EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2019-214 LHCb-PAPER-2019-024 5 March 2020

Measurement of the ${\eta_{c}}(1S)$ production cross-section in $p$ $p$
collisions at $\sqrt{s}=13$ TeV

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

Using a data sample corresponding to an integrated luminosity of 2.0
$\text{\,fb}^{-1}$, collected by the LHCb experiment, the production of the
${\eta_{c}}(1S)$ state in proton-proton collisions at a centre-of-mass energy
of $\sqrt{s}=13$ TeV is studied in the rapidity range $2.0<y<4.5$ and in the
transverse momentum range
$6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-1.00006ptV}$. The cross-section for
prompt production of ${\eta_{c}}(1S)$ mesons relative to that of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson is measured using the $p$
$\overline{p}$ decay mode and is found to be
${\sigma_{{\eta_{c}}(1S)}/\sigma_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}=1.69\pm 0.15\pm 0.10\pm 0.18}$. The quoted uncertainties are, in
order, statistical, systematic and due to uncertainties on the branching
fractions of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ and
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ decays. The prompt
${\eta_{c}}(1S)$ production cross-section is determined to be
${\sigma_{{\eta_{c}}(1S)}=1.26\pm 0.11\pm 0.08\pm 0.14\,\upmu\text{b}}$, where
the last uncertainty includes that on the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson cross-section. The ratio
of the branching fractions of $b$-hadron decays to the ${\eta_{c}}(1S)$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ states is measured to be
${{\mathcal{B}}_{{b}\\!\rightarrow{\eta_{c}}X}/{\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}=0.48\pm 0.03\pm 0.03\pm 0.05}$, where the last uncertainty is due to
those on the branching fractions of the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ and
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ decays. The difference between the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and ${\eta_{c}}(1S)$ masses is
also determined to be $113.0\pm 0.7\pm 0.1\text{\,Me\kern-1.00006ptV}$, which
is the most precise single measurement of this quantity to date.

Published in Eur. Phys. J. C80 (2020) 191

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

##  1 Introduction

Nonrelativistic quantum chromodynamics (NRQCD) [1] is a powerful framework to
describe the production from initial parton scattering (hadroproduction) of
charmonium states with quantum numbers $J^{PC}=1^{--}$, for instance the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson, over a wide range of
transverse momentum, $p_{\mathrm{T}}$, and rapidity, $y$. Nevertheless, it
remains a challenge to provide a comprehensive theoretical description of
measurements of the prompt production, comprising the hadroproduction and
feed-down from excited resonant states, and the polarisation of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons at the Tevatron [2] and
the LHC [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] collision
energies over the entire $p_{\mathrm{T}}$ range.

A factorisation approach together with a heavy-quark spin symmetry assumption
allows the simultaneous treatment of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ and ${\eta_{c}}(1S)$ (the ground-level charmonium state with
$J^{PC}=0^{-+}$ quantum numbers)111The ${\eta_{c}}(1S)$ meson is denoted as
$\eta_{c}$ throughout the rest of this paper. production observables by
imposing relations between their long-distance matrix elements (LDME) [1]. The
LHCb collaboration measured the prompt ${\eta_{c}}$ production cross-section
in proton-proton collisions at centre-of-mass energies of $\sqrt{s}=7$ and
$8\text{\,Te\kern-1.00006ptV}$ [18] to be below the predictions based on
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ prompt production data [19, 20,
21, 22, 23], which motivated several groups to revisit the theoretical
approach [24, 25, 26, 27, 28, 29, 30]. A study of the ${\eta_{c}}$ prompt
production at $\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$ provides a further
important test for theories predicting the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and ${\eta_{c}}$
hadroproduction cross-sections and the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ polarisation [31].

The LHCb collaboration has also measured the branching fractions of inclusive
$b$-hadron decays to ${\eta_{c}}$ [18] and to $\chi_{{c}0}$, $\chi_{{c}1}$ and
$\chi_{{c}2}$ mesons [32]. At the LHC, the $b$-hadron sample comprises a
mixture of ${{B}^{+}}$, ${B}^{0}$, ${B}^{0}_{s}$, ${B}_{c}^{+}$ mesons and $b$
baryons.222Charge conjugation is implied throughout the paper. A simultaneous
study of the hadroproduction and production in inclusive $b$-hadron decays of
the charmonium states with linked LDMEs provides a unique test of basic NRQCD
assumptions [33]. Only marginal consistency was found between measurements and
theoretical predictions at next-to-leading-order [21, 34] for both prompt
production and production in $b$-hadron decays for the ${\eta_{c}}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ states.

Using a sample of ${{{{B}^{+}}}\\!\rightarrow{p}{\overline{p}}{{K}^{+}}}$
decays, the LHCb collaboration has recently measured [35] the mass difference
of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and ${\eta_{c}}$ states,
$\Delta M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}},{\eta_{c}}}$ to be
2.8 standard deviations smaller than the world-average value [36]. A dataset
of $b$-hadron decays to the $\eta_{c}$ meson can be analysed to measure the
$\Delta M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}},{\eta_{c}}}$ with
improved precision.

This paper reports measurements of the $\eta_{c}$ prompt production cross-
section and branching fraction of $b$-hadron inclusive decays to the
$\eta_{c}$ meson. A dedicated selection of $\eta_{c}$ mesons produced in
$b$-hadron decays is developed to perform the most precise measurement of the
$\Delta M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}},{\eta_{c}}}$. Both
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\eta_{c}$ mesons are
reconstructed via their decays to $p$ $\overline{p}$.

##  2 The LHCb detector and data sample

The LHCb detector [37, 38] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of the momentum, $p$,
of charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200 GeV.333Natural units are used throughout the paper.
The minimum distance of a track to a $p$ $p$ collision vertex (PV), the impact
parameter (IP), is measured with a resolution of
$(15+29/p_{\mathrm{T}})\,\upmu\text{m}$, where $p_{\mathrm{T}}$ is given in
GeV. Different types of charged hadrons are distinguished using information
from two ring-imaging Cherenkov (RICH) detectors. Photons, electrons and
hadrons are identified by a calorimeter system consisting of scintillating-pad
and preshower detectors, an electromagnetic and a hadronic calorimeter. Muons
are identified by a system composed of alternating layers of iron and
multiwire proportional chambers. The online event selection is performed by a
trigger, which consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage, which applies a
full event reconstruction.

The analysis is based on $p$ $p$ collision data recorded by the LHCb
experiment in 2015 and 2016 at a centre-of-mass energy of
$13\text{\,Te\kern-1.00006ptV}$, corresponding to an integrated luminosity of
$2.0\text{\,fb}^{-1}$. Events enriched in signal decays are selected by the
hardware trigger based on the presence of a single deposit of high transverse
energy in the calorimeter. The trigger also specifically rejects high-
multiplicity events, which produce excessive random combinations of tracks
(combinatorial background). The subsequent software trigger selects charged
particles with a good track-fit quality and
$p_{\mathrm{T}}>2\text{\,Ge\kern-1.00006ptV}$. Proton candidates are
identified using information from the RICH and tracking detectors. Pairs of
oppositely charged proton candidates are required to form a good quality
vertex and to have $p_{\mathrm{T}}>6.5\text{\,Ge\kern-1.00006ptV}$. The
selection follows that of Ref. [18]. The signal selection of both prompt
charmonia and charmonia from $b$-hadron decays is largely performed at the
trigger level.

For the measurement of the ${\eta_{c}}$ mass, a low-background data sample
enriched in ${b}\\!\rightarrow{\eta_{c}}X$ decays is used. This sample is
obtained using a software-trigger selection based on a multivariate algorithm
that requires the presence of two, three or four charged tracks that form a
common vertex and are inconsistent with originating from a PV [39, 40].
Precise mass measurements require a momentum-scale calibration. The absolute
scale is determined using
${{{B}^{+}}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ decays with known particle masses as input [36]. Decays of
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}}{\mu^{-}}$
are used to cross-calibrate a relative momentum scale between different data-
taking periods [41]. The final calibration is checked with a variety of
reconstructed quarkonia, ${{B}^{+}}$ and ${K}^{0}_{\mathrm{S}}$ meson decays.
No residual momentum bias is observed within the experimental resolution.

