the present
analysis, at the hardware trigger stage the presence of a
high-$p_{\mathrm{T}}$ muon candidate is required. In the first stage of the
software trigger, this candidate must be matched to a good-quality track which
is inconsistent with originating directly from any PV and has a
$p_{\mathrm{T}}$ above $1\text{\,}\mathrm{\\!\per}$. The second stage requires
a two-, three-, or four-track secondary vertex with a significant displacement
from all PVs, where at least one of the tracks is consistent with being a
muon. At least one charged particle must have
$\mbox{$p_{\mathrm{T}}$}>$1.6\text{\,}\mathrm{\\!\per}$$ and must be
inconsistent with originating from any PV. A multivariate algorithm [14] is
used for the identification of secondary vertices consistent with the decays
of beauty hadrons.

In the offline selection, tracks are selected on the criteria that they have a
significant impact parameter with respect to all PVs, and also on the particle
identification information being consistent with one of the proton, kaon, or
pion hypotheses. Sets of three tracks with
$\sum\mbox{$p_{\mathrm{T}}$}>$1.8\text{\,}\mathrm{\\!\per}$$ are combined to
form ${\mathchar 28931\relax}_{{c}}^{+}$ candidates. Each candidate is
required to be displaced significantly from all PVs, to have a good quality
vertex, and to have an invariant mass between 2230 and
$2350\text{\,}\mathrm{\\!\per\squared}$. The ${\mathchar
28931\relax}_{{c}}^{+}$ candidate is combined with a displaced muon to form
the ${\mathchar 28931\relax}^{0}_{b}$ candidate, which must have a good
quality vertex and also satisfy the invariant mass requirement
$2.5<m({\mathchar
28931\relax}_{{c}}^{+}{\mu^{-}})<$6\text{\,}\mathrm{\\!\per\squared}$$. The
offline ${\mathchar 28931\relax}^{0}_{b}$ candidate is required to be matched
to the candidate formed in the second stage of the software trigger.

Contributions from the Cabibbo-favoured decays ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow{p}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ and ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow{\mathchar 28931\relax}{{\pi}^{+}}$, and
their charge conjugates, are observed in the background-subtracted
$m({{\pi}^{-}}{{\pi}^{+}})$ and $m({p}{{\pi}^{-}})$ spectra. These are removed
by applying a veto in the two-pion invariant mass spectrum
$485<m({{\pi}^{-}}{{\pi}^{+}})<$510\text{\,}\mathrm{\\!\per\squared}$$ to
remove ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ meson contributions, and in
the proton-pion invariant mass spectrum
$1110<m({p}{{\pi}^{-}})<$1120\text{\,}\mathrm{\\!\per\squared}$$ to remove
$\mathchar 28931\relax$ baryons. Contributions from misidentified charm meson
and background ${\mathchar 28931\relax}_{{c}}^{+}$ decays are removed by
applying a $16\text{\,}\mathrm{\\!\per\squared}$ wide veto centred on the
world average mass value [2] for the charm hadron in question. Such vetoes are
applied in the misidentified mass distributions for the following backgrounds:
${{D}^{+}}\\!\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{+}}$, and ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow p{{K}^{-}}{{\pi}^{+}}$ for
$p{{K}^{-}}{{K}^{+}}$ candidates; and
${{D}^{+}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$,
${{D}^{+}}\\!\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{+}}$, and
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{-}}{{K}^{+}}{{\pi}^{+}}$ for
$p{{\pi}^{-}}{{\pi}^{+}}$ candidates.

After the selection, less than $2\text{\,}\mathrm{\char 37\relax}$ of the
events contain more than one ${\mathchar 28931\relax}^{0}_{b}$ candidate. All
candidates are kept for the rest of the analysis, as other techniques of
dealing with multiple candidates per event have been shown to be biased for
asymmetry measurements [15].

The data were taken at two centre-of-mass energies,
$\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ in 2011 and $8\text{\,}\mathrm{TeV}$ in
2012, and with two configurations of the dipole magnet polarity. As the
experimental efficiencies vary with these conditions, due to different
momentum production spectra and the left-right asymmetries in the detector
construction, the data are split into four independent subsamples by centre-
of-mass-energy and magnet polarity. Each stage of the analysis is carried out
on each subsample independently, and then the individual results are combined
in an average as described in Section 7.

