EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-054 LHCb-PAPER-2018-002 1 August 2018

Measurement of $\mathchar 28935\relax$ production in $pp$ collisions at
$\sqrt{s}=13\mathrm{\,Te\kern-2.07413ptV}$

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

The production cross-sections of $\mathchar 28935\relax{(1S)}$, $\mathchar
28935\relax{(2S)}$ and $\mathchar 28935\relax{(3S)}$ mesons in proton-proton
collisions at $\sqrt{s}=13\mathrm{\,Te\kern-1.00006ptV}$ are measured with a
data sample corresponding to an integrated luminosity of $277\pm
11\mbox{\,pb}^{-1}$ recorded by the LHCb experiment in 2015. The $\mathchar
28935\relax$ mesons are reconstructed in the decay mode $\mathchar
28935\relax\rightarrow\mu^{+}\mu^{-}$. The differential production cross-
sections times the dimuon branching fractions are measured as a function of
the $\mathchar 28935\relax$ transverse momentum, $p_{\rm T}$, and rapidity,
$y$, over the range $0<\mbox{$p_{\rm
T}$}<30{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$. The ratios of
the cross-sections with respect to the LHCb measurement at
$\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$ are also determined. The
measurements are compared with theoretical predictions based on NRQCD.

Published in JHEP 07(2018)134

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

##  1 Introduction

The study of heavy quarkonium ($c\overline{c}$ and $b\overline{b}$) production
in high-energy hadron collisions provides important information to better
understand quantum chromodynamics (QCD). Thanks to theoretical and
experimental efforts in the past forty years, the comprehension of hadronic
production of heavy quarkonia has been improved significantly. The production
of heavy quarkonium in proton-proton ($pp$) collisions at the Large Hadron
Collider (LHC) is expected to start with the production of a heavy quark pair,
$Q\overline{Q}$, followed by its hadronization into a bound state. The heavy
quark pair $Q\overline{Q}$ is produced mainly via Leading Order (LO) gluon-
gluon interactions. Several models have been proposed to describe the
underlying dynamics, such as the colour-singlet model (CSM) [1, 2, 3, 4, 5, 6,
7] and non-relativistic QCD (NRQCD) [8, 9, 10]. In the CSM the intermediate
$Q\overline{Q}$ state is supposed to be colourless and has the same quantum
numbers as the quarkonium final state, while in NRQCD the calculations also
include the colour-octet contribution. However, at present no model can
describe both the heavy quarkonium production cross-section and polarisation
simultaneously.

The production of $\mathchar 28935\relax{(1S)}$, $\mathchar 28935\relax{(2S)}$
and $\mathchar 28935\relax{(3S)}$ mesons has been studied at LHC by ATLAS [11,
12] and CMS [13, 14] collaborations at centre-of-mass energies of
$7\mathrm{\,Te\kern-1.00006ptV}$ and $13\mathrm{\,Te\kern-1.00006ptV}$. The
measurements have also been performed by LHCb at centre-of-mass energies of
$2.76\mathrm{\,Te\kern-1.00006ptV}$ [15], $7\mathrm{\,Te\kern-1.00006ptV}$
[16, 17, 18, 19] and $8\mathrm{\,Te\kern-1.00006ptV}$ [20, 17, 18, 19]. The
NRQCD calculations can describe the trends of the differential production
cross-sections in data for all three $\mathchar 28935\relax$ states within
uncertainties. The measured production cross-section ratios between
$7\mathrm{\,Te\kern-1.00006ptV}$ and $8\mathrm{\,Te\kern-1.00006ptV}$ [18] as
a function of transverse momentum, $p_{\rm T}$, are consistently higher than
the next-to-leading order NRQCD theory predictions [21], and the ratios as a
function of rapidity show a different trend than the predictions [22, 23]. The
measurement performed at $13\mathrm{\,Te\kern-1.00006ptV}$ presented here
provides valuable input to study the quarkonium production at a higher centre-
of-mass energy, enabling ratios to be determined with respect to data taken at
a lower centre-of-mass energy. Most of the theoretical and experimental
uncertainties cancel in the ratios, and more stringent constraints on the
theoretical models can be obtained.

This paper presents a measurement of the differential production cross-
sections times dimuon branching fractions of $\mathchar 28935\relax{(1S)}$,
$\mathchar 28935\relax{(2S)}$ and $\mathchar 28935\relax{(3S)}$ mesons, as
functions of $p_{\rm T}$, and rapidity, $y$, over the range $0<\mbox{$p_{\rm
T}$}<30{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$. Ratios between
the cross-section measurements at $13\mathrm{\,Te\kern-1.00006ptV}$ and
$8\mathrm{\,Te\kern-1.00006ptV}$ [18] are also presented. The measurements are
compared with theoretical predictions based on NRQCD [24].