Samples of simulated events are used to model the effects of the detector
acceptance and the imposed selection requirements. In the simulation, $pp$
collisions are generated using Pythia [42, 43] with a specific LHCb
configuration [44]. Decays of hadronic particles are described by EvtGen [45],
in which final-state radiation is generated using Photos [46]. The interaction
of the generated particles with the detector material, and its response, are
implemented using the Geant4 toolkit [47, *Agostinelli:2002hh] as described in
Ref. [49]. A simulated sample of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}$ decays is used to study the
corresponding background contribution. The $\eta_{c}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decays are generated with
uniform phase-space density, and the prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons are generated without
polarisation. Inclusive $b$-hadron decays are modelled using a combination of
many exclusive final states based on measurements from the $B$ factories,
Tevatron and LHC experiments [45].

##  3 Analysis technique

In this analysis, $\eta_{c}$ production is studied in a fiducial region of
${6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-1.00006ptV}}$ and ${2.0<y<4.5}$. The
measurement of the differential production cross-section is performed as a
function of the transverse momentum relative to that of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson [6, 36]. Both the
$\eta_{c}$ and the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons are
reconstructed in the $p$ $\overline{p}$ final state. The measured ratio is
determined as

$\displaystyle\frac{\sigma^{\text{prompt
({$b$})}}_{{\eta_{c}}}}{\sigma^{\text{prompt
({$b$})}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}}$
$\displaystyle=\frac{N^{\text{prompt ({$b$})}}_{{\eta_{c}}}}{N^{\text{prompt
({$b$})}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}}\times\frac{\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}}{\epsilon_{{\eta_{c}}}}\times\frac{{\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}}{{\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}},$
(1)

where $\sigma^{\text{prompt}}_{{\eta_{c}}}$ is the ${\eta_{c}}$ prompt
production cross-section and $\sigma^{{b}}_{{\eta_{c}}}$ is the production
cross-section in inclusive $b$-hadron decays; $N^{\text{prompt}}_{{\eta_{c}}}$
and $N^{{b}}_{{\eta_{c}}}$ are the signal yields of $\eta_{c}$ mesons produced
promptly and in $b$-hadron decays, respectively. Similar definitions apply for
the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yields and cross-sections.
The $\frac{\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}}{\epsilon_{{\eta_{c}}}}$ is the ratio of total efficiencies to
trigger, reconstruct and select ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ and
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ decays, which is found to be the
same, within uncertainties, for prompt and $b$-decay charmonia. The ratio of
branching fractions of $b$-hadron inclusive decays to $\eta_{c}$ and to
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons,
$\frac{{\mathcal{B}}_{{b}\\!\rightarrow{\eta_{c}}X}}{{\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}}=\frac{\sigma^{{b}}_{{\eta_{c}}}}{\sigma^{{b}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}}$, is defined in the same way as for prompt production. The values of
the branching fractions of the $\eta_{c}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decays to $p$ $\overline{p}$,
${\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}=(1.50\pm
0.16)\times 10^{-3}$ and
${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}=(2.120\pm 0.029)\times 10^{-3}$,
correspond to the current world-average values [36]. While the branching
fraction of $b$-hadron inclusive decays to
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson,
${\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}=(1.16\pm 0.10)\times 10^{-3}$, was measured at LEP [36], this
analysis assumes the same value for the $b$-hadron mixture at LHC.

Since the masses of the $\eta_{c}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ states and kinematic distributions in
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ and
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ decays are similar, they have
similar reconstruction, trigger and selection efficiencies. Using simulation,
the efficiency ratio of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ and
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ modes is determined to be
$\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}/\epsilon_{{\eta_{c}}}=1.00\pm 0.02$, where the uncertainty is due to
the size of the simulation samples. The efficiency ratio is also obtained in
bins of $p_{\mathrm{T}}$, with negligible deviation from unity observed.
Prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons are assumed to be
unpolarised. A systematic uncertainty is further assigned related to possible
non-zero polarisation.

In the baseline analysis, promptly produced charmonium candidates are
distinguished from those originating from $b$-hadron decays using the pseudo-
proper decay time

$t_{z}=\frac{\Delta z\cdot M_{{p}{\overline{p}}}}{p_{z}}\,,$ (2)

where $\Delta z$ is the distance along the beam axis between the PV with the
smallest IP significance of the charmonium candidate and the charmonium decay
vertex; $M_{{p}{\overline{p}}}$ is the reconstructed charmonium mass; and
${p_{z}}$ is the projection of its momentum along the beam axis. A prompt-
enriched sample is selected with candidates satisfying $t_{z}<80\text{\,fs}$,
while a $b$-hadron-enriched sample is selected with $t_{z}>80\text{\,fs}$ and
an additional requirement that both proton tracks are significantly displaced
from any PV. These two samples have a small percentage of wrongly classified
candidates. The probability of such cross-feed is estimated using simulation
and is used to derive corrected yields. The cross-feed correction on the yield
ratio ranges from 1.1% to 2.7% in the prompt-enriched sample and 0.7% to 1.2%
in the $b$-hadron-enriched sample, depending on the charmonium
$p_{\mathrm{T}}$.

A cross-check of the results, reported in Appendix A, uses an alternative
approach analysing the $t_{z}$ distribution of the selected candidates. The
results are in good agreement with the baseline analysis.

##  4 Fit to the invariant mass

A binned fit to the $p$ $\overline{p}$ invariant mass of the prompt-enriched
and $b$-hadron-enriched data samples is performed simultaneously in each bin
of charmonium $p_{\mathrm{T}}$ in order to extract the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ signal yield and the
$\eta_{c}$-to-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yield ratio. For
the $\eta_{c}$ state, the signal shape is modelled by a relativistic
Breit–Wigner function convolved with the sum of two Gaussian functions, while
the signal shape of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ state
is modelled by the sum of two Gaussian functions. In the study of the
$\eta_{c}$ production, the mass values
$M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ and $\Delta
M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}},\,{\eta_{c}}}$ are
constrained within uncertainties in each $p_{\mathrm{T}}$ bin to the values
obtained from a fit to the entire data sample, where they are found to be
consistent with the known values [36]. The mass resolutions of charmonium from
$b$-hadron decays and from prompt production are assumed to be the same, as
confirmed by simulation. The ratio between the widths of the resolution
functions for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\eta_{c}$ mesons is fixed from simulation. The only resolution parameter left
free to vary in the fit is the width of the narrower Gaussian in the
$\eta_{c}$ model. A small $p_{\mathrm{T}}$-dependence of resolution parameters
is seen in the simulation and is accounted for in the fit. The natural width
of the $\eta_{c}$ meson is fixed to its known value [36]. The combinatorial
background is parametrised using an exponential multiplied by a second-order
polynomial. A partially reconstructed background of proton-antiproton pairs
from the decays of higher mass charmonium states could exhibit structures in
the ${p}{\overline{p}}$ invariant mass spectrum. The only contribution
relevant for this analysis is that from
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}$ decays, where the
${\pi}^{0}$ meson is not reconstructed. This background produces a broad, non
peaking, contribution to the $p$ $\overline{p}$ invariant mass below the known
$\eta_{c}$ mass. In this region, the ${p}{\overline{p}}{{\pi}^{0}}$ background
is described by a square-root shape, $\sqrt{M_{T}-M_{{p}{\overline{p}}}}$,
below the phase-space limit, $M_{T}$. The yield of this contribution is
related to that of the decay ${{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}\rightarrow{{p}{\overline{p}}}$ by means of the ratio of branching
fractions ${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}}/{\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}=0.56\pm 0.04$ [36] and the ratio of
efficiencies $\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}}/\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}=0.062\pm 0.002$ for considered $p$
$\overline{p}$ invariant mass window.

The $p$ $\overline{p}$ invariant mass of selected candidates is shown in Fig.
1. Projections of the simultaneous fit result integrated over the entire
$p_{\mathrm{T}}$ range are overlaid. In general, the fit provides a good
description of all $M_{{p}{\overline{p}}}$ distributions. The charmonium
yields in bins of $p_{\mathrm{T}}$ and for the entire data sample are
summarised in Table 1. These yields are corrected to take into account the
cross-feed probabilities.

