EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-150 LHCb-PAPER-2021-018 February 7, 2022

Evidence for a new structure

in the $J/\psi p$ and $J/\psi\bar{p}$ systems

in $B_{s}^{0}\rightarrow J/\psi p\bar{p}$ decays

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

An amplitude analysis of flavour-untagged $B_{s}^{0}\rightarrow J/\psi
p\bar{p}$ decays is performed using a sample of $797\pm 31$ decays
reconstructed with the LHCb detector. The data, collected in proton-proton
collisions between 2011 and 2018, correspond to an integrated luminosity of 9
$\text{fb}^{-1}$. Evidence for a new structure in the $J/\psi p$ and
$J/\psi\bar{p}$ systems with a mass of $4337\ ^{+7}_{-4}\
{}^{+2}_{-2}~{}\text{MeV}$ and a width of $29\ ^{+26}_{-12}\
{}^{+14}_{-14}~{}\text{MeV}$ is found, where the first uncertainty is
statistical and the second systematic, with a significance in the range of 3.1
to 3.7 $\sigma$, depending on the assigned $J^{P}$ hypothesis.

Published in PhysRevLett.128.062001

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

The observation of pentaquark candidates ($P_{c}$) in
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}$ final states produced in ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{{K}^{-}}$
decays 111The charge-conjugate decay is implied, unless otherwise stated, and
natural units with $\hbar=c=1$ are used throughout the paper. [1, 2] by the
LHCb experiment has stimulated interest in exotic spectroscopy. Recently,
evidence for a structure in the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\mathchar
28931\relax}$ invariant-mass spectrum, consistent with a charmonium-like
pentaquark with strangeness, was found in ${{{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\mathchar
28931\relax}{{K}^{-}}}$ decays [3]. The mass of these states is just below
threshold for the joint production of a charm baryon and a charm meson, i.e.
the ${\mathchar 28934\relax}_{c}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{*}}$ and the ${{\mathchar
28932\relax}_{c}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{*}}$
thresholds for the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}$ and the
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\mathchar 28931\relax}$ resonances,
respectively. The mass separation from these thresholds might provide useful
information for the phenomenological interpretation for these states. Proposed
interpretation can be grouped into three classes: QCD-inspired models [4, 5],
residual hadron-hadron interaction models [6] and rescattering effects
particle [7]. Additional measurements in different productions and decay
channels are crucial to disentangle the various models [8].

The
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$
decay was observed for the first time by the LHCb experiment in 2019 [9]. This
channel may have sensitivity to the resonant $P_{c}$ structures [1, 2] within
the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}$ invariant-mass range of
$[4034,4429]\text{\,Me\kern-1.00006ptV}$. Additionally, it could proceed via
an intermediate glueball candidate $f_{J}(2220)$ decaying to
${p}{\overline{p}}$ [10]. Unlike ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{{K}^{-}}$
decays receiving a relatively large contribution from the intermediate excited
${\mathchar 28931\relax}$ resonances, no conventional states are expected to
be produced in the ${B}^{0}_{s}$ decay, offering a clean environment to search
for new resonant structures. Baryonic ${B}_{({s})}^{0}$ decays also allow for
a study of the dynamics of the baryon-antibaryon system and its characteristic
threshold enhancement, the origin of which is still to be understood [11].

In this Letter, an amplitude analysis of
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$
decay is presented, including a search for pentaquark and glueball states,
using proton-proton ($pp$) collision data at centre-of-mass energies of 7 TeV,
8 TeV and 13 TeV, corresponding to a luminosity of 9$\text{\,fb}^{-1}$,
collected between 2011 and 2018. The measurement is performed untagged, such
that decays of ${B}^{0}_{s}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}$ are not distinguished and
analysed together.

The LHCb detector is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, described in detail in Refs. [12, 13, 14,
15]. The online event selection is performed by a trigger [16], comprising a
hardware stage based on information from the muon system which selects
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rightarrow{\mu^{+}}{\mu^{-}}$ decays,
followed by a software stage that applies a full event reconstruction. The
software trigger relies on identifying ${J\mskip-3.0mu/\mskip-2.0mu\psi}$
decays into muon pairs consistent with originating from a $B$ meson decay
vertex detached from the primary $pp$ collision point.

Samples of simulated events are used to study the properties of the signal and
control channels. The $pp$ collisions are generated using Pythia [17] with a
specific LHCb configuration [18]. Decays of hadronic particles and
interactions with the detector material are described by EvtGen [19], using
Photos [20], and by the Geant4 toolkit [21, *Agostinelli:2002hh, 23],
respectively. The signal
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$
decays are generated from a uniform phase space distribution, while the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\phi(\rightarrow{{K}^{+}}{{K}^{-}})$
control mode is generated according to the model of Ref. [24].

The event selection follows the same strategy as Ref. [9]. Signal
${B}^{0}_{s}$ candidates are formed from two pairs of oppositely charged
tracks. The first pair is required to be consistent with muons originating
from a ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ meson with a decay vertex
significantly displaced from its associated primary $pp$ vertex (PV). For a
given particle, the associated PV is the one with the smallest impact
parameter $\chi^{2}_{\rm IP}$, defined as the difference in the vertex-fit
$\chi^{2}$ of a given PV reconstructed with and without the track under
consideration. The second pair is required to be consistent with protons
originating from the muon-pair vertex. A kinematic fit [25] to the
${{B}^{0}_{s}}$ candidate is performed, with the dimuon mass constrained to
the known ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ mass [26]. The selection is
optimised using multivariate techniques [27] trained with simulation and data.
Simulated events are weighted such that the distributions of momentum, $p$,
transverse momentum, $p_{\mathrm{T}}$, and number of tracks per event for
${B}^{0}_{s}$ candidates match the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\phi$ control-mode
distributions in data. In simulation the particle identification (PID)
variables for each charged track are resampled as a function of its $p$,
$p_{\mathrm{T}}$ and the number of tracks in the event using ${{\mathchar
28931\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ and
$D^{\ast+}\rightarrow D^{0}(\rightarrow K^{-}{{\pi}^{+}})\pi^{+}$ calibration
samples from data [28]. The selection consists of two boosted decision tree
(BDT) classifiers. The first classifier, $\text{BDT}_{\text{sel}}$, is a
selection trained on
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\phi$ simulation
and sideband data with the
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$ invariant mass above
$5450\text{\,Me\kern-1.00006ptV}$ using the $p$, $p_{\mathrm{T}}$, and
$\chi^{2}_{\rm IP}$ variables of the ${{B}^{0}_{s}}$ candidate, the $\chi^{2}$
probability from the kinematic fit of the candidate, and the impact parameter
distances of the two muons. The second classifier, $\text{BDT}_{\text{PID}}$,
is trained on
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}p{\overline{p}}$
simulation and sideband data using proton identification variables: the hadron
PID from the ring-imaging Cherenkov detectors, the $p$, $p_{\mathrm{T}}$ and
$\chi^{2}_{\rm IP}$ of the protons. The $\text{BDT}_{\text{PID}}$ output
selection criterion is chosen by maximising the figure of merit
$\mathcal{S}^{2}/(\mathcal{S}+\mathcal{B})^{3/2}$, where $\mathcal{S}$ and
$\mathcal{B}$ are the signal and background yields in a region of $\pm
10\text{\,Me\kern-1.00006ptV}$ around the ${B}^{0}_{s}$ mass peak. These are
determined from a fit to the
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}p{\overline{p}}$ invariant-mass
distribution in data after the $\text{BDT}_{\text{sel}}$ selection, multiplied
by the efficiency of the $\text{BDT}_{\text{PID}}$ output requirement,
obtained from simulation and from sideband data, respectively.

Figure 1: Invariant-mass distribution
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}p\bar{p})$ for reconstructed signal
candidates; the result of the fit described in the text is overlaid.

After applying these selection criteria, a maximum-likelihood fit is performed
to the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}p\bar{p}$ invariant-mass
distribution, shown in Fig. 1, yielding $797\pm 31$ ${B}^{0}_{s}$ signal
decays. The ${B}^{0}_{s}$ signal shape is modelled as the sum of two Crystal
Ball [29] functions sharing a common peak position, with asymmetric tails
describing radiative and misreconstruction effects. The signal-model
parameters are determined from simulation and only the ${B}^{0}_{s}$ peak
position is allowed to vary in the fit to data. The combinatorial background
is modelled by a first-order polynomial with parameters determined from the
fit to data. The
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$
component has the same shape as the ${B}^{0}_{s}$ signal. The combinatorial-
background fraction in the ${B}^{0}_{s}$ signal window of 3$\sigma$ around the
mass peak ($[5357,5378]\text{\,Me\kern-1.00006ptV}$) is estimated to be
$(14.9\pm 0.6)\%$, where $\sigma\approx 3.5\text{\,Me\kern-1.00006ptV}$ is the
resolution of the reconstructed invariant mass. The
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})$ and
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})$ invariant mass
distributions of the reconstructed ${B}^{0}_{s}$ candidates in the
${B}^{0}_{s}$ signal region are shown in the bottom row of Fig. 2 (black
dots), where hints of structure in the region around (4.3 - 4.4) GeV are
present. This Letter investigates the nature of these enhancements, which are
not compatible with the pure phase-space hypothesis.

An amplitude analysis of the ${B}^{0}_{s}$ candidates is performed under the
assumption of $C\\!P$ symmetry conservation, i.e. the dynamics is the same in
${B}^{0}_{s}$ and ${\kern 1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}$
decays. Three interfering decay sequences are considered in the amplitude
model:
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}X(\rightarrow{p}{\overline{p}})$,
${{B}^{0}_{s}}\rightarrow
P_{c}^{+}(\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}){\overline{p}}$ and
${{B}^{0}_{s}}\rightarrow
P_{c}^{-}(\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}}){p}$,
all followed by a
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rightarrow{\mu^{+}\mu^{-}}$ decay. These
sequences are labelled as the $X$, $P_{c}^{+}$ and $P_{c}^{-}$ chains,
respectively. Since the data sample is not flavour tagged, the distribution of
the candidates in the phase space is by construction symmetric for
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}p$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\bar{{p}}$ final states, and therefore the
analysis is sensitive to the sum of possible contributions from $P_{c}^{+}$
and $P_{c}^{-}$ pentaquark candidates, denoted as $P_{c}$ in the following.
Due to the small sample size and since the ${B}^{0}_{s}$ or
${\overline{{B}}^{0}_{s}}$ flavour is not identified, there is no sensitivity
to different couplings for the $P_{c}^{+}$ and $P_{c}^{-}$ states, which are
constrained to be equal, up to a phase difference. The amplitude model is
based on the helicity formalism of Refs. [30, 31], which defines a consistent
framework for propagating spin correlations through relativistic decay chains.
To align the spin of the different decay chains, the prescription in Ref. [32]
is followed. Details about the amplitude definition are given in the
Supplemental material.