##  2 The LHCb detector and event selection

The LHCb detector [25, 26] 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 [27], 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 [28] placed
downstream of the magnet. The tracking system provides a measurement of
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at
200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum distance of a track to
a primary vertex, the impact parameter, is measured with a resolution of
$(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm m}$, where $p_{\rm T}$ is expressed in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
[29]. Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad (SPD) and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers [30].

The data sample used in this measurement corresponds to an integrated
luminosity of $277\pm 11\mbox{\,pb}^{-1}$ of $pp$ collisions at a centre-of-
mass energy of $13\mathrm{\,Te\kern-1.00006ptV}$ collected during 2015. The
online event selection is performed by a trigger system [31] that consists of
a hardware stage selecting dimuon candidates with the product of the
transverse momenta of the muons greater than
$(1.3\mathrm{\,Ge\kern-1.00006ptV}/c)^{2}$, followed by a two-stage software
selection based on the information available after full event reconstruction.
In the software trigger, two muons with
$p>6{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\mbox{$p_{\rm
T}$}>300{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ are selected to form a
$\mathchar 28935\relax$ candidate. These two muon candidates are required to
form a common vertex [32] with an invariant mass
$M>4.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. To reject high-multiplicity
events with a large number of $pp$ interactions, a set of global event
requirements [31] is applied, which includes the requirement that the number
of hits in the SPD subdetector be less than 900. In between the first and
second stages of the software trigger, the alignment and calibration of the
detector is performed nearly in real-time [33] and updated constants are made
available for the trigger. The same alignment and calibration information is
propagated to the offline reconstruction, ensuring the consistency and high-
quality of the tracking and particle identification information between the
trigger and offline software. The identical performance of the online and
offline reconstruction offers the opportunity to perform physics analyses
directly using candidates reconstructed in the trigger [31, 34] as done in the
present analysis.

After the trigger, the $\mathchar 28935\relax$ candidates are further selected
offline by requiring two well identified muon candidates with transverse
momentum larger than $1{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and momentum
larger than $10{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The invariant mass of
the two muon candidates is required to be in the range
$8.5<M<11.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. Furthermore, the muons
are required to form a vertex with good fit quality.

The event-selection efficiencies are determined using simulated samples, which
are generated using Pythia 8 [35] with a specific LHCb configuration [36]. The
three $\mathchar 28935\relax$ states are assumed to be produced unpolarised in
this analysis. The decays of hadrons are described by EvtGen [37], in which
final-state radiation is simulated using Photos [38]. The Geant4 toolkit [39]
is used to describe the interactions of the generated particles with the
detector and its response.

##  3 Cross-section determination

The double-differential production cross-section times dimuon branching
fraction (${\cal B}$) is defined as

$\frac{\mathrm{d}^{2}\sigma}{\mathrm{d}y\mathrm{d}\mbox{$p_{\rm
T}$}}\times{\cal B}(\mathchar
28935\relax\rightarrow{\mu^{+}\mu^{-}})=\frac{N(\mbox{$p_{\rm
T}$},y)}{\mathcal{L}\times{\varepsilon_{\rm tot}}(\mbox{$p_{\rm
T}$},y)\times\Delta y\times\Delta\mbox{$p_{\rm T}$}},$ (1)

where $N(\mbox{$p_{\rm T}$},y)$ and ${\varepsilon_{\rm tot}}(\mbox{$p_{\rm
T}$},y)$ are respectively the signal yields and the total efficiencies for
$\mathchar 28935\relax{(1S)}$, $\mathchar 28935\relax{(2S)}$ and $\mathchar
28935\relax{(3S)}$ states in the given kinematic bin, $\mathcal{L}$ is the
integrated luminosity, and $\Delta\mbox{$p_{\rm T}$}$ and $\Delta y$ are the
bin widths.

To determine the signal yields in each kinematic bin, an extended unbinned
maximum-likelihood fit is performed to the dimuon invariant mass distribution
of the selected candidates. The dimuon mass distribution is described by three
Crystal Ball functions [40], one for each of the three $\mathchar 28935\relax$
states, and the combinatorial background is described by an exponential
function. In each bin, the tail parameters of the Crystal Ball functions are
fixed as done in the previous analysis [16]. The mass and mass resolution of
the $\mathchar 28935\relax{(1S)}$ state are free parameters. For the
$\mathchar 28935\relax{(2S)}$ and $\mathchar 28935\relax{(3S)}$ states, the
mass differences with respect to the $\mathchar 28935\relax{(1S)}$ state are
fixed to the current world averages [41] and the ratios of the mass
resolutions with respect to that of the $\mathchar 28935\relax{(1S)}$ state
are fixed to those in the simulated samples.