Figure 1: Invariant-mass distribution of the $p$ $\overline{p}$ candidates for (top left) prompt-enriched and (top right) $b$-hadron-enriched samples in the entire $p_{\mathrm{T}}$ range, $6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-1.00006ptV}$. The solid blue lines represent the total fit result. The dashed magenta and dotted red lines show the signal and background components, respectively. Signal distributions with the background components from the fit subtracted are shown on the bottom plots for the two samples. Table 1: Yield of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons and the $\eta_{c}$-to-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yield ratio for prompt and $b$-hadron decay production, corrected for the cross-feed, in bins of transverse momentum. $p_{\mathrm{T}}$ range $[\text{\,Ge\kern-0.90005ptV}\,]$ | $N^{\text{prompt}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ | $N^{{b}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ | $\frac{N^{\text{prompt}}_{{\eta_{c}}}}{N^{\text{prompt}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}}$ | $\frac{N^{{b}}_{{\eta_{c}}}}{N^{{b}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}}$
---|---|---|---|---
$6.5-\phantom{1}8.0$ | $21600\pm 1800$ |  1$5080\pm 140$ | $0.98\pm 0.22$ | $0.26\pm 0.04$
$8.0-10.0$ | $26500\pm 1700$ |  1$7930\pm 170$ | $1.12\pm 0.18$ | $0.40\pm 0.03$
$10.0-12.0$ | $15100\pm 1100$ |  1$5240\pm 130$ | $1.24\pm 0.19$ | $0.30\pm 0.04$
$12.0-14.0$ | $\phantom{1}5700\pm\phantom{1}700$ | $\phantom{1}2830\pm 100$ | $2.24\pm 0.44$ | $0.35\pm 0.05$
$6.5-14.0$ | $69000\pm 2800$ | $21040\pm 270$ | $1.18\pm 0.10$ | $0.33\pm 0.02$

##  5 Systematic uncertainties

The systematic uncertainties on the $\eta_{c}$ production corresponding to the
signal and background descriptions in the invariant-mass fit are estimated
using alternative fit models. Each uncertainty is estimated in
$p_{\mathrm{T}}$ bins as a difference between the baseline fit result and the
alternative fit result. Generally, bin-to-bin variations of uncorrelated
systematic uncertainties addressed in this paragraph are small compared to the
statistical uncertainties. These variations are parametrised using a linear
$p_{\mathrm{T}}$ dependence to reduce statistical fluctuations. The
uncertainty related to a potential $p_{\mathrm{T}}$ dependence of the
resolution ratio is evaluated by modelling it using a linear function with the
slope constrained by simulation. This systematic effect is relevant for the
differential cross-section measurement. The uncertainty corresponding to the
combinatorial background description is estimated by using an alternative
model using a third-order polynomial function. The uncertainty associated to
the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}$ background contribution is
estimated by varying the efficiency ratio
$\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}}/\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}$ and the branching fraction ratio
${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}/{\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}}$ [36] within their
uncertainties.

The systematic uncertainty associated with the cross-feed probability is
estimated by varying the efficiency of the separation requirements. Separation
efficiencies are found to be in good agreement between data and simulation
within uncertainties. The uncertainty related to the ratio of $\eta_{c}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ efficiencies is estimated by
varying its value by the uncertainty corresponding to the simulation sample
sizes.

A potential effect due to the invariant-mass resolution modelling is evaluated
considering, as an alternative model, the sum of two Crystal Ball functions
[50] with symmetric tails on both sides of the peak. The uncertainty on the
$\eta_{c}$ natural width is accounted for by the difference in relative yields
when using the world average value of $31.9\pm 0.7$ MeV [36] and the value,
$34.0\pm 1.9\pm 1.3$ MeV, recently measured by LHCb collaboration [35]. Since
this uncertainty is correlated among $p_{\mathrm{T}}$ bins, the relative
systematic uncertainty obtained from the $p_{\mathrm{T}}$-integrated data
sample is taken as an estimate of the relative systematic uncertainty in each
bin. This uncertainty is also correlated between $p_{\mathrm{T}}$ bins.
Possible nonzero polarisation of prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons affects their reconstruction efficiency. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ polarisation has not been
measured at $\sqrt{s}$ =13 TeV, although several experiments have measured
small polarisation values at lower energy [13, 16, 15]. The associated
systematic uncertainty is estimated by weighting the prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ simulation sample assuming
polarisation parameter values $\lambda_{\theta}=\pm 0.1$ [51] in the $p$ $p$
collision frame. This uncertainty is correlated among $p_{\mathrm{T}}$ bins.

Systematic uncertainties on the relative cross-sections of the $\eta_{c}$
production for prompt and $b$-hadron decays are given in Tables 2 and 3. The
total systematic uncertainty is calculated as the quadratic sum of the
individual sources. The dominant source of uncorrelated systematic uncertainty
for the production of $\eta_{c}$ meson for both prompt and from $b$-hadron
decays is related to the combinatorial background description. The dominant
sources of correlated systematic uncertainty for prompt production are related
to the knowledge of the $\eta_{c}$ natural width and the invariant-mass
resolution model. The uncertainty on the knowledge of the $\eta_{c}$ natural
width is the dominant source of correlated systematic uncertainty for
$b$-hadron decay production. Systematic uncertainties are in general smaller
than the corresponding statistical uncertainties.

Table 2: Relative uncertainties (in %) on the ratio of prompt cross-sections $\sigma^{\text{prompt}}_{{\eta_{c}}}/\sigma^{\text{prompt}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$. Uncertainties on ${\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}$ and ${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{p}{\overline{p}}}$ are considered separately and given in the text. |  $p_{\mathrm{T}}$ range $[\text{\,Ge\kern-0.90005ptV}\,]$
---|---
| $6.5-8.0$ | $8.0-10.0$ | $10.0-12.0$ | $12.0-14.0$ | $6.5-14.0$
Stat. unc. | 22.7 | 16.1 | 16.9 | 18.3 | 8.8
$p_{\mathrm{T}}$ dependence of resolution | 0.4 | 0.4 | 0.4 | 0.4 | 0.2
Comb. bkg. description | 2.1 | 3.3 | 4.6 | 6.0 | 2.0
Contribution from ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}$ | 0.2 | 0.2 | 0.3 | 0.3 | $<0.1\ \ \ $
Cross-feed | 1.9 | 1.1 | 1.2 | 1.4 | 0.9
Efficiency ratio | 2.0 | 2.0 | 2.0 | 2.0 | 2.0
Total uncorrelated syst. unc. | 3.5 | 4.0 | 5.2 | 6.5 | 3.0
Mass resolution model | 2.7 | 2.7 | 2.7 | 2.7 | 2.7
Variation of $\Gamma_{{\eta_{c}}}$ | 4.8 | 4.8 | 4.8 | 4.8 | 4.8
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ polarisation | 2.1 | 1.8 | 1.6 | 1.6 | 1.8
Total correlated syst. unc. | 5.8 | 5.7 | 5.7 | 5.7 | 5.7
Total systematic uncertainty | 6.8 | 7.0 | 7.7 | 8.6 | 6.4
Table 3: Relative uncertainties (in %) on the ratio of cross-sections for production in inclusive $b$-hadron decays $\sigma^{b}_{{\eta_{c}}}/\sigma^{b}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$. Uncertainties on ${\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}$ and ${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{p}{\overline{p}}}$ are considered separately and given in the text. |  $p_{\mathrm{T}}$ range $[\text{\,Ge\kern-0.90005ptV}\,]$
---|---
| $6.5-8.0$ | $8.0-10.0$ | $10.0-12.0$ | $12.0-14.0$ | $6.5-14.0$
Stat. unc. | 15.4 | 8.2 | 12.8 | 13.4 | 5.8
$p_{\mathrm{T}}$ dependence of resolution | 0.2 | 0.2 | 0.2 | 0.2 | 0.1
Comb. bkg. description | 2.5 | 3.5 | 4.7 | 5.8 | 2.3
Contribution from ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}$ | 0.7 | 0.5 | 0.3 | 0.1 | 0.2
Cross-feed | 1.4 | 1.3 | 1.7 | 1.0 | 0.8
Efficiency ratio | 2.0 | 2.0 | 2.0 | 2.0 | 2.0
Total uncorrelated syst. unc. | 3.6 | 4.3 | 5.4 | 6.2 | 3.2
Mass resolution model | 3.1 | 3.1 | 3.1 | 3.1 | 3.1
Variation of $\Gamma_{{\eta_{c}}}$ | 3.6 | 3.6 | 3.6 | 3.6 | 3.6
Total correlated syst. unc. | 4.8 | 4.8 | 4.8 | 4.8 | 4.8
Total systematic uncertainty | 6.0 | 6.4 | 7.2 | 7.8 | 5.8

Uncertainties on the branching fractions of the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ and
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ decays are considered separately.
They are correlated among $p_{\mathrm{T}}$ bins and amount to about 10%. When
deriving the absolute ${\eta_{c}}$ production cross-section, the uncertainty
on the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production cross-section
[6] is also taken into account.