Candidates in the ${B}^{0}_{s}$ signal region are used to perform an amplitude
fit in the four-dimensional phase space,
$(m_{{p}{\overline{p}}},\vec{\Omega})$. This phase space is defined by the
invariant mass $m_{{p}{\overline{p}}}$ of the ${p}{\overline{p}}$ pair and
$\vec{\Omega}=(\theta_{p},\theta_{\mu},\varphi)$, where
$\theta_{p},\theta_{\mu}$ are the two helicity angles of the ${p}$ and the
$\mu^{-}$ in the $X$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ rest frame,
respectively, and $\varphi$ is the azimuthal angle between the decay planes,
of the $\mu^{-}\mu^{+}$ and the ${p}{\overline{p}}$ pairs. The distributions
of $(m_{{p}{\overline{p}}},\cos\theta_{\mu},\cos\theta_{p},\varphi)$, together
with the $m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})$ and
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})$ invariant mass
projections, are shown in Fig. 2 for selected candidates.

Figure 2: One-dimensional projections of the angular
$(\cos\theta_{\mu},\cos\theta_{p},\varphi)$ and invariant-mass distributions
$(m({p}{\overline{p}}),m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}),m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}}))$,
superimposed with the results of the fit from the baseline model (blue) and
the default model (red) comprising a NR term and the $P_{c}$ contribution.

The amplitude fit minimises the negative log-likelihood function

$\displaystyle-2\log\mathcal{L}(\vec{\omega})=-2\sum_{i}\log[(1-\beta)\mathcal{P}_{\text{sig}}\left(m_{p\bar{p},i},\Omega_{i}|\vec{\omega}\right)$
$\displaystyle+\beta\mathcal{P}_{\text{bkg}}\left(m_{p\bar{p},i},\Omega_{i}\right)],$
(1)

where the total probability density function (PDF) calculated for
$i^{\text{th}}$ candidate has a signal, $\mathcal{P}_{\text{sig}}$, and a
background, $\mathcal{P}_{\text{bkg}}$, component where $\beta$ is the
fraction of background events observed within the ${B}^{0}_{s}$ signal window.
The signal PDF is proportional to the matrix element squared,
$|\mathcal{M}\left(m_{p\bar{p},i},\Omega_{i}|\vec{\omega}\right)|^{2}$, and
depends on the fit parameters, $\vec{\omega}$, i.e. the couplings, the masses
and the widths, which define the contributing resonances

$\displaystyle\mathcal{P}_{\mathrm{sig}}\left(m_{p\bar{p},i},\Omega_{i}|\vec{\omega}\right)\equiv$
$\displaystyle\frac{1}{I(\vec{w})}\left|\mathcal{M}\left(m_{p\bar{p}i},\Omega_{i}|\vec{\omega}\right)\right|^{2}\Phi\left(m_{p{\overline{p}},i}\right)\epsilon\left(m_{p\bar{p},i},\Omega_{i}\right).$
(2)

The phase-space element is
$\Phi\left(m_{p{\overline{p}},i}\right)=|\vec{p}||\vec{q}|$, where $\vec{p}$
is the momentum of the $X$ system in the ${{B}^{0}_{s}}$ rest frame and
$\vec{q}$ is the proton momentum in the $X$ rest frame. The efficiency,
$\epsilon\left(m_{p\bar{p},i},\Omega_{i}\right)$, is included in the PDF, and
is parameterised by a Legendre polynomial expansion on the four-dimensional
phase space. The denominator, $I(\vec{\omega})$, normalises the probability.
The fit fractions of each signal component are defined as the corresponding
PDF integral divided by $I(\vec{\omega})$. The background contribution,
$\mathcal{P}_{\mathrm{bkg}}$, is parameterised by the product of one-
dimensional Legendre polynomials describing candidates in the ${B}^{0}_{s}$
sideband region of $[5420,5700]\text{\,Me\kern-1.00006ptV}$.

No well established resonances are expected either in the ${p}{\overline{p}}$
or in the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}}$ channels. However, some
resonances could potentially decay into ${p}{\overline{p}}$ [26], e.g. the
$f_{J}(2220)$[33] and the $X(1835)$ [34, 35]; thus they have been included in
alternative models. The simplest model used to fit the data has no resonant
contributions in the $P_{c}^{+}$, $P_{c}^{-}$ and $X$ decay chains, and is
denoted as the baseline model. This model includes a nonresonant (NR)
contribution in the $X$ decay sequence with spin-parity quantum numbers equal
to $J^{P}=1^{-}$, which has $S$-wave terms in both its production and decay.
Indeed, due to the low $Q$-value of the decay, the $S$-wave contribution is
expected to be favoured since higher values of orbital momentum are
suppressed. Models including NR contributions with different quantum numbers
(i.e. $J^{P}=0^{\pm},1^{+}$) are excluded because their $-2\log\mathcal{L}$
values are significantly worse than that of the $J^{P}=1^{-}$ hypothesis.

Due to the limited sample size, the baseline model is described by two
independent $LS$ couplings for both
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}X$ and
$X\rightarrow{p}\bar{{p}}$ decays, where $L$ is the decay orbital angular
momentum, and $S$ is the sum of spins of the decay products. Fixing the two
lowest orbital momentum couplings as the normalisation choice and three
parameters, which are consistent with zero, reduces the number of free
parameters to three.

The fit results of the baseline model are shown in Fig 2. The baseline model
does not describe the data distribution, with a $\chi^{2}$ goodness-of-fit
test result of $\chi^{2}/ndf=64/38$ corresponding to a $p$-value of ${4\times
10^{-5}}$. Therefore, two resonant contributions from $P_{c}^{+}$ and
$P_{c}^{-}$ are added, with identical masses, widths and couplings. First, the
$P_{c}(4312)$ state previously observed by the LHCb experiment in the
${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{{K}^{-}}$
analysis [2] is included in the model with mass and width fixed at their known
values. The broad $P_{c}$ structure with a mass around
$4380\text{\,Me\kern-1.00006ptV}$, observed in 2015 [1], is not considered in
this fit, since the helicity formalism used in Ref. [36] requires
modifications in order to properly align the half-integer spin particles of
different decay chains and, thus, those results need to be confirmed with an
updated analysis of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{{K}^{-}}$
data [37, 38]. In this analysis no evidence for the $P_{c}(4312)$ state is
found since the $p$-value, computed from the $-2\Delta\log\mathcal{L}$ of the
alternative fit with respect to the default model, is measured to be $0.5$.
Exploiting the $\text{CL}_{s}$ method [39], an upper limit on the modulus of
its coupling is set to $0.043$ at 90% of confidence level, which corresponds
to a fit fraction of $2.86\%$. A model with a new $P_{c}^{\pm}$ state given a
free mass and width is chosen as the default model. Different spin-parity
hypotheses for the $P_{c}$ states are investigated, i.e. $J^{P}=1/2^{\pm}$ and
$J^{P}=3/2^{\pm}$. Due to a limited sample size, only the lowest values of $L$
are considered and the same coupling is assumed for all $J^{P}$ hypotheses,
resulting in two free parameters: the modulus $A(P_{c})$ and the phase
$\phi(P_{c})$ of the coupling. The seven fit parameters $\vec{\omega}$ contain
the baseline model parameters, see Eq. 2, the coupling
$[A(P_{c}),\phi(P_{c})]$, the mass and width of the $P_{c}$ state.

The fit result for the $J^{P}=1/2^{+}$ hypothesis of the $P_{c}^{+}$ state is
shown in Fig. 2. The $\chi^{2}/ndf$ is $36.7/36.8$, where the number of
degrees of freedom $ndf$ is determined from fits to the $\chi^{2}$
distribution extracted from pseudoexperiments. The statistical significance is
estimated from pseudoexperiments generated with the baseline model and fitted
with the default model, using amplitude parameters determined by the fit to
data. The mass and width of the $P_{c}$ states are not defined in the baseline
model, thus multiple fits to the same pseudodata are performed to account for
the look-elsewhere effect, scanning the initial mass value in intervals of
size $50\text{\,Me\kern-1.00006ptV}$. The test statistic $t$ is built as the
maximum of the $-2\log\mathcal{L}$ difference between the baseline and the
default model [40] among all the fits obtained by scanning the initial mass
values. The $p$-value is computed using a frequentist method as the fraction
of pseudoexperiments with $t$ larger than the $t_{\text{data}}$ value from the
fits to data. The $p$-value ranges between $0.02\%$ and $0.2\%$ for different
$J^{P}$ hypotheses, the lowest being associated to $1/2^{+}$ and the highest
to $3/2^{+}$, as reported in the Supplemental material. These $p$-values
correspond to a signal significance in the range of $3.1$ to $3.7\sigma$,
providing evidence for a new pentaquark-like state. Using the $\text{CL}_{s}$
method [39], none of the $J^{P}$ hypotheses considered can be excluded at 95%
confidence level.

The hypothesis of a glueball state with mass equal to
$2230\text{\,Me\kern-1.00006ptV}$ and width of around
$20\text{\,Me\kern-1.00006ptV}$ [10] is also tested, by adding to the default
model a resonance in the $X$ decay chain with fixed mass and width. No
evidence of $f_{J}(2220)$ is observed, as the fit with this contribution gives
a $p$-value, computed from the $-2\Delta\log\mathcal{L}$ with respect to the
default model, of $0.75$ and an associated complex coupling of $[-0.04\pm
0.09,-0.06\pm 0.16]$.

Systematic uncertainties are evaluated for the mass, width, coupling, and fit
fractions of the sum of the $P_{c}^{\pm}$ contributions. For each source of
uncertainty, pseudoexperiments are generated according to the alternative
model with the same sample size as in data. The fit to such pseudoexperiments
is performed using the default model. The systematic uncertainties, listed in
Table 1, are assigned as the mean of the residual distributions between the
fitted and the default parameter results. The main contributions are due to
different NR models for the $X$ decay chain, alternative $J^{P}$ hypotheses
for the $P_{c}$ state and possible mismodelling of the efficiency
distribution. The systematic uncertainty associated to the NR model is
obtained including, in addition to the NR term with $J^{P}=1^{-}$ and lowest
values of $L$ allowed, a $P$-wave resonant contribution with $J^{P}=0^{-}$,
modelled with a Breit–Wigner lineshape in order to account for possible
resonances, such as the $X(1835)$ [34, 35], decaying to a ${p}{\overline{p}}$
final state. Since none of the $J^{P}$ hypotheses investigated for the
$P_{c}^{\pm}$ state can be excluded, an additional systematic uncertainty is
assigned as the difference between the least and the most significant
hypotheses. Finally, the uncertainty associated with the efficiency
parameterisation is evaluated by summing two contributions. The first is
obtained by replacing the default efficiency map with one determined from
simulation of different data-taking conditions, and the second by using a
parameterisation given by the product of one-dimensional functions of the
considered fit variables. Other systematic uncertainties include alternative
parameterisation of the background shape and the uncertainty in the background
normalisation, which is varied within its statistical uncertainty. The
background is parameterised using data in a sideband region around the
${B}^{0}_{s}$ invariant-mass peak with
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}})\in[5300,5350]\text{\,Me\kern-1.00006ptV}$
and
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}})\in[5420,5460]\text{\,Me\kern-1.00006ptV}$,
to account for variations of the background as a function of the invariant
mass. The default value of the hadron radius size for the Blatt–Weisskopf
coefficients [41], equal to $3\text{\,Ge\kern-1.00006ptV}^{-1}$, is replaced
by two alternate values, $1.5\text{\,Ge\kern-1.00006ptV}^{-1}$ and
$5\text{\,Ge\kern-1.00006ptV}^{-1}$. Fit biases in the parameters estimation
are extracted from the residual distribution of the generated and fitted
parameters of pseudoexperiments based on the default model. Systematic
uncertainties from orbital momentum for the NR, $P_{c}$ contributions, and
invariant-mass resolution are found to be negligible. More details about
systematic uncertainties can be found in the Supplemental material. The final
significance including systematic uncertainties is equal to 3.1$\sigma$, which
is the minimal value among the different sources of systematic uncertainty, as
reported in Table 1.