Simulated ${p}{p}$ collisions are used to determine experimental efficiencies
and are generated using Pythia [16, *Sjostrand:2006za] with a specific LHCb
configuration [18]. Particle decays are described by EvtGen [19], in which
final-state radiation is generated using Photos [20]. The interaction of the
generated particles with the detector, and its response, are implemented using
the Geant4 toolkit [21, *Agostinelli:2002hh] as described in Ref. [23].

##  4 Mass spectrum parameterisation

The $ph^{-}h^{+}$ invariant mass is used as a discriminating variable between
signal and combinatorial background. Fits to the mass spectrum, shown in Fig.
1, are used to measure the $ph^{-}h^{+}$ signal yields in order to compute
$A_{\text{raw}}$, as defined in Eq. 2. The sPlot procedure [24] is employed to
statistically subtract the combinatorial background component in the data, as
required for the kinematic weighting procedure, and takes the fitted model as
input.

The chosen fit model is the sum of a signal component and a background
component, each weighted by a corresponding yield parameter. The signal is
modelled as the sum of two Gaussian distributions which share a common mean
but have separate width parameters, and the combinatorial background is
modelled as a first-order polynomial.

A cost function is defined as Neyman’s $\chi^{2}$,

$\chi^{2}=\sum_{i=1}^{B}\frac{(N_{i}-Nf_{\text{Tot}}(m_{i};\xi))^{2}}{N_{i}},$
(8)

where $i$ is the bin index over the number of bins $B$ in the $m(ph^{-}h^{+})$
spectrum, $N_{i}$ is the observed number of entries in the $i$th bin, $N$ is
the expected number of entries in the dataset as the sum of the fitted signal
and background yield parameters, and $f_{\text{Tot}}(m_{i};\xi)$ represents
the integral of the total model in the $m_{i}$ bin with parameter vector
$\xi$. The binning is set as 120 bins of width
$1\text{\,}\mathrm{\\!\per\squared}$ in the range
$2230<m(ph^{-}h^{+})<$2350\text{\,}\mathrm{\\!\per\squared}$$. Fits to the
$p{{K}^{-}}{{K}^{+}}$ and $p{{\pi}^{-}}{{\pi}^{+}}$ data, summed over all
conditions, are shown in Fig. 1. A good description of the data by the model
is seen in all fits to the data subsamples. The $p{{K}^{-}}{{K}^{+}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}$ signal yields, separated by data-taking conditions,
are given in Table 1.

Figure 1:  The $ph^{-}h^{+}$ invariant mass spectra from the fully selected ${\mathchar 28931\relax}_{{c}}^{+}\\!\rightarrow p{{K}^{-}}{{K}^{+}}$ (left) and ${\mathchar 28931\relax}_{{c}}^{+}\\!\rightarrow p{{\pi}^{-}}{{\pi}^{+}}$ (right) datasets summed over all data-taking conditions. The results of the fit to each dataset are shown for illustration. The widths of the signal distributions differ due to the different $Q$-value between the two decays, where the larger value for the ${\mathchar 28931\relax}_{{c}}^{+}\\!\rightarrow p{{\pi}^{-}}{{\pi}^{+}}$ mode results in a broader shape.  Table 1:  Signal yields measured in the fit for each of the four subsets of the $p{{K}^{-}}{{K}^{+}}$ and $p{{\pi}^{-}}{{\pi}^{+}}$ data (two centre-of-mass energies, 7 and $8\text{\,}\mathrm{TeV}$, and two polarities of the dipole magnet, up and down). The corresponding integrated luminosity of each subset is also given.  $\sqrt{s}$ | Polarity | Int. lumi. [pb-1] |  $p{{K}^{-}}{{K}^{+}}$ yield |  $p{{\pi}^{-}}{{\pi}^{+}}$ yield
---|---|---|---|---
$7\,$TeV | Up |  $422$ p m 7 |  $2880$ p m 70 |  $18\,450$ p m 190
$7\,$TeV | Down |  $563$ p m 9 |  $3940$ p m 80 |  $25\,130$ p m 230
$8\,$TeV | Up |  $1000$ p m 11 |  $9040$ p m 120 |  $57\,730$ p m 350
$8\,$TeV | Down |  $992$ p m 11 |  $9330$ p m 120 |  $60\,080$ p m 360