##  6 Results and discussion on the $\eta_{c}$ production

Using Eq. 1 and the corrected yields from Table 1, the relative prompt
production cross-section in the chosen fiducial region is measured to be

$\displaystyle\left(\sigma_{{\eta_{c}}}^{\text{prompt}}/\sigma_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}^{\text{prompt}}\right)_{13\text{\,Te\kern-0.70004ptV}}^{6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-0.70004ptV},\,2.0<y<4.5}$
$\displaystyle=1.69\pm 0.15\pm 0.10\pm 0.18.$

Here and hereinafter, the quoted uncertainties are statistical, systematic and
systematic due to uncertainties on the branching fractions
${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}$ and
${\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}$, respectively.
Using the corresponding cross-section value of $0.749\pm 0.005\pm 0.028\pm
0.037\,\upmu\text{b}$ for prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ production [6], the prompt $\eta_{c}$ production cross-section in the
chosen fiducial region is derived to be

$\displaystyle\left(\sigma_{{\eta_{c}}}^{\text{prompt}}\right)_{13\text{\,Te\kern-0.70004ptV}}^{6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-0.70004ptV},\,2.0<y<4.5}$
$\displaystyle=1.26\pm 0.11\pm 0.08\pm 0.14\,\upmu\text{b},$

where the last uncertainty includes in addition the uncertainty on the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production cross-section
measurement. This is the first measurement of prompt $\eta_{c}$ production
cross-section in proton-proton collisions at $\sqrt{s}$ =13 TeV, and it
supports the conclusions of Ref. [18] that suggests an enhanced $\eta_{c}$
production compared to that of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ meson. This measurement is in good agreement with the colour-singlet
model prediction of $1.56^{+0.83}_{-0.49}\,{}^{+0.38}_{-0.17}\,\upmu\text{b}$
[31]. This result leaves limited room for a potential colour-octet
contribution, and confirms the theoretical analyses [21, 23, 22, 20] following
the $\eta_{c}$ production studies at ${\sqrt{s}=7}$ and
${8\text{\,Te\kern-1.00006ptV}}$ [18].

Using the LHCb measurements of prompt $\eta_{c}$ production at the centre-of-
mass energies ${\sqrt{s}=7}$ and ${8\text{\,Te\kern-1.00006ptV}}$ [18], the
prompt $\eta_{c}$ production cross-section dependence on the LHC energy is
shown in Fig. 2. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production
cross-section from Ref. [6] is also shown for reference. While the individual
cross-sections grow with centre-of-mass energy, no evolution of the cross-
section ratio is observed.

Figure 2: The prompt $\eta_{c}$ production cross-section as a function of
centre-of-mass energy. (Left) Relative $\eta_{c}$ prompt production cross-
section. (Right) Absolute $\eta_{c}$ (black rectangles) and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ (blue circles) prompt
production cross-sections. The error bars show uncertainties due to
statistical, systematic, and to the
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ branching fractions and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production cross-section.

The relative $\eta_{c}$ inclusive branching fraction from $b$-hadron decays is
measured to be

$\displaystyle{\mathcal{B}}_{{b}\\!\rightarrow{\eta_{c}}X}/{\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}$ $\displaystyle=0.48\pm 0.03\pm 0.03\pm 0.05,$

which combined with
${\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}=1.16\pm 0.10\%$ [36] gives

$\displaystyle{\mathcal{B}}_{{b}\\!\rightarrow{\eta_{c}}X}$
$\displaystyle=(5.51\pm 0.32\pm 0.29\pm 0.77)\times 10^{-3}.$

The last uncertainty includes the uncertainty on
${\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}$. This result is the most precise measurement of the inclusive
${b}\\!\rightarrow{\eta_{c}}X$ branching fraction to date and is in good
agreement with the previous LHCb measurement from Ref. [18]. The measurement
is limited by the knowledge of the branching fractions
${\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}$ and
${\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}$.

Numerical results of the measurements of $p_{\mathrm{T}}$-differential
$\eta_{c}$ production are given in Appendix B. The relative $\eta_{c}$ to
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ $p_{\mathrm{T}}$-differential
cross-sections for prompt and $b$-hadron decay production are compatible to
those measured at ${\sqrt{s}=7}$ and ${8\text{\,Te\kern-1.00006ptV}}$ [18] and
are shown in Fig. 3. This is the first $p_{\mathrm{T}}$-differential cross-
section measurement of $\eta_{c}$ prompt production at
${\sqrt{s}=13\text{\,Te\kern-1.00006ptV}}$. The $p_{\mathrm{T}}$ dependence of
the prompt cross-section ratio is found to be linear with a slope of $0.22\pm
0.11\text{\,Ge\kern-1.00006ptV}^{-1}$. While the integrated cross-section is
in good agreement with the colour-singlet model prediction [31], a hint of a
difference between the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\eta_{c}$ slopes motivates the extension of the measurement to larger
$p_{\mathrm{T}}$ values. A larger measured slope with respect to the
prediction from Ref. [31] would indicate a possible colour-octet contribution.

Figure 3: Relative $\eta_{c}$ to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ differential production cross-sections for (left) prompt production
and (right) production in $b$-hadron inclusive decays. The uncertainties are
statistical, systematic, and due to the
${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ branching fractions, respectively. For
the relative prompt production cross-section, the result of a fit with a
linear function is overlaid.

The absolute $\eta_{c}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
differential production cross-sections are shown in Fig. 4. The exponential
slopes for the $\eta_{c}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
prompt differential cross-sections are determined from the fit to data points
to be $0.41\pm 0.07\text{\,Ge\kern-1.00006ptV}^{-1}$ and $0.57\pm
0.01\text{\,Ge\kern-1.00006ptV}^{-1}$, respectively.

Figure 4: Differential production cross-sections of $\eta_{c}$ (red
rectangles) and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ (blue circles)
for (left) prompt production and (right) production in $b$-hadron inclusive
decays. The uncertainties for $\eta_{c}$ production are statistical,
systematic, and due to the ${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ branching fractions and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production cross-section. For
the prompt production cross-sections, the results of fits with an exponential
function are overlaid. The $p_{\mathrm{T}}$ values of the data points
correspond to the average values of the fit function over the bins.

##  7 Measurement of the $\boldsymbol{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}$–$\boldsymbol{{\eta_{c}}}$ mass difference

While the prompt ${\eta_{c}}$ production measurement requires stringent
selection criteria at the trigger level to compete with the challenging
background conditions, charmonia produced in $b$-hadron decays are
reconstructed in an environment with a controlled background level and are
more suitable for a mass measurement. For this reason, a looser selection is
applied for the entire data sample to measure the ${\eta_{c}}$ mass relative
to the well-known ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass.

Proton and antiproton candidates are required to have good track-fit quality,
to be incompatible with originating from any PV, and to have a transverse
momentum greater than 1.0 GeV. The proton-antiproton system is required to
have a vertex with a good fit quality, a large significance,
$\chi^{2}_{\text{FD}}>81$, of the distance between this vertex and any PV, and
to have a transverse momentum greater than $5.5\text{\,Ge\kern-1.00006ptV}$.
The contamination of the selected sample from
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\eta_{c}$ prompt
production is estimated to be below $0.1\%$.