Table 1: Systematic uncertainties associated to the mass $M_{P_{c}}$ (in  MeV), width $\Gamma_{P_{c}}$ (in  MeV), modulus of coupling $A(P_{c})$, fit fractions $f(P_{c})$ (in %), $p$-values and associated significance ($\sigma$) of the $P_{c}^{\pm}$ state. Source | $M_{P_{c}}$ | $\Gamma_{P_{c}}$ | $A(P_{c})$ | $f(P_{c})$ |  $p$ (%) | $\sigma$
---|---|---|---|---|---|---
NR($X$) model | 0.1 | 1.4 | 0.013 | 6.4 | 0.003 | 4.2
$J^{P}(P_{c})$ assignment | 2 | 12 | 0.100 | 5.5 | 0.2 | 3.1
Efficiency | 0.2 | 4 | 0.012 | 0.4 | 0.001 | 4.4
Background | 0.1 | 2 | 0.001 | 0.7 | 0.001 | 4.3
Hadron radius | 0.7 | 4 | 0.034 | 1.7 | 0.02 | 3.7
Fit bias | ${}^{+0.2}_{-0.1}$ | ${}^{+5}_{-2}$ | ${}^{+0.040}_{-0.040}$ | – | – | –
Total | $2$ | $14$ | $0.11$ | 8.6 | – | 3.1

The mass and width of this new pentaquark-like state are measured to be

$\displaystyle M_{P_{c}}=4337\ ^{+7}_{-4}\
{}^{+2}_{-2}\text{\,Me\kern-1.00006ptV},$ (3)
$\displaystyle\text{$\Gamma$}_{P_{c}}=29\ ^{+26}_{-12}\
{}^{+14}_{-14}\text{\,Me\kern-1.00006ptV},$

where the first uncertainty is statistical and the second systematic. The
analysis of flavour untagged ${B}^{0}_{s}$ decays is not sensitive to the
$P_{c}^{+}$ and $P_{c}^{-}$ contributions separately, therefore a single
coupling is determined, which has modulus $A(P_{c})=0.19\ ^{+0.19}_{-0.08}\
{}^{+0.11}_{-0.11}$ and phase $\phi(P_{c})$ consistent with zero,
corresponding to a fit fraction of $(22.0\ ^{+8.5}_{-4.0}\pm 8.6)\%$ for the
$P_{c}$ states. Due to the limited sample size, it is not possible to
distinguish among different $J^{P}$ quantum numbers. A state compatible with
this $P_{c}$ state is predicted in Ref. [42] with $J^{P}=1/2^{+}$.

In conclusion, an amplitude analysis of
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$
decays is presented, using data collected with the LHCb detector between 2011
and 2018, and corresponding to an integrated luminosity of 9
$\text{\,fb}^{-1}$. No evidence is seen for either a $P_{c}$ state at a mass
of $4312\text{\,Me\kern-1.00006ptV}$ [2] or the glueball state $f_{J}(2220)$
predicted in Ref. [10]. Unlike in other $B$ decays [43, 44, 45, 46], no
threshold enhancement is observed in the ${p}{\overline{p}}$ invariant-mass
spectrum, which is well modelled by a nonresonant contribution. Evidence for a
Breit–Wigner shaped resonance in the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}$
and ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}}$ invariant masses is
obtained with a statistical significance in the range of 3.1 to $3.7\sigma$,
depending on the assigned $J^{P}$ hypothesis.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MICINN (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and NERSC (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 ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, IPhU and Labex P2IO, and Région Auvergne-Rhône-Alpes (France);
Fondazione Fratelli Confalonieri (Italy); Key Research Program of Frontier
Sciences of CAS, CAS PIFI, CAS CCEPP, Fundamental Research Funds for the
Central Universities, and Sci. & Tech. Program of Guangzhou (China); RFBR, RSF
and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Leverhulme
Trust, the Royal Society and UKRI (United Kingdom).

Supplemental material

A. Matrix element model

The amplitude model is constructed using the helicity formalism [30] where a
two body decay $A\rightarrow(1)(2)$ contributes to the amplitude with a term

$\widetilde{\mathcal{H}}^{A\rightarrow(1)(2)}_{\lambda_{1},\lambda_{2}}\mathcal{D}^{J_{A}}_{\lambda_{A},\lambda_{1}-\lambda_{2}}(\phi_{1},\theta_{1},0)R(m_{12}).$
(4)

where $\lambda$ is the particle helicity, defined as the projection of the
spin $J_{A}$ onto the momentum direction, and
$\widetilde{H}^{A\rightarrow(1)(2)}$ are complex helicity couplings which
describe the decay dynamics and take into account the Jacob-Wick phase factor
of particle $(2)$ [31]222Particle $(2)$ is the particle with opposite momentum
with respect to particle $(1)$ in the particle-$A$ rest frame:
$\vec{p}_{2}^{\\{A\\}}=-\vec{p}_{1}^{\\{A\\}}$.  and are defined as
$\widetilde{H}^{A\rightarrow(1)(2)}_{\lambda_{1},\lambda_{2}}\equiv(-1)^{J_{2}-\lambda_{2}}{H}^{A\rightarrow(1)(2)}_{\lambda_{1},\lambda_{2}}$.
The Wigner $D$-matrix rotates the initial coordinate system of particle $A$,
with the $z$ axis aligned along the helicity axis of $A$, to the coordinate
system with the $z$ axis aligned along the particle $1$ helicity axis. The
angles $\phi_{1}$ and $\theta_{1}$ (known as “helicity angle” of $A$)
represent the azimuthal and polar angles of particle $1$ in the rest frame of
$A$. The third angle is set to zero by convention. The last term of Eq. 4,
$R(m_{12})$, is the lineshape dependence that contains either the
Blatt–Weisskopf coefficients and threshold factors or, if $A$ is a resonant
contribution, a Breit–Wigner lineshape. Details are given below.

The helicity couplings are expressed in the $LS$ basis, where $L$ is the
orbital and $S$ is the spin angular momentum, using Clebsch–Gordan
coefficients, $B_{L,S}$, as

$\displaystyle\mathcal{H}_{\lambda_{B},\lambda_{C}}^{A\rightarrow
BC}=\sum_{L}\sum_{S}\sqrt{\frac{2L+1}{2J_{A}+1}}B_{L,S}$
$\displaystyle\langle{J_{B}},{\lambda_{B}},{J_{C}},{-\lambda_{C}}|{S},{\lambda_{B}-\lambda_{C}}\rangle$
$\displaystyle\times$
$\displaystyle\langle{L},{0},{S},{\lambda_{B}-\lambda_{C}}|{J_{A}},{\lambda_{B}-\lambda_{C}}\rangle.$
(5)

For strong decays, possible $L$ values are constrained by the conservation of
parity: ${P_{A}=P_{1}P_{2}(-1)^{L}}$.

The four-body phase space of the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$
decay is described by the ${p}{\overline{p}}$ invariant mass,
$m({p}{\overline{p}})$, the two helicity angles $\theta_{p}$, $\theta_{\mu}$
of the $p$ and $\mu$ in their parent reference frame and the azimuthal angle
$\varphi$ between the dihadron and dilepton decay planes.

In order to align different decay sequences, the cyclic ordering of the final
particles is adopted to define the helicity angles, as suggested in Ref. [32],
and the Jacob-Wick convention for particle (2). The ordering is important in
order to guarantee a proper spin matching of the final particles and to ensure
that all resonances share the same $y$ axis instead of the opposite axis. For
the decay under study, the following ordering is considered:
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}(1){p}(2){\overline{p}}(3)$,
where the angles are defined with respect to particle (1) for the $P_{c}^{+}$
chain, to particle (2) for the $X$ chain and to particle (3) for the
$P_{c}^{-}$ chain. In particular, in the $X$ chain the $p$ direction defines
the $X$ helicity angle, while in the
$P_{c}^{-}\rightarrow\bar{p}{{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ chain the
$\bar{p}$ direction defines the $P_{c}^{-}$ helicity angle. The Jacob-Wick
phase-factor is also needed in order to properly align the final spin. Indeed,
the rotation in the $X\rightarrow{p}{\overline{p}}$ decay aligns the spin axis
along the $p$ momentum, while the rotation in the
$P_{c}^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}p$ frame aligns the
spin axis in the direction opposite to the $p$ momentum. Therefore, an
additional rotation to align the $z$ axis between the $P_{c}^{+}$ and $X$
chains generates the particle (2) phase factor equal to
$(-1)^{J_{p}-\lambda_{p}}$ in the amplitude of the $P_{c}^{+}$ chain, where
$J_{p}$ and $\lambda_{p}$ are the spin and the helicity of the proton in the
$P_{c}^{+}$ rest frame, respectively.