To measure $A_{\text{raw}}$ as in Eq. 2, each data subsample is split by
proton charge into ${\mathchar 28931\relax}_{{c}}^{+}$ and ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}_{{c}}^{-}$ subsets.
The model used in the previously described fit is used to define charge-
dependent models, where the parameter vectors of each model, $\xi^{+}$ and
$\xi^{-}$, are independent. Rather than fitting charge-dependent signal and
background yields directly, however, they are parameterised using the total
number of signal and background candidates, $N_{\text{Sig}}$ and
$N_{\text{Bkg}}$, and the signal and background asymmetries, $A_{\text{raw}}$
and $A_{\text{raw}}^{\text{Bkg}}$,

$\displaystyle N_{\text{Sig}}^{\pm}$
$\displaystyle=\frac{1}{2}N_{\text{Sig}}(1\pm A_{\text{raw}}),$ (9)
$\displaystyle N_{\text{Bkg}}^{\pm}$
$\displaystyle=\frac{1}{2}N_{\text{Bkg}}(1\pm A_{\text{raw}}^{\text{Bkg}}).$
(10)

The addition of per-candidate weights, which are described in the following
section, requires a cost function that uses the sum of weights in each bin,
rather than the count as in Eq. 8, defined as

$\chi^{2}=\sum_{i=1}^{B}\left[\frac{(W_{i}^{+}-N^{+}f_{\text{Tot}}^{+}(m_{i};\xi^{+}))^{2}}{(\delta{}W_{i}^{+})^{2}}+\frac{(W_{i}^{-}-N^{-}f_{\text{Tot}}^{-}(m_{i};\xi^{-}))^{2}}{(\delta{}W_{i}^{-})^{2}}\right],$
(11)

where $W_{i}^{\pm}$ is the sum of the weights of candidates in the $i$th bin
in the ${\mathchar 28931\relax}_{{c}}^{\pm}$ sample, and $\delta{}W_{i}^{\pm}$
is the uncertainty on that sum.

##  5 Kinematic and efficiency corrections

The experimental asymmetries listed in Eq. 3 are specific to the production
environment at the LHC and the construction of the LHCb detector, and so their
cancellation in $\Delta A_{{C\\!P}}^{\text{wgt}}$ is crucial in providing an
unbiased measurement. This section presents the statistical methods used to
compute the kinematic and efficiency corrections, which are evaluated as per-
candidate weights to be used in the simultaneous $\chi^{2}$ fit previously
described.

###  5.1 Kinematic weighting

The production and detection asymmetries depend on the kinematics of the
particles involved. If the ${\mathchar 28931\relax}^{0}_{b}$, muon, and proton
kinematic spectra are the same between the $p{{K}^{-}}{{K}^{+}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}$ data, then the ${\mathchar 28931\relax}^{0}_{b}$
production asymmetry and muon and proton detection asymmetries will cancel in
$\Delta A_{{C\\!P}}^{\text{wgt}}$. If the $h^{-}$ and $h^{+}$ kinematics are
equal _within_ each separate $p{{K}^{-}}{{K}^{+}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}$ sample, then the kaon ($f=p{{K}^{-}}{{K}^{+}}$) or
pion ($f=p{{\pi}^{-}}{{\pi}^{+}}$) detection asymmetries will cancel in
$A_{\text{raw}}(f)$. The $h^{-}$ kinematics agree well with the $h^{+}$
spectra in the data, but the ${\mathchar 28931\relax}^{0}_{b}$, muon, and
proton kinematics do not, and so a per-candidate weighting technique is
employed to match the kinematic spectra of the
$p{{\pi}^{-}}{{\pi}^{+}}{\mu^{-}}$ state to those of the
$p{{K}^{-}}{{K}^{+}}{\mu^{-}}$ state.