The mass difference $\Delta M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}},\,{\eta_{c}}}$ is extracted from an extended maximum-likelihood fit to
the $M_{{p}{\overline{p}}}$ distribution. The fit provides a good description
of the $p$ $\overline{p}$ invariant-mass distribution (Fig. 5) yielding

$\Delta M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}},\,{\eta_{c}}}=113.0\pm 0.7\pm 0.1\text{\,Me\kern-1.00006ptV},$

where the uncertainties are statistical and systematic.

Figure 5: Distribution of the ${p}{\overline{p}}$ invariant mass. The solid
line represents the fit result, while the dashed line shows the $\eta_{c}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ signal contributions.

The majority of the sources of systematic uncertainty are common to the
production measurement. The systematic uncertainty related to the momentum-
scale calibration is estimated by comparing the fit result with and without
the calibration applied. The total systematic uncertainty is calculated as the
quadratic sum of the individual contributions (Table 4). The dominant source
of systematic uncertainty is related to the resolution model and its
$p_{\mathrm{T}}$ dependence.

Table 4: Systematic uncertainties on the measurement of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$–${\eta_{c}}$ mass difference. | $\Delta M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}},\,{\eta_{c}}}\,[\text{\,Me\kern-1.00006ptV}\,]$
---|---
Statistical uncertainty |  $0.67$00000
Mass resolution model |  $0.08$00000
Variation of resolution ratio |  $0.01$00000
Variation of $\Gamma_{\eta_{c}}$ |  $0.04$00000
Comb. bkg. description |  $0.03$00000
Contribution from ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{p}{\overline{p}}{{\pi}^{0}}$ |  $<0.01$00000
Momentum scale |  $0.05$00000
Total systematic uncertainty |  $0.11$00000
Total uncertainty |  $0.68$00000

As a cross-check, the invariant-mass fit is performed simultaneously in seven
bins of charmonium transverse momentum to take into account a possible
dependence of the resolution on charmonium $p_{\mathrm{T}}$. The value
obtained for the mass difference is consistent with the baseline result.

This measurement is currently statistically limited and can be improved with
larger data samples. It represents the most precise measurement from a single
experiment to date. The result is in good agreement with the PDG value [36],
the recent BES III result [52], the latest BaBar measurement [53] and LHCb
measurements [18, 32, 35].

##  8 Summary

Using data corresponding to an integrated luminosity of 2.0$\text{\,fb}^{-1}$,
the prompt ${\eta_{c}}$ production cross-section at a centre-of-mass energy of
$\sqrt{s}=13$ TeV is measured for the first time. The ratio of the prompt
production rates of the ${\eta_{c}}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ states in the fiducial region
${6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-1.00006ptV}}$ and ${2.0<y<4.5}$ is
measured to be

$\displaystyle\left(\sigma_{{\eta_{c}}}^{\text{prompt}}/\sigma_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}^{\text{prompt}}\right)_{13\text{\,Te\kern-0.70004ptV}}^{6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-0.70004ptV},\,2.0<y<4.5}$
$\displaystyle=1.69\pm 0.15\pm 0.10\pm 0.18,$

where the quoted uncertainties are, in order, statistical, systematic and
systematic due to uncertainties on the branching fractions,
${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}$ and
${\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}$.

Using the prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production
cross-section measurement at $\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$ [6], the
prompt ${\eta_{c}}$ production cross-section in the chosen fiducial region is
derived to be

$\displaystyle\left(\sigma_{{\eta_{c}}}^{\text{prompt}}\right)_{13\text{\,Te\kern-0.70004ptV}}^{6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-0.70004ptV},\,2.0<y<4.5}$
$\displaystyle=1.26\pm 0.11\pm 0.08\pm 0.14\,\upmu\text{b},$

where the last uncertainty includes in addition the uncertainty of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production cross-section
measurement. The result is in good agreement with the colour-singlet model
prediction [31]. Contrary to NRQCD expectations, a steeper $p_{\mathrm{T}}$
dependence of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ cross-section
compared to that of the $\eta_{c}$ is preferred.

The relative ${\eta_{c}}$ inclusive branching fraction from $b$-hadron decays
is measured to be

$\displaystyle{\mathcal{B}}_{{b}\\!\rightarrow{\eta_{c}}X}/{\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}$ $\displaystyle=0.48\pm 0.03\pm 0.03\pm 0.05.$

Using ${\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}$ [36] the absolute $\eta_{c}$ inclusive branching fraction is
obtained to be

$\displaystyle{\mathcal{B}}_{{b}\\!\rightarrow{\eta_{c}}X}$
$\displaystyle=(5.51\pm 0.32\pm 0.29\pm 0.77)\times 10^{-3},$

where the last uncertainty includes in addition the uncertainty on
${\mathcal{B}}_{{b}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X}$. This result is consistent with the previous LHCb measurement [18].
Compatible results are obtained with an alternative analysis technique.

The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$–${\eta_{c}}$ mass
difference is measured using an enlarged data sample of
${b}\\!\rightarrow{\eta_{c}}X$ decays. The measurement,

$\displaystyle\Delta M_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}},\,{\eta_{c}}}=113.0\pm 0.7\pm 0.1\text{\,Me\kern-1.00006ptV},$

is compatible with both the result of Refs. [35] and [36]. It is the most
precise ${\eta_{c}}$ mass determination to date.

## Acknowledgements

We thank J.-P. Lansberg and H.-S. Shao for useful discussions. We express our
gratitude to our colleagues in the CERN accelerator departments for the
excellent performance of the LHC. We thank the technical and administrative
staff at the LHCb institutes. We acknowledge support from CERN and from the
national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO
(Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE (Russia);
MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United
Kingdom); 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 OSC (USA). We are indebted to the communities behind the multiple
open-source software packages on which we depend. Individual groups or members
have received support from AvH Foundation (Germany); EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union); ANR, Labex P2IO and OCEVU,
and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier
Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF
and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal Society
and the Leverhulme Trust (United Kingdom).

## Appendices

##  Appendix A Alternative analysis based on $t_{z}$ distributions

A cross-check of the results is performed using an alternative approach via a
two-step procedure. Signal yields in bins of $p_{\mathrm{T}}$ and $t_{z}$ are
obtained from a simultaneous fit to the corresponding $p$ $\overline{p}$
invariant mass distributions of candidates in the bin. Prompt and $b$-decay
charmonium contributions are then determined using a simultaneous $\chi^{2}$
fit to the resulting $t_{z}$ distributions in $p_{\mathrm{T}}$ bins, similarly
to Ref. [6].

Projections of the simultaneous fit for the entire $p_{\mathrm{T}}$-range are
shown in Fig. 6 for illustration purposes.

Figure 6: Invariant mass distributions of the $p$ $\overline{p}$ candidates
for seven bins of $t_{z}$ for the $p_{\mathrm{T}}$-integrated sample
$6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-1.00006ptV}$. The solid blue lines
represent the total fit result. Dashed magenta and dotted red lines show the
signal and background components, respectively. The distributions with the
background component of the fit subtracted are shown below.

In the alternative analysis discussed in this appendix, the $p$ $\overline{p}$
invariant-mass fit is performed simultaneously in 28 two-dimensional bins of
$p_{\mathrm{T}}$ and $t_{z}$ with the model described in Sect. 4. This model
is modified to correct for systematic mass shifts as a function of $t_{z}$.
The corrections are derived from simulation, where the same behaviour is
observed.444This effect cancels in the method described in Sect. 4, which
integrates over all values of $t_{z}$.