Denoting the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ as $\psi$, the matrix
element for the ${{B}^{0}_{s}}\rightarrow X{{J\mskip-3.0mu/\mskip-2.0mu\psi}}$
chain is

$\displaystyle\mathcal{M}^{X}_{\lambda_{p},\lambda_{{\overline{p}}},\Delta\lambda}=\sum_{\lambda_{\psi},\lambda_{X}}\widetilde{\mathcal{H}}^{{{B}^{0}_{s}}}_{\lambda_{X},\lambda_{\psi}}\mathcal{R}(m_{{p}{\overline{p}}}^{2})\mathcal{D}^{*J_{X}}_{\lambda_{X},\lambda_{p}-\lambda_{{\overline{p}}}}(\phi_{p}^{\\{X\\}},\theta_{p}^{\\{X\\}},0)\widetilde{\mathcal{H}}^{X}_{\lambda_{p},\lambda_{{\overline{p}}}}\mathcal{D}^{*1}_{\lambda_{\psi},\Delta\lambda}(\phi_{\mu}^{\\{\psi\\}},\theta_{\mu}^{\\{\psi\\}},0),$
(6)

where the first Wigner-$D$ matrix of the ${{B}^{0}_{s}}$ decay is omitted
because the ${{B}^{0}_{s}}$ has spin zero, implying that, for conservation of
total angular momentum, the helicity of the $\psi$ is equal to the helicity of
$X$ ($|\lambda_{X}-\lambda_{\psi}|\leq 0$). The $y$ axis of the $\psi$ rest
frame for all three decay sequences is chosen to be parallel to the $y$ axis
in the ${B}^{0}_{s}$ rest frame to ensure a correct alignment. The angles
$\phi_{p}^{\\{X\\}}$ and $\theta_{p}^{\\{X\\}}$ are the azimuthal and polar
angles of the proton momentum in the $X$ helicity frame, while the angles
$\theta_{\mu}^{\\{\psi\\}}$ and $\phi_{\mu}^{\\{\psi\\}}$ are the polar and
azimuthal angles of the $\mu^{-}$ momentum in the $\psi$ helicity frame. In
the ${B}^{0}_{s}$ rest frame, the proton momentum projected on the $x$ axis is
positively defined in order to satisfy $\phi_{p}=0$. Since the $\psi$ decay
occurs through an electromagnetic interaction, the difference of the muon
helicities, $\Delta\lambda$, restricts to the values:
$\Delta\lambda=\lambda_{{\mu^{-}}}-\lambda_{{\mu^{+}}}=\pm 1$. As the value of
$\Delta\lambda=0$ is suppressed by $m_{\mu}/m_{\psi}$ for the electromagnetic
transition, it is omitted in the summation. The helicity coupling of the
$\psi$ decay is, therefore, ignored because it can be absorbed in the
${B}^{0}_{s}$ couplings. The factor $\mathcal{R}(m_{{p}{\overline{p}}}^{2})$
is the lineshape term of the ${p}{\overline{p}}$ invariant mass, as described
below.

For $J^{P}(X)=1^{-}$, which is the best choice to fit the data, there are 3
(2) independent couplings
$\widetilde{\mathcal{H}}^{{{B}^{0}_{s}}}_{\lambda_{\psi},\lambda_{X}}$
($\widetilde{\mathcal{H}}^{X}_{\lambda_{p},\lambda_{{\overline{p}}}}$) to fit,
already reduced by the parity conservation in the strong decay of the $X$
resonance. Those couplings are then expressed in the $LS$ basis; the lowest
$L$ and $S$ of the ${B}^{0}_{s}$ decay, $B^{{{B}^{0}_{s}}}_{L_{min}S_{min}}$,
is always fixed to $(1,0)$ for each contribution. Therefore, the NR
contribution contains two complex couplings for the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}X$ decay,
associated to relative angular momenta $L_{{{B}^{0}_{s}}}=0,1,2$ and one for
the decay $X\rightarrow{p}{\overline{p}}$, with $L_{X}=0,2$, due to parity
conservation. Here, $L_{{{B}^{0}_{s}}}$ and $L_{X}$ refer to the relative
angular momentum between ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}X$ and
$p{\overline{p}}$ final states, respectively. In addition, due to the limited
sample size, the couplings relative to $L_{{{B}^{0}_{s}}}=1$ for the
production and to the phase $\phi$ of $L_{X}=2$ are consistent with zero and,
therefore, are fixed to zero in the default model, reducing the number of free
parameters to three. The number of $LS$ couplings and free parameters are
summarised in Table 2.

Table 2: $LS$ couplings and free parameters for the NR $1^{--}$ model and the models with the $P_{c}$ states for different $J^{P}$ hypotheses. Here, $(L,S)$ and $(l,s)$ refer to the relative angular momentum and spin of $P_{c}^{+}{\overline{p}}\ (P_{c}^{-}{p})$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}p\ ({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})$ final states, respectively, for the $P_{c}^{+}$ ($P_{c}^{-}$) decay chain. The free parameters are denoted as $(A,\phi)$, where $A$ is the modulus and $\phi$ the phase of the coupling. Model |  $LS$ couplings | Free parameters
---|---|---
NR $J^{P}(X)=1^{--}$ |  $(L,S)_{{{B}^{0}_{s}}}$=(0,0),(2,2), $(L,S)_{X}$=(0,1),(2,1) | $(A,\phi)_{L_{{{B}^{0}_{s}}}=2},(A,0)_{L_{X}=2}$
$J^{P}(P_{c})=1/2^{+}$ | $(L,S)=(0,0),(l,s)=(1,1/2)$ | $(A,0)$
$J^{P}(P_{c})=1/2^{-}$ | $(L,S)=(0,0),(l,s)=(0,1/2)$ | $(A,\phi)$
$J^{P}(P_{c})=3/2^{-}$ | $(L,S)=(1,1),(l,s)=(0,3/2)$ | $(A,0)$
$J^{P}(P_{c})=3/2^{+}$ | $(L,S)=(1,1),(l,s)=(1,1/2)$ | $(A,\phi)$

Similarly, the matrix elements for the $P_{c}^{+}$ and $P_{c}^{-}$ decay
chains are given by

$\displaystyle\mathcal{M}^{P_{c}^{+}}_{\lambda_{p},\lambda_{{\overline{p}}},\Delta\lambda}=\sum_{\lambda_{\psi},\lambda_{P_{c}^{+}}}{\widetilde{\mathcal{H}}^{{{B}^{0}_{s}}\rightarrow
P_{c}^{+}{\overline{p}}}_{\lambda_{P_{c}^{+}},\lambda_{{\overline{p}}}}}\mathcal{R}(m_{J/\psi
p}^{2})\mathcal{D}^{*J_{P_{c}}}_{\lambda_{P_{c}^{+}},\lambda_{\psi}-\lambda_{{p}}}(\phi_{\psi}^{\\{P_{c}^{+}\\}},\theta_{\psi}^{\\{P_{c}^{+}\\}},0){\widetilde{\mathcal{H}}^{P_{c}^{+}\rightarrow\psi
p}_{\lambda_{\psi},\lambda_{p}}}$
$\displaystyle\cdot\mathcal{D}^{*1}_{\lambda_{\psi},\Delta\lambda}(\phi^{\\{P_{c}^{+}\\}}_{\mu},\theta_{\mu}^{\\{P_{c}^{+}\\}},0)$
(7)
$\displaystyle\mathcal{M}^{P_{c}^{-}}_{\lambda_{p},\lambda_{{\overline{p}}},\Delta\lambda}=\sum_{\lambda_{\psi},\lambda_{P_{c}^{-}}}{\widetilde{\mathcal{H}}^{{{B}^{0}_{s}}\rightarrow
P_{c}^{-}p}_{\lambda_{P_{c}^{-}},\lambda_{p}}}\mathcal{R}(m_{J/\psi{\overline{p}}}^{2})\mathcal{D}^{*J_{P_{c}}}_{\lambda_{P_{c}^{-}},\lambda_{{\overline{p}}}-\lambda_{\psi}}(\phi_{{\overline{p}}}^{\\{P_{c}^{-}\\}},\theta_{{\overline{p}}}^{\\{P_{c}^{-}\\}},0){\widetilde{\mathcal{H}}^{P_{c}^{-}\rightarrow{\overline{p}}\psi}_{\lambda_{{\overline{p}}},\lambda_{\psi}}}$
$\displaystyle\cdot\mathcal{D}^{*1}_{\lambda_{\psi},\Delta\lambda}(\phi^{\\{P_{c}^{-}\\}}_{\mu},\theta_{\mu}^{\\{P_{c}^{-}\\}},0)$
(8)

where, as above, for angular momentum conservation, the following relations
between helicities hold: $\lambda_{P_{c}^{+}}=\lambda_{{\overline{p}}}$ and
$\lambda_{P_{c}^{-}}=\lambda_{{p}}$ for the $P_{c}^{+}$ and $P_{c}^{-}$
chains, respectively. The $x$-axes are chosen in order to have
$\phi_{\psi}^{\\{P_{c}^{+}\\}}=0$ and
$\phi_{{\overline{p}}}^{\\{P_{c}^{-}\\}}=0$. The angle
$\theta_{\psi}^{\\{P_{c}^{+}\\}}$
($\theta_{{\overline{p}}}^{\\{P_{c}^{-}\\}}$) is the polar angle of the $\psi$
($\overline{p}$) momentum in the $P_{c}^{+}$ ($P_{c}^{-}$) helicity frame,
while $\theta_{\mu}^{\\{P_{c}^{\pm}\\}}$ and $\phi_{\mu}^{\\{P_{c}^{\pm}\\}}$
are the polar and azimuthal angles of the $\mu^{-}$ momentum in the $\psi$
helicity frame in the two decay chains. Due to the limited sample size, from
the fit to data neither two unique couplings for the $P_{c}$ states nor a
relative phase between them can be extracted. A relation between the helicity
couplings of $P_{c}^{+}$ and $P_{c}^{-}$ is thus imposed

$\displaystyle{\mathcal{H}^{{{B}^{0}_{s}}\rightarrow
P_{c}^{-}p}_{\lambda_{P_{c}^{-}},\lambda_{p}}}=-{\mathcal{H}^{{{B}^{0}_{s}}\rightarrow
P_{c}^{+}{\overline{p}}}_{\lambda_{P_{c}^{+}},\lambda_{{\overline{p}}}}}$
$\displaystyle{\mathcal{H}^{P_{c}^{-}\rightarrow{\overline{p}}\psi}_{\lambda_{{\overline{p}}},\lambda_{\psi}}}=(-1)^{J_{Pc}-s_{p}-s_{\psi}}{\mathcal{H}^{P_{c}^{+}\rightarrow\psi
p}_{\lambda_{\psi},\lambda_{p}}}$ (9)

where the sign in the second line comes from the permutation of the final
helicities, while the one of the first line depends on the weak dynamics and
is chosen as such. This choice is arbitrary and does not impact the results
because, due to limited sample size, there is no sensitivity to the relative
interference between $P_{c}^{\pm}$ states. It is made such that it simplifies
the model by constraining the two $P_{c}^{\pm}$ couplings to be equal and
obtains the same interference pattern for all $J^{P}$ hypotheses, as discussed
below in Eq. 23. The helicity couplings expressed in the LS basis are reduced
to the lowest $L$ values allowed. There is one independent coupling to fit,
which is reduced to one free parameter for $J^{P}=1/2^{+}$ and $3/2^{-}$
because the phase $\phi$ of the coupling is consistent with zero due to the
limited sample size, as summarised in Table 2.