To compute the per-candidate weights, a forest of shallow decision trees with
gradient boosting (a GBDT) is used [25, 26, 27]. This method recursively bins
the $p{{K}^{-}}{{K}^{+}}$ and $p{{\pi}^{-}}{{\pi}^{+}}$ input data such that
regions with larger differences between the two samples are more finely
partitioned. After fitting, each $p{{\pi}^{-}}{{\pi}^{+}}$ candidate is
assigned a weight $d$. To reduce biases that may result from overfitting,
where the GBDT model becomes sensitive to the statistical fluctuations in the
input data, the data are split in two, and independent GBDTs are fitted to
each subset. The GBDT built with one half of the data is used to evaluate
weights for the other half, and vice versa.

The ${\mathchar 28931\relax}_{{c}}^{+}$ and proton $p_{\mathrm{T}}$ and
pseudorapidity for each $p{{K}^{-}}{{K}^{+}}$ and $p{{\pi}^{-}}{{\pi}^{+}}$
candidate are used as input to the GBDT. The ${\mathchar
28931\relax}_{{c}}^{+}$ kinematics are chosen since the large boost in the
laboratory frame induces a large correlation with ${\mathchar
28931\relax}^{0}_{b}$ and muon kinematics. An agreement in the ${\mathchar
28931\relax}_{{c}}^{+}$ kinematics therefore results in an agreement in the
${\mathchar 28931\relax}^{0}_{b}$ and muon spectra. The proton kinematics are
chosen as the different $Q$ values of the decays will a priori result in
different proton spectra.

The ${\mathchar 28931\relax}^{0}_{b}$, muon, proton, and $h^{-}$/$h^{+}$
kinematics agree well after weighting, as demonstrated for a subset of
kinematic variables in Fig. 2. Any remaining differences will result in
residual asymmetries in $\Delta A_{{C\\!P}}^{\text{wgt}}$, and the presence of
these differences is studied in the context of systematic effects as described
in Section 6.

Figure 2:  Background-subtracted distributions of the ${\mathchar
28931\relax}^{0}_{b}$ candidate transverse momentum (top row), the muon
candidate transverse momentum (middle row), and the proton candidate
pseudorapidity (bottom row) both before (left column) and after (right column)
weighting the $p{{\pi}^{-}}{{\pi}^{+}}$ sample (blue points) to match the
$p{{K}^{-}}{{K}^{+}}$ sample (black points). The data are summed across all
data-taking conditions.

###  5.2 Efficiency corrections

The acceptance, reconstruction, and selection efficiencies as a function of
the 5D $ph^{-}h^{+}$ phase space are also modelled using GBDTs. Simulated
events are generated with a uniform ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow ph^{-}h^{+}$ matrix element and used as
input to the training, sampled before and after the detector acceptance and
data processing steps. One- and two-dimensional efficiency estimates are made
as histogram ratios of the before and after data, and projections of the
efficiency model obtained using the simulation agrees well with these. The
model is then used to predict per-candidate efficiencies in the data.

###  5.3 Use in determining $A_{\text{raw}}$

The cost function in Eq. 11 uses the sum of per-candidate weights in each bin
and its uncertainty. The weights are defined using the kinematic weight
$d_{j}$, equal to unity for ${\mathchar 28931\relax}_{{c}}^{+}\\!\rightarrow
p{{K}^{-}}{{K}^{+}}$ candidates, and the efficiency correction
$\varepsilon_{j}$ of the $j$th candidate in the $i$th $m(ph^{-}h^{+})$ bin,

$W_{i}=W\sum_{j=1}^{N_{i}}\frac{d_{j}}{\varepsilon_{j}},\quad\delta{}W_{i}^{2}=W_{i},$
(12)

where the normalisation factor $W$ is defined as

$W=\frac{\sum_{j=1}^{N_{i}}\frac{d_{j}}{\varepsilon_{j}}}{\sum_{j=1}^{N_{i}}\left(\frac{d_{j}}{\varepsilon_{j}}\right)^{2}}.$
(13)

The term $W_{i}$ can be called the number of ‘effective’ entries in the bin,
as it encodes the size of an unweighted data sample with the same statistical
power as the weighted sample. For the $p{{\pi}^{-}}{{\pi}^{+}}$ data, which is
weighted to match the $p{{K}^{-}}{{K}^{+}}$ kinematics, the effective sample
size is around $80\text{\,}\mathrm{\char 37\relax}$ that of the unweighted
$p{{\pi}^{-}}{{\pi}^{+}}$ sample. The weighted data are shown in the
$m^{2}({p}h^{-})$–$m^{2}(h^{-}h^{+})$ plane in Fig. 3.