The mass fits result in four $t_{z}$ distributions, each corresponding to a
$p_{\mathrm{T}}$ bin. Promptly produced charmonium is distinguished from that
produced in $b$-hadron decays by performing a simultaneous $\chi^{2}$ fit to
the four $t_{z}$ distributions. This fit method does not use the bin centre
for the value of $t_{z}$, but rather the average value of the fit function in
the bin. The model to describe the $t_{z}$ distribution comprises
contributions due to prompt charmonia, due to charmonia from $b$-hadron decays
and a contribution due to candidates with a wrongly associated PV. The prompt
charmonium component is parametrised with a function to account only for
resolution, while the component related to charmonia produced in inclusive
$b$-hadron decays is parametrised by an exponential decay function convolved
with the same resolution function. The exponential slope of the decay
function, $\tau_{b}$, is allowed to vary over $p_{\mathrm{T}}$ according to
simulation. The resolution is described by the sum of two Gaussian functions,
with the width of the narrow Gaussian component a free fit parameter and the
other parameters fixed from the simulation. The $p_{\mathrm{T}}$ dependence of
the resolution, as obtained from simulation, is taken into account in the
$t_{z}$-fit to data. The contribution due to candidates associated to a wrong
PV are described in the same way as in Ref. [6]. Results of the simultaneous
fit to $t_{z}$ for the entire $p_{\mathrm{T}}$ range are shown in Fig. 7.

Figure 7: Distributions of $t_{z}$ for (left)
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and (right) ${\eta_{c}}$ mesons
for the entire $p_{\mathrm{T}}$ range
${6.5<p_{\mathrm{T}}<14.0\text{\,Ge\kern-1.00006ptV}}$ and the result of the
simultaneous $\chi^{2}$ fit. The solid blue lines show the fit function, the
red dashed areas show the prompt components, the green dotted areas show the
contributions from inclusive $b$-hadron decays, the grey lines show
contributions from the events with wrongly associated PV. The $t_{z}$ values
of the data points correspond to the average values of the fit function over
the bins.

In addition to the sources of systematic uncertainty discussed in Sect. 5 for
the baseline analysis, contributions from the signal description in the fit to
$t_{z}$ and from corrections of the invariant-mass peak positions in $t_{z}$
bins are considered. This approach is free from the systematic uncertainty
associated with the cross-feed effect. The dominant sources of systematic
uncertainties are the same as for the baseline analysis.

The relative differential cross-sections of $\eta_{c}$ production obtained
with this approach are shown in Fig. 8, where they are compared with those
from the baseline approach. The two measurements are strongly correlated. The
difference between the results obtained with the two techniques varies in
$p_{\mathrm{T}}$ bins between factors of 0.5 and 1.5 of the estimated
uncorrelated uncertainty.

Figure 8: Relative $\eta_{c}$ to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ differential production cross-sections for (left) prompt production
and (right) production in $b$-hadron inclusive decays obtained using the
alternative technique (points) and the baseline technique (red boxes). The
uncertainties shown are statistical, systematic, and the uncertainty due to
the ${\eta_{c}}\\!\rightarrow{p}{\overline{p}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}$ branching fractions.

##  Appendix B Tables of $p_{\mathrm{T}}$-differential $\eta_{c}$ production
cross-sections

###  B.1 Prompt production of $\eta_{c}$ mesons

The results on relative $p_{\mathrm{T}}$-differential $\eta_{c}$ prompt
production are shown in Table 5. Here and in the following tables, the first
uncertainty is statistical, the second is the uncorrelated systematic
uncertainty, the third is the systematic uncertainty that is correlated among
$p_{\mathrm{T}}$ bins, and the last one is related to the
${\mathcal{B}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{p}{\overline{p}}}$ and
${\mathcal{B}}_{{\eta_{c}}\\!\rightarrow{p}{\overline{p}}}$ branching
fractions. The results on $p_{\mathrm{T}}$-differential $\eta_{c}$ prompt
production cross-section are shown in Table 6. Here, the last uncertainty
includes the uncertainty on the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
production cross-section.

Table 5: Relative $p_{\mathrm{T}}$-differential $\eta_{c}$ prompt production cross-section. $p_{\mathrm{T}}$ $[\text{\,Ge\kern-0.90005ptV}\,]$ | $d\sigma^{\text{prompt}}_{{\eta_{c}}}/d\sigma^{\text{prompt}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$
---|---
$\phantom{1}6.5-\phantom{1}8.0$ |  1.53 $\pm$ 0.35 $\pm$ 0.05 $\pm$ 0.09 $\pm$ 0.19
1$8.0-10.0$ |  1.74 $\pm$ 0.28 $\pm$ 0.07 $\pm$ 0.10 $\pm$ 0.22
$10.0-12.0$ |  1.93 $\pm$ 0.33 $\pm$ 0.10 $\pm$ 0.11 $\pm$ 0.24
$12.0-14.0$ |  3.48 $\pm$ 0.64 $\pm$ 0.23 $\pm$ 0.20 $\pm$ 0.43
Table 6: Differential $\eta_{c}$ prompt production cross-section. $p_{\mathrm{T}}$ $[\text{\,Ge\kern-0.90005ptV}\,]$ |  $d\sigma^{\text{prompt}}_{{\eta_{c}}}/dp_{\mathrm{T}}$ $[\text{\,nb}/\text{\,Ge\kern-1.00006ptV}\,]$
---|---
$\phantom{1}6.5-\phantom{1}8.0$ | 488 | $\pm$ | 111 | $\pm$ | 17 | $\pm$ | 28 | $\pm$ | 64
1$8.0-10.0$ | 157 | $\pm$ |  125 | $\pm$ |  16 | $\pm$ |  19 | $\pm$ | 22
$10.0-12.0$ |  163 | $\pm$ |  111 | $\pm$ |  13 | $\pm$ |  14 | $\pm$ |  19
$12.0-14.0$ |  144 | $\pm$ |  118 | $\pm$ |  13 | $\pm$ |  13 | $\pm$ |  16

###  B.2 Production of $\eta_{c}$ mesons from $b$-hadron decays

The results on relative $p_{\mathrm{T}}$-differential $\eta_{c}$ production in
inclusive $b$-hadron decays are shown in Table 7. The results on
$p_{\mathrm{T}}$-differential $\eta_{c}$ production cross-section in inclusive
$b$-hadron decays are shown in Table 8. As above, the last uncertainty
includes the uncertainty on the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
production cross-section.

Table 7: Relative $p_{\mathrm{T}}$-differential $\eta_{c}$ production cross-section in inclusive $b$-hadron decays. $p_{\mathrm{T}}$ $[\text{\,Ge\kern-0.90005ptV}\,]$ | $d\sigma^{{b}}_{{\eta_{c}}}/d\sigma^{{b}}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$
---|---
$\phantom{1}6.5-\phantom{1}8.0$ |  0.41 $\pm$ 0.06 $\pm$ 0.01 $\pm$ 0.02 $\pm$ 0.05
1$8.0-10.0$ |  0.61 $\pm$ 0.05 $\pm$ 0.03 $\pm$ 0.03 $\pm$ 0.08
$10.0-12.0$ |  0.45 $\pm$ 0.06 $\pm$ 0.02 $\pm$ 0.02 $\pm$ 0.06
$12.0-14.0$ |  0.54 $\pm$ 0.07 $\pm$ 0.03 $\pm$ 0.02 $\pm$ 0.07
Table 8: The $p_{\mathrm{T}}$-differential $\eta_{c}$ production cross-section in inclusive $b$-hadron decays. $p_{\mathrm{T}}$ $[\text{\,Ge\kern-0.90005ptV}\,]$ |  $d\sigma^{{b}}_{{\eta_{c}}}/dp_{\mathrm{T}}$ $[\text{\,nb}/\text{\,Ge\kern-1.00006ptV}\,]$
---|---
$\phantom{1}6.5-\phantom{1}8.0$ | 27.2 | $\pm$ | 4.2 | $\pm$ | 1.0 | $\pm$ | 1.3 | $\pm$ | 3.7
1$8.0-10.0$ | 18.8 | $\pm$ | 1.5 | $\pm$ | 0.8 | $\pm$ | 0.9 | $\pm$ | 2.6
$10.0-12.0$ |  16.6 | $\pm$ | 0.8 | $\pm$ | 0.3 | $\pm$ | 0.3 | $\pm$ | 0.9
$12.0-14.0$ |  13.8 | $\pm$ | 0.5 | $\pm$ | 0.2 | $\pm$ | 0.2 | $\pm$ | 0.6