A single resonant contribution in the $P_{c}$ decay chains is parametrised by

$\mathcal{R}(m)=B_{L}^{\prime}\left(p,p_{0},d\right)\left(\frac{p}{M_{B_{s}^{0}}}\right)^{L_{B_{s}^{0}}}\mathrm{BW}\left(m|M_{0},\Gamma_{0}\right)B_{L_{P_{cj}}}^{\prime}\left(q,q_{0},d\right)\left(\frac{q}{M_{0}}\right)^{L_{P_{cj}}}.$
(10)

where

$\displaystyle\mathrm{BW}\left(m|M_{0},\Gamma_{0}\right)=\frac{1}{M_{0}^{2}-m^{2}-iM_{0}\Gamma(m)},$
(11)

is the Breit–Wigner function which includes the mass-dependent width

$\displaystyle\Gamma(m)=\Gamma_{0}\left(\frac{q}{q_{0}}\right)^{2L_{P_{cj}}+1}\frac{M_{0}}{m}B_{L_{P_{cj}}}^{\prime}\left(q,q_{0},d\right)^{2}.$
(12)

Here, $p$ is the momentum of the $P_{c}$ resonance in the ${B}^{0}_{s}$ rest
frame, $q$ is the momentum of one of the decay products in the $P_{c}$ rest
frame, while the momenta $p_{0}$ and $q_{0}$ denote their values at the
resonance peak ($m=M_{0}$), and $d$ is the hadron radius size fixed to
$3\text{\,Ge\kern-1.00006ptV}^{-1}$ in the default fit and varied to
$1.5\text{\,Ge\kern-1.00006ptV}^{-1}$ and $5\text{\,Ge\kern-1.00006ptV}^{-1}$
in the systematic uncertainty evaluation. The orbital momentum of the
${B}^{0}_{s}$ decay is denoted as $L_{B_{s}^{0}}$ and that of the $P_{c}$
decay as $L_{P_{cj}}$. In order to properly account for the suppression due to
higher values of $L$, the Blatt-Weisskopf coefficients are used together with
the orbital barrier factor $p^{L}B_{L}(p,p_{0},d)$. For NR contributions in
the $X$ chain, $\text{BW}(m)$ is set to 1 and $M_{0(NR)}$ to the midrange
mass.

To sum the amplitudes from different decay chains coherently, the final state
helicities of ${p},{\overline{p}}$ and ${\mu}$ in the $P_{c}$ chains must be
rotated in order to match the helicities of the $X$ chain

$\displaystyle\left|{\mathcal{M}}\right|^{2}=\sum_{\lambda_{p}}\sum_{\lambda_{{\overline{p}}}}\sum_{\Delta\lambda}\mid\mathcal{M}^{X}+e^{i\Delta\lambda\cdot\alpha_{\mu}}\sum_{\lambda_{p}^{P_{c}}}\sum_{\lambda_{{\overline{p}}}^{P_{c}}}d^{1/2}_{\lambda_{{\overline{p}}}^{P_{c}},\lambda_{{\overline{p}}}}(-\theta_{{\overline{p}}}^{P_{c}^{+}})d^{1/2}_{\lambda_{p}^{P_{c}},\lambda_{p}}(\theta_{p}^{P_{c}^{+}})\mathcal{M}^{P_{c}^{+}}(\lambda_{p}^{P_{c}},\lambda_{{\overline{p}}}^{P_{c}},\Delta\lambda)+$
$\displaystyle+e^{i\Delta\lambda\cdot\alpha_{\bar{\mu}}}\sum_{\lambda_{p}^{P_{c}}}\sum_{\lambda_{{\overline{p}}}^{P_{c}}}d^{1/2}_{\lambda_{p}^{P_{c}},\lambda_{p}}(\theta_{p}^{P_{c}^{-}})d^{1/2}_{\lambda_{{\overline{p}}}^{P_{c}},\lambda_{{\overline{p}}}}(-\theta_{{\overline{p}}}^{P_{c}^{-}})\mathcal{M}^{P_{c}^{-}}(\lambda_{{\overline{p}}}^{P_{c}},\lambda_{p}^{P_{c}},\Delta\lambda)\mid^{2}$
(13)

where $\theta_{p}^{P_{c}^{\pm}}$ ( $\theta_{{\overline{p}}}^{P_{c}^{\pm}}$)
are the polar angles in the ${p}$ (${\overline{p}}$) rest frame between the
boost directions from the $P_{c}^{\pm}$ to the $X$ rest frames and
$\alpha_{\mu}$ is the azimuthal angle in the $\psi$ rest frame to correct the
muon helicity states in the two chains. Regarding the definition of the polar
angles, for the $P_{c}^{+}$ chain, $\theta_{p}^{P_{c}^{+}}$ and
$\theta_{\bar{{p}}}^{P_{c}^{+}}$ are defined as the opening angle between the
$\bar{p}$ and $\psi$ mesons in the ${p}$ rest frame and between the $p$ and
the $P_{c}$ momenta in the $\bar{p}$ rest frame, respectively

$\cos\theta_{p}^{P_{c}^{+}}=\hat{p}_{\bar{p}}^{\\{p\\}}\cdot\hat{p}_{\psi}^{\\{p\\}}\
\text{and}\
\cos\theta_{\bar{p}}^{P_{c}^{+}}=\hat{p}_{{p}}^{\\{\bar{p}\\}}\cdot\hat{p}_{P_{c}}^{\\{\bar{p}\\}}.$
(14)

For the $P_{c}^{-}$ chain, the $\theta_{p}^{P_{c}^{-}}$ and
$\theta_{\bar{{p}}}^{P_{c}^{-}}$ angles are obtained by substituting
${p}\leftrightarrow{\overline{p}}$. Since the $y$ axis is outgoing from the
plane, the rotation to align the $P_{c}^{+}$ decay chain to the $X$ decay
chain is counterclockwise between the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ and
the $\bar{p}$ momenta. While in the $\bar{p}$ rest frame, the rotation from
the direction of $P_{c}^{+}$ to that of $p$ is clockwise, hence of an angle
$-\theta_{p}^{P_{c}^{+}}$. For the $P_{c}^{-}$ chain, the rotation is always
clockwise in the proton rest frame and counterclockwise in the $\bar{p}$ rest
frame. For the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ decay, since the muons
come from the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ for both decay chains, the
polar angle is 0, implying the following:
$d^{1/2}_{\lambda_{\mu}^{P_{c}},\lambda_{\mu}}=\delta_{\lambda_{\mu}^{P_{c}},\lambda_{\mu}}$.
However, there is an azimuthal angle $\alpha_{\mu}$ because of the offset in
the $x$ axis. Since the boost to the $\mu$ rest frame is the same for both
decay chains, i.e. always from the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ rest
frame, $\alpha_{\mu}$ can be determined in the
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ rest frame as

$\alpha_{\mu}=\text{atan2}((\hat{z}_{3}^{\\{\psi\\}P_{c}}\times\hat{x}_{3}^{\\{\psi\\}P_{c}})\cdot\hat{x}_{3}^{\\{\psi\\}X},\hat{x}_{3}^{\\{\psi\\}P_{c}}\cdot\hat{x}_{3}^{\\{\psi\\}X}),$
(15)

where the index $3$ refers to the rest frame after rotations;
$\hat{z}_{3}^{\psi}=\hat{p}_{\mu}^{\psi}$ and the $\hat{x}_{3}$ axis can be
derived as

$\displaystyle\hat{x}_{3}^{\\{\psi\\}P_{c}}=-a_{z_{0}\perp\mu}$ (16)
$\displaystyle
a_{z_{0}\perp\mu}=-\hat{p}_{p}^{\\{\psi\\}}+(\hat{p}_{p}^{\\{\psi\\}}\cdot\hat{p}_{\mu}^{\\{\psi\\}})\hat{p}_{\mu}^{\\{\psi\\}},$
(17)

as well as

$\displaystyle\hat{x}_{3}^{\\{\psi\\}X}=-a_{z_{0}\perp\mu}$ (18)
$\displaystyle
a_{z_{0}\perp\mu}=-\hat{p}_{X}^{\\{\psi\\}}+(\hat{p}_{X}^{\\{\psi\\}}\cdot\hat{p}_{\mu}^{\\{\psi}\\})\hat{p}_{\mu}^{\\{\psi\\}}.$
(19)

The term aligning the muon helicity states between the two reference frames is
given by

$\sum_{\lambda_{\mu}}D^{J_{\mu}}_{\lambda_{\mu}^{P_{c}},\lambda_{\mu}}(\alpha_{\mu},0,0)=\sum_{\lambda_{\mu}}e^{i\lambda_{\mu}^{P_{c}}\alpha_{\mu}}\delta_{\lambda_{\mu}^{P_{c}},\lambda_{\mu}}=e^{i\lambda_{\mu}\alpha_{\mu}}.$
(20)

The transformation for the $\mu^{-}$ is equal to that of the $\mu^{+}$ where
the azimuthal angle takes a negative sign:
$\alpha_{\mu^{-}}=-\alpha_{\mu^{+}}$. Considering the transformations of both
muons, the final rotation is the multiplication of the two exponentials

$e^{i\lambda_{\mu}\alpha_{\mu}}e^{i\lambda_{\bar{\mu}}\alpha_{\bar{\mu}}}=e^{i\alpha_{\mu}(\lambda_{\mu}-\lambda_{\bar{\mu}})}=e^{i\alpha_{\mu}\Delta\lambda}.$
(21)

This implementation is found to be equivalent to the one proposed in Ref.
[32], where the spin of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ in the
different chains is aligned with a polar rotation before the
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rightarrow\mu^{+}\mu^{-}$ decay.

Since the flavour of the ${B}^{0}_{s}$ candidate is not tagged, the overall
amplitude is the average of the ${B}^{0}_{s}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}$ amplitudes, where the
${{\kern 1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}$ amplitude is equal
to that of ${B}^{0}_{s}$ due to the absence of direct $C\\!P$ violation and is
obtained inverting particles with antiparticles, i.e.
${p}\leftrightarrow{\overline{p}}$, ${\mu^{-}}\leftrightarrow{\mu^{+}}$ and
inverting all azimuthal angles, $\phi\leftrightarrow-\phi$. To impose $C\\!P$
symmetry, the flavour eigenstates are projected onto the $C\\!P$ basis of
${B}_{L}$ and ${B}_{H}$. Enforcing $C\\!P$ symmetry conservation, the
${B}^{0}_{s}$ and ${{\kern 1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}$
and their decay products can be written in terms of $CP$ eigenstates. If
$C\\!P$ is applied to the ${B}^{0}_{s}$ final states, then

$\displaystyle{C\\!P}|X{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rangle$
$\displaystyle=+|X{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rangle,$
$\displaystyle{C\\!P}|P_{c}^{+}{\overline{p}}\rangle$
$\displaystyle=e^{i\phi}|P_{c}^{-}{p}\rangle,$
$\displaystyle{C\\!P}|P_{c}^{-}{p}\rangle$
$\displaystyle=e^{i\phi}|P_{c}^{+}{\overline{p}}\rangle,$ (22)

is obtained. Indeed, the contribution in the $X$ chain is already a $C\\!P$
eigenstate, and in particular for $J^{P}=1^{-}$ a $C\\!P$-even one, while the
two single $P_{c}$ are not. However, a combination of the $P_{c}^{+}$ and
$P_{c}^{-}$ contributions can be projected onto a $C\\!P$ eigenstate
orthogonal to the $X$ contribution ($C\\!P$-odd) by choosing the specific
phase convention: $e^{i\phi}=-1(-1)^{J_{P_{c}}-3/2}$, hence resulting in

${C\\!P}(|P_{c}^{+}\rangle-(-1)^{J_{P_{c}}-3/2}|P_{c}^{-}\rangle)=-(|P_{c}^{+}\rangle-(-1)^{J_{P_{c}}-3/2}|P_{c}^{-}\rangle)$
(23)

which spin dependent factor follows from Eq. Acknowledgements. Therefore, the
interference between the $X$ and the combination of the $P_{c}$ contributions
cancels out upon integration over the Dalitz plane, as they are orthogonal
$C\\!P$ eigenstates.