The statistical treatment of the weights in the fit is validated by randomly
sorting candidates into ${\mathchar 28931\relax}_{{c}}^{+}$ and ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}_{{c}}^{-}$ datasets
and fitting the model 500 times, where it is seen that the distribution of
$A_{\text{raw}}(f)$ divided by its uncertainty is centred around zero, the
expected value, and has a standard deviation of 1, indicating that the error
estimate is correct.

Figure 3:  Background-subtracted and efficiency-corrected ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow p{{K}^{-}}{{K}^{+}}$ (left) and
${\mathchar 28931\relax}_{{c}}^{+}\\!\rightarrow p{{\pi}^{-}}{{\pi}^{+}}$
(right) data in the $m^{2}({p}h^{-})$–$m^{2}(h^{-}h^{+})$ plane, integrated
across all data-taking subsamples. The $p{{K}^{-}}{{K}^{+}}$ data feature a
prominent $\phi\\!\rightarrow{{K}^{-}}{{K}^{+}}$ component, whilst the
$p{{\pi}^{-}}{{\pi}^{+}}$ data exhibit
$\rho(770)/\omega(782)\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ and
$f_{0}(980)\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ components.

##  6 Systematic effects

To evaluate possible biases on the measurement of $\Delta
A_{{C\\!P}}^{\text{wgt}}$ due to systematic effects, several studies are
performed and deviations from the nominal results are computed. Statistically
significant deviations are assigned to the measurement as systematic
uncertainties.

The model used in the simultaneous $\chi^{2}$ fit, described in Section 4, is
derived empirically, and there may be other models which described the data
similarly well. Variations of the choice of background model are found to have
a negligible effect on the measurement of $\Delta A_{{C\\!P}}^{\text{wgt}}$,
however different signal models can change the results significantly. To
assess an associated systematic uncertainty based on the choice of signal
model, the signal ${\mathchar 28931\relax}_{{c}}^{+}$ and ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}_{{c}}^{-}$ yields
are determined using the method of sideband subtraction. Here, data from the
regions on either side of the ${\mathchar 28931\relax}_{{c}}^{\pm}$ signal
peak are assumed to be linearly distributed and are used to approximate the
background yield in the peak region. Given that the data used for sideband
subtraction are the same as for the nominal $\chi^{2}$ fit, the measurements
using the two techniques are assumed to be fully correlated, such that even
small differences between them are statistically significant. On the average
of $\Delta A_{{C\\!P}}^{\text{wgt}}$, taken across all data-taking conditions,
a difference of $0.2\text{\,}\mathrm{\char 37\relax}$ is seen with respect to
the average of the results using the full fit, and this difference is assigned
as a systematic uncertainty.

The kinematic weighting procedure defined in Section 5 can only equalise the
$p{{K}^{-}}{{K}^{+}}{\mu^{-}}$ and $p{{\pi}^{-}}{{\pi}^{+}}{\mu^{-}}$
kinematics approximately, and so residual differences will remain. These
differences can cause a bias on $\Delta A_{{C\\!P}}^{\text{wgt}}$, with a size
depending on the size of the relevant asymmetry. Measurements of the
${\mathchar 28931\relax}^{0}_{b}$ production asymmetry and the muon, kaon, and
pion detection asymmetries using LHCb data exist [8, 9, 5, 10], and estimates
of the proton detection asymmetry using simulated events have been used
previously [8], and so the measurement of $\Delta A_{{C\\!P}}^{\text{wgt}}$
can be corrected for directly. The correction is found to be less than one per
mille, but with a relative uncertainty of $20\text{\,}\mathrm{\char
37\relax}$, and so a systematic uncertainty of $0.1\text{\,}\mathrm{\char
37\relax}$ is assigned to $\Delta A_{{C\\!P}}^{\text{wgt}}$.