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LHCb collaboration

R. Aaij28, C. Abellán Beteta46, T. Ackernley56, B. Adeva43, M. Adinolfi50, H.
Afsharnia6, C.A. Aidala77, S. Aiola22, Z. Ajaltouni6, S. Akar61, P.
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L. An18, L. Anderlini18, G. Andreassi45, M. Andreotti17, F. Archilli13, P.
d’Argent13, J. Arnau Romeu7, A. Artamonov41, M. Artuso63, K. Arzymatov38, E.
Aslanides7, M. Atzeni46, B. Audurier23, S. Bachmann13, J.J. Back52, S.
Baker57, V. Balagura8,b, W. Baldini17,44, A. Baranov38, R.J. Barlow58, S.
Barsuk8, W. Barter57, M. Bartolini20,h, F. Baryshnikov74, G. Bassi25, V.
Batozskaya32, B. Batsukh63, A. Battig11, V. Battista45, A. Bay45, M. Becker11,
F. Bedeschi25, I. Bediaga1, A. Beiter63, L.J. Bel28, V. Belavin38, S. Belin23,
N. Beliy66, V. Bellee45, K. Belous41, I. Belyaev35, E. Ben-Haim9, G.
Bencivenni19, S. Benson28, S. Beranek10, A. Berezhnoy36, R. Bernet46, D.
Berninghoff13, H.C. Bernstein63, E. Bertholet9, A. Bertolin24, C.
Betancourt46, F. Betti16,e, M.O. Bettler51, M. van Beuzekom28, Ia.
Bezshyiko46, S. Bhasin50, J. Bhom30, M.S. Bieker11, S. Bifani49, P. Billoir9,
A. Birnkraut11, A. Bizzeti18,u, M. Bjørn59, M.P. Blago44, T. Blake52, F.
Blanc45, S. Blusk63, D. Bobulska55, V. Bocci27, O. Boente Garcia43, T.
Boettcher60, A. Boldyrev39, A. Bondar40,x, N. Bondar34, S. Borghi58,44, M.
Borisyak38, M. Borsato13, J.T. Borsuk30, M. Boubdir10, T.J.V. Bowcock56, C.
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Brossa Gonzalo52, D. Brundu23,44, E. Buchanan50, A. Buonaura46, C. Burr44, A.
Bursche23, J.S. Butter28, J. Buytaert44, W. Byczynski44, S. Cadeddu23, H.
Cai68, R. Calabrese17,g, S. Cali19, R. Calladine49, M. Calvi21,i, M. Calvo
Gomez42,m, A. Camboni42,m, P. Campana19, D.H. Campora Perez44, L.
Capriotti16,e, A. Carbone16,e, G. Carboni26, R. Cardinale20,h, A. Cardini23,
P. Carniti21,i, K. Carvalho Akiba28, A. Casais Vidal43, G. Casse56, M.
Cattaneo44, G. Cavallero20, R. Cenci25,p, J. Cerasoli7, M.G. Chapman50, M.
Charles9,44, Ph. Charpentier44, G. Chatzikonstantinidis49, M. Chefdeville5, V.
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Graugés42, E. Graverini45, G. Graziani18, A. Grecu33, R. Greim28, P.
Griffith17, L. Grillo58, L. Gruber44, B.R. Gruberg Cazon59, C. Gu3, X. Guo67,
E. Gushchin37, A. Guth10, Yu. Guz41,44, T. Gys44, C. Göbel65, T.
Hadavizadeh59, C. Hadjivasiliou6, G. Haefeli45, C. Haen44, S.C. Haines51, P.M.
Hamilton62, Q. Han69, X. Han13, T.H. Hancock59, S. Hansmann-Menzemer13, N.
Harnew59, T. Harrison56, R. Hart28, C. Hasse44, M. Hatch44, J. He66, M.
Hecker57, K. Heijhoff28, K. Heinicke11, A. Heister11, A.M. Hennequin44, K.
Hennessy56, L. Henry76, E. van Herwijnen44, J. Heuel10, M. Heß71, A.
Hicheur64, R. Hidalgo Charman58, D. Hill59, M. Hilton58, P.H. Hopchev45, J.
Hu13, W. Hu69, W. Huang66, Z.C. Huard61, W. Hulsbergen28, T. Humair57, R.J.
Hunter52, M. Hushchyn39, D. Hutchcroft56, D. Hynds28, P. Ibis11, M. Idzik31,
P. Ilten49, A. Inglessi34, A. Inyakin41, K. Ivshin34, R. Jacobsson44, S.
Jakobsen44, J. Jalocha59, E. Jans28, B.K. Jashal76, A. Jawahery62, V.
Jevtic11, F. Jiang3, M. John59, D. Johnson44, C.R. Jones51, B. Jost44, N.
Jurik59, S. Kandybei47, M. Karacson44, J.M. Kariuki50, S. Karodia55, N.
Kazeev39, M. Kecke13, F. Keizer51, M. Kelsey63, M. Kenzie51, T. Ketel29, B.
Khanji44, A. Kharisova75, C. Khurewathanakul45, K.E. Kim63, T. Kirn10, V.S.
Kirsebom45, S. Klaver19, K. Klimaszewski32, S. Koliiev48, A. Kondybayeva74, A.
Konoplyannikov35, P. Kopciewicz31, R. Kopecna13, P. Koppenburg28, I.
Kostiuk28,48, O. Kot48, S. Kotriakhova34, M. Kozeiha6, L. Kravchuk37, R.D.
Krawczyk44, M. Kreps52, F. Kress57, S. Kretzschmar10, P. Krokovny40,x, W.
Krupa31, W. Krzemien32, W. Kucewicz30,l, M. Kucharczyk30, V. Kudryavtsev40,x,
H.S. Kuindersma28, G.J. Kunde78, A.K. Kuonen45, T. Kvaratskheliya35, D.
Lacarrere44, G. Lafferty58, A. Lai23, D. Lancierini46, J.J. Lane58, G.
Lanfranchi19, C. Langenbruch10, T. Latham52, F. Lazzari25,v, C. Lazzeroni49,
R. Le Gac7, A. Leflat36, R. Lefèvre6, F. Lemaitre44, O. Leroy7, T. Lesiak30,
B. Leverington13, H. Li67, P.-R. Li66,ab, X. Li78, Y. Li4, Z. Li63, X.
Liang63, R. Lindner44, P. Ling67, F. Lionetto46, V. Lisovskyi8, G. Liu67, X.
Liu3, D. Loh52, A. Loi23, J. Lomba Castro43, I. Longstaff55, J.H. Lopes2, G.
Loustau46, G.H. Lovell51, D. Lucchesi24,o, M. Lucio Martinez28, Y. Luo3, A.
Lupato24, E. Luppi17,g, O. Lupton52, A. Lusiani25, X. Lyu66, R. Ma67, S.
Maccolini16,e, F. Machefert8, F. Maciuc33, V. Macko45, P. Mackowiak11, S.
Maddrell-Mander50, L.R. Madhan Mohan50, O. Maev34,44, A. Maevskiy39, K.
Maguire58, D. Maisuzenko34, M.W. Majewski31, S. Malde59, B. Malecki44, A.
Malinin73, T. Maltsev40,x, H. Malygina13, G. Manca23,f, G. Mancinelli7, R.
Manera Escalero42, D. Manuzzi16,e, D. Marangotto22,q, J. Maratas6,w, J.F.
Marchand5, U. Marconi16, S. Mariani18, C. Marin Benito8, M. Marinangeli45, P.
Marino45, J. Marks13, P.J. Marshall56, G. Martellotti27, L. Martinazzoli44, M.
Martinelli44,21, D. Martinez Santos43, F. Martinez Vidal76, A. Massafferri1,
M. Materok10, R. Matev44, A. Mathad46, Z. Mathe44, V. Matiunin35, C.
Matteuzzi21, K.R. Mattioli77, A. Mauri46, E. Maurice8,b, M. McCann57,44, L.
Mcconnell14, A. McNab58, R. McNulty14, J.V. Mead56, B. Meadows61, C. Meaux7,
N. Meinert71, D. Melnychuk32, S. Meloni21,i, M. Merk28, A. Merli22,q, E.
Michielin24, D.A. Milanes70, E. Millard52, M.-N. Minard5, O. Mineev35, L.
Minzoni17,g, S.E. Mitchell54, B. Mitreska58, D.S. Mitzel44, A. Mogini9, R.D.
Moise57, T. Mombächer11, I.A. Monroy70, S. Monteil6, M. Morandin24, G.
Morello19, M.J. Morello25,t, J. Moron31, A.B. Morris7, A.G. Morris52, R.
Mountain63, H. Mu3, F. Muheim54, M. Mukherjee69, M. Mulder28, C.H. Murphy59,
D. Murray58, P. Muzzetto23, A. Mödden 11, D. Müller44, J. Müller11, K.
Müller46, V. Müller11, P. Naik50, T. Nakada45, R. Nandakumar53, A. Nandi59, T.
Nanut45, I. Nasteva2, M. Needham54, N. Neri22,q, S. Neubert13, N. Neufeld44,
R. Newcombe57, T.D. Nguyen45, C. Nguyen-Mau45,n, E.M. Niel8, S. Nieswand10, N.
Nikitin36, N.S. Nolte44, D.P. O’Hanlon16, A. Oblakowska-Mucha31, V.
Obraztsov41, S. Ogilvy55, R. Oldeman23,f, C.J.G. Onderwater72, J. D. Osborn77,
A. Ossowska30, J.M. Otalora Goicochea2, T. Ovsiannikova35, P. Owen46, A.
Oyanguren76, P.R. Pais45, T. Pajero25,t, A. Palano15, M. Palutan19, G.
Panshin75, A. Papanestis53, M. Pappagallo54, L.L. Pappalardo17,g, W. Parker62,
C. Parkes58,44, G. Passaleva18,44, A. Pastore15, M. Patel57, C.
Patrignani16,e, A. Pearce44, A. Pellegrino28, G. Penso27, M. Pepe Altarelli44,
S. Perazzini16, D. Pereima35, P. Perret6, L. Pescatore45, K. Petridis50, A.
Petrolini20,h, A. Petrov73, S. Petrucci54, M. Petruzzo22,q, B. Pietrzyk5, G.
Pietrzyk45, M. Pikies30, M. Pili59, D. Pinci27, J. Pinzino44, F. Pisani44, A.
Piucci13, V. Placinta33, S. Playfer54, J. Plews49, M. Plo Casasus43, F.
Polci9, M. Poli Lener19, M. Poliakova63, A. Poluektov7, N. Polukhina74,c, I.