B. Event-by-event efficiency parameterisation

Event-by-event acceptance corrections are applied to the data using an
efficiency parameterisation based on the decay kinematics. The 4-body phase
space of the topology
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}(\rightarrow{\mu^{+}}{\mu^{-}})p{\overline{p}}$
is fully described by four independent kinematic variables, one mass and three
angles: $m_{{p}{\overline{p}}},\theta_{p},\theta_{\mu},\varphi$, where the
angles are defined as,

  * •

$\theta_{\mu}$ and $\theta_{p}$: the helicity angles defined in the dimuon and
dihadron rest frames, respectively;

  * •

$\varphi$: the azimuthal angle between the two decay planes of the dilepton
and dihadron systems.

Since the final state is as self-conjugate, the ${p}$ and the ${\mu^{-}}$ are
chosen to define the angles, for both ${{B}^{0}_{s}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}$. For the signal mode, the
overall efficiency, including trigger, detector acceptance and selection
procedure, is obtained from simulation as a function of the four kinematic
variables,
$\vec{\omega}\equiv\\{m^{\prime}_{{p}{\overline{p}}},\cos\theta_{\mu},\cos\theta_{p},\varphi^{\prime}\\}$.
Here, $m^{\prime}_{{p}{\overline{p}}}$ and $\varphi^{\prime}$ are transformed
such that all four variables in $\vec{\omega}$ lie in the range $(-1,1]$. The
efficiency is parameterised as the product of Legendre polynomials

$\varepsilon(\vec{\varphi})=\sum_{i,j,k,l}c_{i,j,k,l}~{}P(\cos\theta_{\mu},i)P(\cos\theta_{p},j)P(\varphi^{\prime},k)P(m^{\prime}_{{p}{\overline{p}}},l),$

where $P(x,n)$ is a Legendre polynomial of order $n$ in $x\in(-1,1]$.
Employing the order of the polynomials as $\\{3,7,7,5\\}$ for
$\\{m^{\prime}_{{p}{\overline{p}}},\cos\theta_{\mu},\cos\theta_{p},\varphi^{\prime}\\}$,
respectively, was found to give a good parameterisation. The coefficients,
$c_{i,j,k,l}$, are determined from the simulation using a moments technique
employing the orthogonality of Legendre polynomials

$\displaystyle c_{i,j,k,l}\;=\;$ $\displaystyle\frac{C}{\sum
w_{n}}\sum_{n=0}^{N_{\rm
recon}}w_{n}\left(\frac{2i+1}{2}\right)\left(\frac{2j+1}{2}\right)\left(\frac{2k+1}{2}\right)\left(\frac{2l+1}{2}\right)$
(24) $\displaystyle\hskip 28.45274pt\times
P(\cos\theta_{\mu},i)P(\cos\theta_{p},j)P(\varphi^{\prime},k)P(m^{\prime}_{{p}{\overline{p}}},l)$
(25)

where $w_{n}$ is the per-event weight taking into account both the generator
level phase-space element, $\mathrm{d}\Phi$, and the kinematic event weights.
Simulation samples are employed where
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}{\overline{p}}$
events are generated uniformly in phase space. In order to render the
simulation flat also in $m(p\bar{p})$, the inverted phase-space factor,
$1/\mathrm{d}\Phi$, is considered. The factors of $(2a+1)/2$ arise from the
orthogonality of the Legendre polynomials,

$\int_{-1}^{+1}P(x,a)P(x,a^{\prime})\mathrm{d}x=\frac{2}{2a+1}\delta_{aa^{\prime}}~{}.$
(26)

The sum in Eq. 24 is over the reconstructed events in the simulation sample
after all selection criteria. The factor $C$ ensures appropriate normalisation
and it is computed such that

$\displaystyle\sum_{n=0}^{N_{\rm gen}}\varepsilon(\vec{x}_{n})=N_{\rm rec},$
(27)

where $N_{\rm rec}$ is the total number of reconstructed signal events.

Up to statistical fluctuations, the parameterisation follows the simulated
data in all the distributions.

C. Significance studies for different $J^{P}$ hypotheses of the $P_{c}$ state

The significance studies for different $J^{P}$ hypotheses are reported in
Table 3, together with the fit results. The significance is computed using a
frequentist approach, by counting the number of pseudoexperiments above the
$-2\Delta\log\mathcal{L}$ observed in data. The $p$-value and corresponding
two-sided significance are reported in Tab. 3.

Table 3: Results for all spin-parity hypotheses. Values of $-2\Delta\log\mathcal{L}$ (-2DLL), $p$-value and two-sided significance extracted from pseudoexperiments, together with mass (in  MeV), width (in  MeV), fit fraction and complex coupling (A,$\phi$) of the $P_{c}$ states are reported.  $J^{P}$ | -2DLL |  $p$ ($\times 10^{-3}$) | $\sigma$ | $M_{0}$ | $\Gamma_{0}$ |  $f(P_{c})$(%) | A$(P_{c})$ | $\phi(P_{c})$
---|---|---|---|---|---|---|---|---
$1/2^{-}$ | 26.2 | $0.5\pm 0.3$ | 3.5 $\pm$ 0.1 | 4335${}^{+3}_{-3}$ | 23${}^{+11}_{-8}$ | 17.4${}^{+7.0}_{-3.8}$ | 0.15${}^{+0.07}_{-0.05}$ | 2.8${}^{+1.3}_{-1.4}$
$1/2^{+}$ | 26.8 | $0.2\pm 0.1$ | 3.7 $\pm$ 0.1 | 4337${}^{+7}_{-4}$ | 29${}^{+26}_{-12}$ | 22.0${}^{+8.5}_{-4.4}$ | 0.19${}^{+0.19}_{-0.08}$ | -0.6${}^{+2.4}_{-3.0}$
$3/2^{-}$ | 25.8 | $0.3\pm 0.2$ | 3.6 $\pm$ 0.1 | 4337${}^{+5}_{-3}$ | 23${}^{+16}_{-9}$ | 18.6${}^{+6.9}_{-3.0}$ | 0.14${}^{+0.08}_{-0.05}$ | -1.3${}^{+1.9}_{-2.0}$
$3/2^{+}$ | 23.6 | $2\pm 1$ | 3.1 $\pm$ 0.1 | 4336${}^{+3}_{-2}$ | 15${}^{+9}_{-6}$ | 11.7${}^{+4.2}_{-2.7}$ | 0.10${}^{+0.05}_{-0.03}$ | -3.1${}^{+0.6}_{-0.6}$

D. Systematic uncertainties studies

In this section, more details about systematic uncertainties are presented.
The systematic uncertainties are studied using pseudoexperiments generated
according to the alternative model with the same statistics as in data.
Parameters are then fitted with the default model. For each parameter, the
uncertainty is taken as the mean value of the residual distribution between
the fitted ensemble and the generated one. The main systematic uncertainties
are described in the document. To estimate the uncertainty associated to the
NR model parameterisation for the $X$ decay chain, alternative NR models are
used, also with different quantum numbers ($J^{P}=0^{\pm},1^{+}$).
Combinations of NR and a resonant term are used to account for possible
resonances decaying to a $p\bar{p}$ final state. The model, which yields
comparable results in terms of $-\log\cal{L}$, comprises a NR term with
$J^{P}=1^{+}$ and a Breit–Wigner resonance with $J^{P}=0^{-}$, and is used to
assign the systematic uncertainty. The impact of this model on the
significance of the $P_{c}$ state is also studied and is found to be
negligible. The other alternative models have been excluded based on the
-2$\Delta\log\mathcal{L}$, with respect to the baseline model, which is
greater than $40$. In addition, amplitude models including all values of
orbital momentum for both the $X$ and the $P_{c}$ decay chains are considered
and their effect is found to be negligible. For the systematic uncertainty
associated with the efficiency parameterisation, two different contributions
are summed in quadrature. First, the default efficiency map extracted from all
simulation events is replaced by using simulations from the Run 1 and the Run
2 data-taking periods, separately. Second, a simplified parameterisation with
one-dimensional Legendre polynomials is considered, neglecting the effect of
correlations among the phase-space variables. Other sources of uncertainty
regard different $J^{P}$ assignment for the $P_{c}$ state, the background
parameterisation, the hadron radius size and the fit bias. The last
uncertainty is estimated from pseudoexperiments by generating and fitting the
parameters of the default model. Possible biases on the fit parameters are
accounted for as the mean of the residual distributions between the generated
and the fitted values.

E. Dalitz plot distribution

The Dalitz plot distribution of the reconstructed ${B}^{0}_{s}$ candidates in
the ${B}^{0}_{s}$ signal region is shown in Fig. 3, where hints of horizontal
and vertical bands in the region around
$(18.8-19.0)\text{\,Ge\kern-1.00006ptV}^{2}$ are present in the
$m^{2}({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})$ and
$m^{2}({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})$ distributions,
respectively.

Figure 3: Dalitz plot distribution for reconstructed candidates (black dots)
within the ${B}^{0}_{s}$ signal region. The colour scale represents the number
of candidates in each Dalitz plot interval.

F. Maximum and minimum of $m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})$ and
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})$ distributions

Since the amplitude model is symmetric for ${p}\leftrightarrow{\overline{p}}$
inversion by construction, it is not possible to distinguish between the
$P_{c}^{+}$ and $P_{c}^{-}$ states. Therefore, the distribution of the maximum
and minimum of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}}$ invariant masses, defined
as

$\displaystyle m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})_{\text{high}}$
$\displaystyle=\max(m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}),m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})),$
$\displaystyle m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})_{\text{low}}$
$\displaystyle=\min(m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p}),m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})),$

is shown in Fig. 4. In this way, both $P_{c}^{+}$ and $P_{c}^{-}$
contributions are visible in the distribution of
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})_{\text{high}}$ (left), while their
reflections are projected in the distribution of
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})_{\text{low}}$ (right).

Figure 4: Distribution of the maximum (left) and minimum (right) of
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{p})$ and
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{\overline{p}})$. Results of the
amplitude fit are superimposed, where the sum of the $P_{c}^{+}$ and
$P_{c}^{-}$ contributions is shown in blue.