The limited size of the simulated sample results in a statistical uncertainty
on the efficiencies taken from the phase space efficiency model. The size of
this uncertainty is evaluated by resampling the simulated data 500 times, each
time building a new model and computing the efficiencies of the data using
that model. The simultaneous $\chi^{2}$ fit to measure $A_{\text{raw}}(f)$ is
then performed for each set of efficiencies, resulting in a spread of values
of $\Delta A_{{C\\!P}}^{\text{wgt}}$ with a standard deviation of
$0.57\text{\,}\mathrm{\char 37\relax}$, which is taken as the systematic
uncertainty due to the limited simulated sample size.

Due to the presence of ${\mathchar 28931\relax}_{{c}}^{+}$ decays originating
from sources other than ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{\mathchar
28931\relax}_{{c}}^{+}{\mu^{-}}{}X$ decays, such as directly from the PV or
from other $b$-hadron decays, the measurement may be biased, as such sources
can carry different experimental asymmetries. The composition of the data
sample is inferred from the reconstructed ${\mathchar 28931\relax}^{0}_{b}$
mass and from the impact parameter distribution of the ${\mathchar
28931\relax}_{{c}}^{+}$ vertex. The latter is seen to be consistent with that
for ${\mathchar 28931\relax}_{{c}}^{+}$ produced exclusively in $b$-hadron
decays, whilst the former is consistent between $p{{K}^{-}}{{K}^{+}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}$ samples, such that asymmetries from other sources
will cancel in $\Delta A_{{C\\!P}}^{\text{wgt}}$. Any associated systematic
uncertainty is assumed to be negligible.

The total systematic uncertainty is found to be $0.61\text{\,}\mathrm{\char
37\relax}$, computed as the sum in quadrature of the individual uncertainties.
These are assumed to be uncorrelated and are summarised in Table 2.

Table 2:  Systematic uncertainties on $\Delta A_{{C\\!P}}^{\text{wgt}}$ and
their magnitudes. The dash indicates that the uncertainty is assessed to be
negligible.

Source Uncertainty [$\mathrm{\char 37\relax}$] Fit signal model $0.20$ Fit
background model — Residual asymmetries $0.10$ Limited simulated sample size
$0.57$ Prompt ${\mathchar 28931\relax}_{{c}}^{+}$ — Total $0.61$

##  7 Results

The value of $A_{\text{raw}}(f)$ is found for each final state and data-taking
condition separately, and for a given centre-of-mass energy is taken as the
arithematic average of the polarity-dependent measurements. The average across
$\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ and $8\text{\,}\mathrm{TeV}$ is made by
weighting the measurements by their variances. The asymmetries for
$p{{K}^{-}}{{K}^{+}}$ and $p{{\pi}^{-}}{{\pi}^{+}}$ are measured to be

$\displaystyle A_{\text{raw}}(p{{K}^{-}}{{K}^{+}})$ $\displaystyle=$3.72\pm
0.78\text{\,}\mathrm{\char 37\relax}$,$ $\displaystyle
A_{\text{raw}}^{\text{wgt}}(p{{\pi}^{-}}{{\pi}^{+}})$ $\displaystyle=$3.42\pm
0.47\text{\,}\mathrm{\char 37\relax}$.$

where the uncertainties are statistical and take into account the reduction in
statistical power due to the weighting. The difference is

$\Delta A_{{C\\!P}}^{\text{wgt}}=(0.30\pm 0.91\pm 0.61)$\mathrm{\char
37\relax}$,$

where the first uncertainty is statistical and the second is systematic. The
measurements of $A_{\text{raw}}(p{{K}^{-}}{{K}^{+}})$,
$A_{\text{raw}}^{\text{wgt}}(p{{\pi}^{-}}{{\pi}^{+}})$, and $\Delta
A_{{C\\!P}}^{\text{wgt}}$ as a function of data-taking conditions are
presented in Fig. 4.