Polyakov63, E. Polycarpo2, G.J. Pomery50, S. Ponce44, A. Popov41, D. Popov49,
S. Poslavskii41, K. Prasanth30, L. Promberger44, C. Prouve43, V. Pugatch48, A.
Puig Navarro46, H. Pullen59, G. Punzi25,p, W. Qian66, J. Qin66, R. Quagliani9,
B. Quintana6, N.V. Raab14, B. Rachwal31, J.H. Rademacker50, M. Rama25, M.
Ramos Pernas43, M.S. Rangel2, F. Ratnikov38,39, G. Raven29, M. Ravonel
Salzgeber44, M. Reboud5, F. Redi45, S. Reichert11, A.C. dos Reis1, F. Reiss9,
C. Remon Alepuz76, Z. Ren3, V. Renaudin59, S. Ricciardi53, S. Richards50, K.
Rinnert56, P. Robbe8, A. Robert9, A.B. Rodrigues45, E. Rodrigues61, J.A.
Rodriguez Lopez70, M. Roehrken44, S. Roiser44, A. Rollings59, V.
Romanovskiy41, M. Romero Lamas43, A. Romero Vidal43, J.D. Roth77, M.
Rotondo19, M.S. Rudolph63, T. Ruf44, J. Ruiz Vidal76, J. Ryzka31, J.J.
Saborido Silva43, N. Sagidova34, B. Saitta23,f, C. Sanchez Gras28, C. Sanchez
Mayordomo76, B. Sanmartin Sedes43, R. Santacesaria27, C. Santamarina Rios43,
M. Santimaria19,44, E. Santovetti26,j, G. Sarpis58, A. Sarti27, C.
Satriano27,s, A. Satta26, M. Saur66, D. Savrina35,36, L.G. Scantlebury
Smead59, S. Schael10, M. Schellenberg11, M. Schiller55, H. Schindler44, M.
Schmelling12, T. Schmelzer11, B. Schmidt44, O. Schneider45, A. Schopper44,
H.F. Schreiner61, M. Schubiger28, S. Schulte45, M.H. Schune8, R. Schwemmer44,
B. Sciascia19, A. Sciubba27,k, S. Sellam64, A. Semennikov35, A. Sergi49,44, N.
Serra46, J. Serrano7, L. Sestini24, A. Seuthe11, P. Seyfert44, D.M.
Shangase77, M. Shapkin41, T. Shears56, L. Shekhtman40,x, V. Shevchenko73,74,
E. Shmanin74, J.D. Shupperd63, B.G. Siddi17, R. Silva Coutinho46, L. Silva de
Oliveira2, G. Simi24,o, S. Simone15,d, I. Skiba17, N. Skidmore13, T.
Skwarnicki63, M.W. Slater49, J.G. Smeaton51, E. Smith10, I.T. Smith54, M.
Smith57, M. Soares16, L. Soares Lavra1, M.D. Sokoloff61, F.J.P. Soler55, B.
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S. Stemmle13, O. Stenyakin41, M. Stepanova34, H. Stevens11, S. Stone63, S.
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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
4Institute Of High Energy Physics (IHEP), Beijing, China
5Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
6Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
7Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
8LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
9LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
10I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
11Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
12Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
13Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
14School of Physics, University College Dublin, Dublin, Ireland
15INFN Sezione di Bari, Bari, Italy
16INFN Sezione di Bologna, Bologna, Italy
17INFN Sezione di Ferrara, Ferrara, Italy
18INFN Sezione di Firenze, Firenze, Italy
19INFN Laboratori Nazionali di Frascati, Frascati, Italy
20INFN Sezione di Genova, Genova, Italy
21INFN Sezione di Milano-Bicocca, Milano, Italy
22INFN Sezione di Milano, Milano, Italy
23INFN Sezione di Cagliari, Monserrato, Italy
24INFN Sezione di Padova, Padova, Italy
25INFN Sezione di Pisa, Pisa, Italy
26INFN Sezione di Roma Tor Vergata, Roma, Italy
27INFN Sezione di Roma La Sapienza, Roma, Italy
28Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
29Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
30Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
31AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
32National Center for Nuclear Research (NCBJ), Warsaw, Poland
33Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
34Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
35Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia, Moscow, Russia
36Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
37Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
38Yandex School of Data Analysis, Moscow, Russia
39National Research University Higher School of Economics, Moscow, Russia
40Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
41Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
42ICCUB, Universitat de Barcelona, Barcelona, Spain
43Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
44European Organization for Nuclear Research (CERN), Geneva, Switzerland
45Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
46Physik-Institut, Universität Zürich, Zürich, Switzerland
47NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
48Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
49University of Birmingham, Birmingham, United Kingdom
50H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
51Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
52Department of Physics, University of Warwick, Coventry, United Kingdom
53STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
54School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
55School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
56Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
57Imperial College London, London, United Kingdom
58Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
59Department of Physics, University of Oxford, Oxford, United Kingdom
60Massachusetts Institute of Technology, Cambridge, MA, United States
61University of Cincinnati, Cincinnati, OH, United States
62University of Maryland, College Park, MD, United States
63Syracuse University, Syracuse, NY, United States
64Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria,
associated to 2
65Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
66University of Chinese Academy of Sciences, Beijing, China, associated to 3
67South China Normal University, Guangzhou, China, associated to 3
68School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
69Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
70Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 9
71Institut für Physik, Universität Rostock, Rostock, Germany, associated to 13
72Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 28
73National Research Centre Kurchatov Institute, Moscow, Russia, associated to
35
74National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 35
75National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
35
76Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 42
77University of Michigan, Ann Arbor, United States, associated to 63
78Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 63

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
vUniversità di Siena, Siena, Italy
wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
xNovosibirsk State University, Novosibirsk, Russia
yINFN Sezione di Trieste, Trieste, Italy
zSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
aaPhysics and Micro Electronic College, Hunan University, Changsha City, China
abLanzhou University, Lanzhou, China
acTaras Shevchenko National University, Kyiv, Ukraine
†Deceased