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LHCb collaboration

R. Aaij32, A.S.W. Abdelmotteleb56, C. Abellán Beteta50, T. Ackernley60, B.
Adeva46, M. Adinolfi54, H. Afsharnia9, C.A. Aidala86, S. Aiola25, Z.
Ajaltouni9, S. Akar65, J. Albrecht15, F. Alessio48, M. Alexander59, A. Alfonso
Albero45, Z. Aliouche62, G. Alkhazov38, P. Alvarez Cartelle55, S. Amato2, J.L.
Amey54, Y. Amhis11, L. An48, L. Anderlini22, A. Andreianov38, M. Andreotti21,
F. Archilli17, A. Artamonov44, M. Artuso68, K. Arzymatov42, E. Aslanides10, M.
Atzeni50, B. Audurier12, S. Bachmann17, M. Bachmayer49, J.J. Back56, P.
Baladron Rodriguez46, V. Balagura12, W. Baldini21, J. Baptista Leite1, R.J.
Barlow62, S. Barsuk11, W. Barter61, M. Bartolini24,h, F. Baryshnikov83, J.M.
Basels14, S. Bashir34, G. Bassi29, B. Batsukh68, A. Battig15, A. Bay49, A.
Beck56, M. Becker15, F. Bedeschi29, I. Bediaga1, A. Beiter68, V. Belavin42, S.
Belin27, V. Bellee50, K. Belous44, I. Belov40, I. Belyaev41, G. Bencivenni23,
E. Ben-Haim13, A. Berezhnoy40, R. Bernet50, D. Berninghoff17, H.C.
Bernstein68, C. Bertella48, A. Bertolin28, C. Betancourt50, F. Betti48, Ia.
Bezshyiko50, S. Bhasin54, J. Bhom35, L. Bian73, M.S. Bieker15, S. Bifani53, P.
Billoir13, M. Birch61, F.C.R. Bishop55, A. Bitadze62, A. Bizzeti22,l, M.
Bjørn63, M.P. Blago48, T. Blake56, F. Blanc49, S. Blusk68, D. Bobulska59, J.A.
Boelhauve15, O. Boente Garcia46, T. Boettcher65, A. Boldyrev82, A. Bondar43,
N. Bondar38,48, S. Borghi62, M. Borisyak42, M. Borsato17, J.T. Borsuk35, S.A.
Bouchiba49, T.J.V. Bowcock60, A. Boyer48, C. Bozzi21, M.J. Bradley61, S.
Braun66, A. Brea Rodriguez46, M. Brodski48, J. Brodzicka35, A. Brossa
Gonzalo56, D. Brundu27, A. Buonaura50, L. Buonincontri28, A.T. Burke62, C.
Burr48, A. Bursche72, A. Butkevich39, J.S. Butter32, J. Buytaert48, W.
Byczynski48, S. Cadeddu27, H. Cai73, R. Calabrese21,f, L. Calefice15,13, L.
Calero Diaz23, S. Cali23, R. Calladine53, M. Calvi26,k, M. Calvo Gomez85, P.
Camargo Magalhaes54, P. Campana23, A.F. Campoverde Quezada6, S. Capelli26,k,
L. Capriotti20,d, A. Carbone20,d, G. Carboni31, R. Cardinale24,h, A.
Cardini27, I. Carli4, P. Carniti26,k, L. Carus14, K. Carvalho Akiba32, A.
Casais Vidal46, G. Casse60, M. Cattaneo48, G. Cavallero48, S. Celani49, J.
Cerasoli10, D. Cervenkov63, A.J. Chadwick60, M.G. Chapman54, M. Charles13, Ph.
Charpentier48, G. Chatzikonstantinidis53, C.A. Chavez Barajas60, M.
Chefdeville8, C. Chen3, S. Chen4, A. Chernov35, V. Chobanova46, S. Cholak49,
M. Chrzaszcz35, A. Chubykin38, V. Chulikov38, P. Ciambrone23, M.F. Cicala56,
X. Cid Vidal46, G. Ciezarek48, P.E.L. Clarke58, M. Clemencic48, H.V. Cliff55,
J. Closier48, J.L. Cobbledick62, V. Coco48, J.A.B. Coelho11, J. Cogan10, E.
Cogneras9, L. Cojocariu37, P. Collins48, T. Colombo48, L. Congedo19,c, A.
Contu27, N. Cooke53, G. Coombs59, I. Corredoira 46, G. Corti48, C.M. Costa
Sobral56, B. Couturier48, D.C. Craik64, J. Crkovská67, M. Cruz Torres1, R.
Currie58, C.L. Da Silva67, S. Dadabaev83, L. Dai71, E. Dall’Occo15, J.
Dalseno46, C. D’Ambrosio48, A. Danilina41, P. d’Argent48, J.E. Davies62, A.
Davis62, O. De Aguiar Francisco62, K. De Bruyn79, S. De Capua62, M. De Cian49,
J.M. De Miranda1, L. De Paula2, M. De Serio19,c, D. De Simone50, P. De
Simone23, J.A. de Vries80, C.T. Dean67, D. Decamp8, L. Del Buono13, B.
Delaney55, H.-P. Dembinski15, A. Dendek34, V. Denysenko50, D. Derkach82, O.
Deschamps9, F. Desse11, F. Dettori27,e, B. Dey77, A. Di Cicco23, P. Di
Nezza23, S. Didenko83, L. Dieste Maronas46, H. Dijkstra48, V. Dobishuk52, C.
Dong3, A.M. Donohoe18, F. Dordei27, A.C. dos Reis1, L. Douglas59, A.
Dovbnya51, A.G. Downes8, M.W. Dudek35, L. Dufour48, V. Duk78, P. Durante48,
J.M. Durham67, D. Dutta62, A. Dziurda35, A. Dzyuba38, S. Easo57, U. Egede69,
V. Egorychev41, S. Eidelman43,w, S. Eisenhardt58, S. Ek-In49, L. Eklund59,x,
S. Ely68, A. Ene37, E. Epple67, S. Escher14, J. Eschle50, S. Esen13, T.
Evans48, A. Falabella20, J. Fan3, Y. Fan6, B. Fang73, S. Farry60, D.
Fazzini26,k, M. Féo48, A. Fernandez Prieto46, A.D. Fernez66, F. Ferrari20,d,
L. Ferreira Lopes49, F. Ferreira Rodrigues2, S. Ferreres Sole32, M.
Ferrillo50, M. Ferro-Luzzi48, S. Filippov39, R.A. Fini19, M. Fiorini21,f, M.
Firlej34, K.M. Fischer63, D.S. Fitzgerald86, C. Fitzpatrick62, T. Fiutowski34,
A. Fkiaras48, F. Fleuret12, M. Fontana13, F. Fontanelli24,h, R. Forty48, D.
Foulds-Holt55, V. Franco Lima60, M. Franco Sevilla66, M. Frank48, E.
Franzoso21, G. Frau17, C. Frei48, D.A. Friday59, J Fu25,6, Q. Fuehring15, W.
Funk48, E. Gabriel32, T. Gaintseva42, A. Gallas Torreira46, D. Galli20,d, S.
Gambetta58,48, Y. Gan3, M. Gandelman2, P. Gandini25, Y. Gao5, M. Garau27, L.M.
Garcia Martin56, P. Garcia Moreno45, J. García Pardiñas26,k, B. Garcia
Plana46, F.A. Garcia Rosales12, L. Garrido45, C. Gaspar48, R.E. Geertsema32,
D. Gerick17, L.L. Gerken15, E. Gersabeck62, M. Gersabeck62, T. Gershon56, D.
Gerstel10, Ph. Ghez8, V. Gibson55, H.K. Giemza36, A.L. Gilman63, M.
Giovannetti23,q, A. Gioventù46, P. Gironella Gironell45, L. Giubega37, C.
Giugliano21,f,48, K. Gizdov58, E.L. Gkougkousis48, V.V. Gligorov13, C.
Göbel70, E. Golobardes85, D. Golubkov41, A. Golutvin61,83, A. Gomes1,a, S.
Gomez Fernandez45, F. Goncalves Abrantes63, M. Goncerz35, G. Gong3, P.
Gorbounov41, I.V. Gorelov40, C. Gotti26, E. Govorkova48, J.P. Grabowski17, T.
Grammatico13, L.A. Granado Cardoso48, E. Graugés45, E. Graverini49, G.
Graziani22, A. Grecu37, L.M. Greeven32, N.A. Grieser4, P. Griffith21,f, L.
Grillo62, S. Gromov83, B.R. Gruberg Cazon63, C. Gu3, M. Guarise21, P. A.
Günther17, E. Gushchin39, A. Guth14, Y. Guz44, T. Gys48, T. Hadavizadeh69, G.
Haefeli49, C. Haen48, J. Haimberger48, T. Halewood-leagas60, P.M. Hamilton66,
J.P. Hammerich60, Q. Han7, X. Han17, T.H. Hancock63, S. Hansmann-Menzemer17,
N. Harnew63, T. Harrison60, C. Hasse48, M. Hatch48, J. He6,b, M. Hecker61, K.
Heijhoff32, K. Heinicke15, A.M. Hennequin48, K. Hennessy60, L. Henry48, J.
Heuel14, A. Hicheur2, D. Hill49, M. Hilton62, S.E. Hollitt15, J. Hu17, J.
Hu72, W. Hu7, X. Hu3, W. Huang6, X. Huang73, W. Hulsbergen32, R.J. Hunter56,
M. Hushchyn82, D. Hutchcroft60, D. Hynds32, P. Ibis15, M. Idzik34, D. Ilin38,
P. Ilten65, A. Inglessi38, A. Ishteev83, K. Ivshin38, R. Jacobsson48, S.
Jakobsen48, E. Jans32, B.K. Jashal47, A. Jawahery66, V. Jevtic15, F. Jiang3,
M. John63, D. Johnson48, C.R. Jones55, T.P. Jones56, B. Jost48, N. Jurik48,
S.H. Kalavan Kadavath34, S. Kandybei51, Y. Kang3, M. Karacson48, M. Karpov82,
F. Keizer48, M. Kenzie56, T. Ketel33, B. Khanji15, A. Kharisova84, S.
Kholodenko44, T. Kirn14, V.S. Kirsebom49, O. Kitouni64, S. Klaver32, K.
Klimaszewski36, M.R. Kmiec36, S. Koliiev52, A. Kondybayeva83, A.
Konoplyannikov41, P. Kopciewicz34, R. Kopecna17, P. Koppenburg32, M.
Korolev40, I. Kostiuk32,52, O. Kot52, S. Kotriakhova21,38, P. Kravchenko38, L.
Kravchuk39, R.D. Krawczyk48, M. Kreps56, F. Kress61, S. Kretzschmar14, P.
Krokovny43,w, W. Krupa34, W. Krzemien36, W. Kucewicz35,u, M. Kucharczyk35, V.
Kudryavtsev43,w, H.S. Kuindersma32,33, G.J. Kunde67, T. Kvaratskheliya41, D.
Lacarrere48, G. Lafferty62, A. Lai27, A. Lampis27, D. Lancierini50, J.J.
Lane62, R. Lane54, G. Lanfranchi23, C. Langenbruch14, J. Langer15, O.
Lantwin83, T. Latham56, F. Lazzari29,r, R. Le Gac10, S.H. Lee86, R. Lefèvre9,
A. Leflat40, S. Legotin83, O. Leroy10, T. Lesiak35, B. Leverington17, H. Li72,
P. Li17, S. Li7, Y. Li4, Y. Li4, Z. Li68, X. Liang68, T. Lin61, R. Lindner48,
V. Lisovskyi15, R. Litvinov27, G. Liu72, H. Liu6, S. Liu4, A. Lobo Salvia45,