Figure 4:  Values of and statistical uncertainties on the asymmetries
$A_{\text{raw}}(p{{K}^{-}}{{K}^{+}})$ (top left),
$A_{\text{raw}}^{\text{wgt}}(p{{\pi}^{-}}{{\pi}^{+}})$ (top right), and
$\Delta A_{{C\\!P}}^{\text{wgt}}$ (bottom centre), for the four data
subsamples (two centre-of-mass energies, 7 and $8\text{\,}\mathrm{TeV}$, and
two polarities of the dipole magnet, up and down). For each asymmetry, the
average of the four data points, as described in the text, is also shown,
where the band indicates the uncertainty.

##  8 Summary

The raw $C\\!P$ asymmetries in the decays ${\mathchar
28931\relax}_{{c}}^{+}\\!\rightarrow p{{K}^{-}}{{K}^{+}}$ and
$p{{\pi}^{-}}{{\pi}^{+}}$ are measured using ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{\mathchar
28931\relax}_{{c}}^{+}{\mu^{-}}{}X$ decays. Kinematics in the
$p{{\pi}^{-}}{{\pi}^{+}}$ data are weighted to match those in the
$p{{K}^{-}}{{K}^{+}}$ data, such that the effect of experimental asymmetries
on the $C\\!P$ asymmetry parameter $\Delta A_{{C\\!P}}^{\text{wgt}}$ is
negligible. Acceptance, reconstruction, and selection efficiencies across the
five-dimensional $ph^{-}h^{+}$ phase space are corrected for. Systematic
effects arising from the mass distribution modelling, imperfect kinematic
weighting, finite simulated sample size, and the inclusion of ${\mathchar
28931\relax}_{{c}}^{+}$ decays from sources other than ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{\mathchar
28931\relax}_{{c}}^{+}{\mu^{-}}{}X$ decays are considered. The total
systematic uncertainty assigned to these effects is smaller than the
statistical uncertainty on $\Delta A_{{C\\!P}}^{\text{wgt}}$, whose central
value is measured to be consistent with zero.

This analysis constitutes the first measurement of a $C\\!P$ violation
parameter in three-body ${\mathchar 28931\relax}_{{c}}^{+}$ decays, but more
data is required to match the sensitivity of similar measurements using charm
mesons. Further studies into the structure of the $ph^{-}h^{+}$ phase space,
across which $C\\!P$-violating effects may strongly vary, would be beneficial
as input to theoretical calculations.

## 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 and OCEVU, and Région Auvergne-Rhône-Alpes (France), RFBR, RSF
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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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.
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Martin6, M. Martinelli41, D. Martinez Santos39, F. Martinez Vidal71, A.
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E. Maurice7,b, B. Maurin41, A. Mazurov47, M. McCann55,40, A. McNab56, R.
McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N. Meinert67, D.
Melnychuk29, M. Merk43, A. Merli22,40,q, E. Michielin23, D.A. Milanes66, E.
Millard50, M.-N. Minard4, L. Minzoni17, D.S. Mitzel12, A. Mogini8, J. Molina
Rodriguez1, T. Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, M.J.
Morello24,t, O. Morgunova68, J. Moron28, A.B. Morris52, R. Mountain61, F.
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Papanestis51, M. Pappagallo52, L.L. Pappalardo17,g, W. Parker60, C. Parkes56,
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A. Pellegrino43, G. Penso26, M. Pepe Altarelli40, S. Perazzini40, D.
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V. Placinta30, S. Playfer52, M. Plo Casasus39, F. Polci8, M. Poli Lener19, A.
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F. Ratnikov35,x, G. Raven44, M. Ravonel Salzgeber40, M. Reboud4, F. Redi41, S.
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M.S. Rudolph61, T. Ruf40, P. Ruiz Valls71, J. Ruiz Vidal71, J.J. Saborido
Silva39, E. Sadykhov32, N. Sagidova31, B. Saitta16,f, V. Salustino
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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
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Universita e INFN, Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di 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 RAS),
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
39Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade 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 University of Science and Technology MISIS, Moscow, Russia,
associated to 32
70National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
71Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
72Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43
73Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

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, Vietnam
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
xNational Research University Higher School of Economics, Moscow, Russia
yNational University of Science and Technology MISIS, Moscow, Russia
†Deceased