A. Loi27, J. Lomba Castro46, I. Longstaff59, J.H. Lopes2, S. Lopez Solino46,
G.H. Lovell55, Y. Lu4, D. Lucchesi28,m, S. Luchuk39, M. Lucio Martinez32, V.
Lukashenko32,52, Y. Luo3, A. Lupato62, E. Luppi21,f, O. Lupton56, A.
Lusiani29,n, X. Lyu6, L. Ma4, R. Ma6, S. Maccolini20,d, F. Machefert11, F.
Maciuc37, V. Macko49, P. Mackowiak15, S. Maddrell-Mander54, O. Madejczyk34,
L.R. Madhan Mohan54, O. Maev38, A. Maevskiy82, D. Maisuzenko38, M.W.
Majewski34, J.J. Malczewski35, S. Malde63, B. Malecki48, A. Malinin81, T.
Maltsev43,w, H. Malygina17, G. Manca27,e, G. Mancinelli10, D. Manuzzi20,d, D.
Marangotto25,j, J. Maratas9,t, J.F. Marchand8, U. Marconi20, S. Mariani22,g,
C. Marin Benito48, M. Marinangeli49, J. Marks17, A.M. Marshall54, P.J.
Marshall60, G. Martellotti30, L. Martinazzoli48,k, M. Martinelli26,k, D.
Martinez Santos46, F. Martinez Vidal47, A. Massafferri1, M. Materok14, R.
Matev48, A. Mathad50, Z. Mathe48, V. Matiunin41, C. Matteuzzi26, K.R.
Mattioli86, A. Mauri32, E. Maurice12, J. Mauricio45, M. Mazurek48, M.
McCann61, L. Mcconnell18, T.H. Mcgrath62, N.T. Mchugh59, A. McNab62, R.
McNulty18, J.V. Mead60, B. Meadows65, G. Meier15, N. Meinert76, D.
Melnychuk36, S. Meloni26,k, M. Merk32,80, A. Merli25, L. Meyer Garcia2, M.
Mikhasenko48, D.A. Milanes74, E. Millard56, M. Milovanovic48, M.-N. Minard8,
A. Minotti21, L. Minzoni21,f, S.E. Mitchell58, B. Mitreska62, D.S. Mitzel48,
A. Mödden 15, R.A. Mohammed63, R.D. Moise61, T. Mombächer46, I.A. Monroy74, S.
Monteil9, M. Morandin28, G. Morello23, M.J. Morello29,n, J. Moron34, A.B.
Morris75, A.G. Morris56, R. Mountain68, H. Mu3, F. Muheim58,48, M. Mulder48,
D. Müller48, K. Müller50, C.H. Murphy63, D. Murray62, P. Muzzetto27,48, P.
Naik54, T. Nakada49, R. Nandakumar57, T. Nanut49, I. Nasteva2, M. Needham58,
I. Neri21, N. Neri25,j, S. Neubert75, N. Neufeld48, R. Newcombe61, T.D.
Nguyen49, C. Nguyen-Mau49,y, E.M. Niel11, S. Nieswand14, N. Nikitin40, N.S.
Nolte64, C. Normand8, C. Nunez86, A. Oblakowska-Mucha34, V. Obraztsov44, T.
Oeser14, D.P. O’Hanlon54, S. Okamura21, R. Oldeman27,e, M.E. Olivares68,
C.J.G. Onderwater79, R.H. O’neil58, A. Ossowska35, J.M. Otalora Goicochea2, T.
Ovsiannikova41, P. Owen50, A. Oyanguren47, K.O. Padeken75, B. Pagare56, P.R.
Pais48, T. Pajero63, A. Palano19, M. Palutan23, Y. Pan62, G. Panshin84, A.
Papanestis57, M. Pappagallo19,c, L.L. Pappalardo21,f, C. Pappenheimer65, W.
Parker66, C. Parkes62, B. Passalacqua21, G. Passaleva22, A. Pastore19, M.
Patel61, C. Patrignani20,d, C.J. Pawley80, A. Pearce48, A. Pellegrino32, M.
Pepe Altarelli48, S. Perazzini20, D. Pereima41, A. Pereiro Castro46, P.
Perret9, M. Petric59,48, K. Petridis54, A. Petrolini24,h, A. Petrov81, S.
Petrucci58, M. Petruzzo25, T.T.H. Pham68, A. Philippov42, L. Pica29,n, M.
Piccini78, B. Pietrzyk8, G. Pietrzyk49, M. Pili63, A Pilloni30,i, D. Pinci30,
F. Pisani48, M. Pizzichemi26,48,k, Resmi P.K10, V. Placinta37, J. Plews53, M.
Plo Casasus46, F. Polci13, M. Poli Lener23, M. Poliakova68, A. Poluektov10, N.
Polukhina83,v, I. Polyakov68, E. Polycarpo2, S. Ponce48, D. Popov6,48, S.
Popov42, S. Poslavskii44, K. Prasanth35, L. Promberger48, C. Prouve46, V.
Pugatch52, V. Puill11, H. Pullen63, G. Punzi29,o, H. Qi3, W. Qian6, J. Qin6,
N. Qin3, R. Quagliani13, B. Quintana8, N.V. Raab18, R.I. Rabadan Trejo10, B.
Rachwal34, J.H. Rademacker54, M. Rama29, M. Ramos Pernas56, M.S. Rangel2, F.
Ratnikov42,82, G. Raven33, M. Reboud8, F. Redi49, F. Reiss62, C. Remon
Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, S. Ricciardi57, K. Rinnert60,
P. Robbe11, G. Robertson58, A.B. Rodrigues49, E. Rodrigues60, J.A. Rodriguez
Lopez74, E.R.R. Rodriguez Rodriguez46, A. Rollings63, P. Roloff48, V.
Romanovskiy44, M. Romero Lamas46, A. Romero Vidal46, J.D. Roth86, M.
Rotondo23, M.S. Rudolph68, T. Ruf48, R.A. Ruiz Fernandez46, J. Ruiz Vidal47,
A. Ryzhikov82, J. Ryzka34, J.J. Saborido Silva46, N. Sagidova38, N. Sahoo56,
B. Saitta27,e, M. Salomoni48, C. Sanchez Gras32, R. Santacesaria30, C.
Santamarina Rios46, M. Santimaria23, E. Santovetti31,q, D. Saranin83, G.
Sarpis14, M. Sarpis75, A. Sarti30, C. Satriano30,p, A. Satta31, M. Saur15, D.
Savrina41,40, H. Sazak9, L.G. Scantlebury Smead63, A. Scarabotto13, S.
Schael14, S. Scherl60, M. Schiller59, H. Schindler48, M. Schmelling16, B.
Schmidt48, O. Schneider49, A. Schopper48, M. Schubiger32, S. Schulte49, M.H.
Schune11, R. Schwemmer48, B. Sciascia23, S. Sellam46, A. Semennikov41, M.
Senghi Soares33, A. Sergi24,h, N. Serra50, L. Sestini28, A. Seuthe15, P.
Seyfert48, Y. Shang5, D.M. Shangase86, M. Shapkin44, I. Shchemerov83, L.
Shchutska49, T. Shears60, L. Shekhtman43,w, Z. Shen5, V. Shevchenko81, E.B.
Shields26,k, Y. Shimizu11, E. Shmanin83, J.D. Shupperd68, B.G. Siddi21, R.
Silva Coutinho50, G. Simi28, S. Simone19,c, N. Skidmore62, T. Skwarnicki68,
M.W. Slater53, I. Slazyk21,f, J.C. Smallwood63, J.G. Smeaton55, A. Smetkina41,
E. Smith50, M. Smith61, A. Snoch32, M. Soares20, L. Soares Lavra9, M.D.
Sokoloff65, F.J.P. Soler59, A. Solovev38, I. Solovyev38, F.L. Souza De
Almeida2, B. Souza De Paula2, B. Spaan15, E. Spadaro Norella25,j, P.
Spradlin59, F. Stagni48, M. Stahl65, S. Stahl48, S. Stanislaus63, O.
Steinkamp50,83, O. Stenyakin44, H. Stevens15, S. Stone68, M.E. Stramaglia49,
M. Straticiuc37, D. Strekalina83, F. Suljik63, J. Sun27, L. Sun73, Y. Sun66,
P. Svihra62, P.N. Swallow53, K. Swientek34, A. Szabelski36, T. Szumlak34, M.
Szymanski48, S. Taneja62, A.R. Tanner54, M.D. Tat63, A. Terentev83, F.
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Herwijnen83, C.B. Van Hulse18, M. van Veghel79, R. Vazquez Gomez45, P. Vazquez
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Zou4, S. Zucchelli20,d, D. Zuliani28, G. Zunica62.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provincial Key Laboratory of Nuclear Science, Guangdong-Hong Kong
Joint Laboratory of Quantum Matter, Institute of Quantum Matter, South China
Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Institut für Physik, Universität Rostock, Rostock, Germany, associated to 17
77Eotvos Lorand University, Budapest, Hungary, associated to 48
78INFN Sezione di Perugia, Perugia, Italy, associated to 21
79Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
80Universiteit Maastricht, Maastricht, Netherlands, associated to 32
81National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
82National Research University Higher School of Economics, Moscow, Russia,
associated to 42
83National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
84National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
85DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
86University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Genova, Genova, Italy
iDipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze
della Terre, Università degli Studi di Messina, Messina, Italy
jUniversità degli Studi di Milano, Milano, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Modena e Reggio Emilia, Modena, Italy
mUniversità di Padova, Padova, Italy
nScuola Normale Superiore, Pisa, Italy
oUniversità di Pisa, Pisa, Italy
pUniversità della Basilicata, Potenza, Italy
qUniversità di Roma Tor Vergata, Roma, Italy
rUniversità di Siena, Siena, Italy
sUniversità di Urbino, Urbino, Italy
tMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
uAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
vP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
wNovosibirsk State University, Novosibirsk, Russia
xDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden
yHanoi University of Science, Hanoi, Vietnam