The invariant mass distribution of $\mathchar 28935\relax$ candidates after
all the selections in the range $0<\mbox{$p_{\rm
T}$}<30{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$ and the fit
results are shown in Fig. 1. The total signal yields are $397\,841\pm 796$ for
the $\mathchar 28935\relax{(1S)}$ state, $99\,790\pm 469$ for the $\mathchar
28935\relax{(2S)}$ state and $50\,677\pm 381$ for the $\mathchar
28935\relax{(3S)}$ state.

Figure 1: Dimuon invariant mass distribution of $\mathchar 28935\relax$
candidates with $0<\mbox{$p_{\rm T}$}<30{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$
and $2.0<y<4.5$. The fit result with the Crystal Ball functions plus an
exponential function is also shown. The black dots refer to the data, the blue
dashed line refers to the three signals and the green dotted line refers to
the background.

The total efficiency, ${\varepsilon_{\rm tot}}$, in each bin is computed as
the product of the detector geometrical acceptance and of the efficiencies
related to particle reconstruction, event selection, muon identification and
trigger. The detector acceptance, selection and trigger efficiencies are
calculated using simulation. The tracking efficiency is obtained from
simulation and corrected using a data-driven method [42] to improve its
modelling in simulation samples. The muon identification efficiency is
determined from simulation and calibrated with
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$
and $\phi\rightarrow{\mu^{+}\mu^{-}}$ data using a tag-and-probe method. The
calibration samples in data are not sufficient to give precise tracking and
muon identification efficiencies for the whole kinematic region.

##  4 Systematic uncertainties

Several sources of systematic uncertainties are associated with the
determination of the signal yields, efficiencies, and integrated luminosity.
They are reported in Table 1 and described below. The dominant uncertainties
are due to the trigger efficiency and the luminosity.

Source | $\mathchar 28935\relax{(1S)}$ | $\mathchar 28935\relax{(2S)}$ | $\mathchar 28935\relax{(3S)}$ | Comment
---|---|---|---|---
Fit models | 1.9 | 1.8 | 2.5 | Correlated
Simulation statistics | $0.4-4.6$ | $0.5-5.1$ | $0.5-4.4$ | Bin dependent
Global event requirements | 0.6 | 0.6 | 0.6 | Correlated
Trigger | $3.9-9.8$ | $3.9-9.8$ | $3.9-9.8$ | Bin dependent
Tracking | $(0.1-6.6)$ | $(0.2-6.4)$ | $(0.2-6.5)$ | Correlated
$\oplus(2\times 0.8)$ | $\oplus(2\times 0.8)$ | $\oplus(2\times 0.8)$
Muon identification | $0.1-7.9$ | $0.1-7.6$ | $0.2-8.5$ | Correlated
Vertexing | 0.2 | 0.2 | 0.2 | Correlated
Kinematic spectrum | $0.0-1.1$ | $0.0-2.2$ | $0.0-2.5$ | Bin dependent
Radiative tail | 1.0 | 1.0 | 1.0 | Correlated
Luminosity | 3.9 | 3.9 | 3.9 | Correlated
Total | $6.2-14.3$ | $6.2-14.6$ | $6.4-14.9$ | Correlated
Table 1: Summary of the relative systematic uncertainties (in $\%$) on the
$\mathchar 28935\relax$ production cross-sections times dimuon branching
fractions. Some of the uncertainties are correlated between intervals. For the
trigger, track reconstruction and muon identification efficiencies, the
uncertainties are larger in the high rapidity region. The uncertainties on the
tracking efficiency account for both the limited size of the control samples
(first parenthesis) and the impact of different multiplicity between data and
simulation on each track (second parenthesis).

The uncertainty related to the fit model predominantly originates from the
description of the signal tails caused by final-state radiation, and from the
description of the background line shape. The former is studied by using the
same fit model to describe the dimuon invariant-mass distribution of a mixed
sample in which the signal is from the full simulation, and the background is
generated with pseudoexperiments using the same shape and fraction as in the
data. The latter is studied by replacing the exponential function with a
second-order Chebyshev polynomial function. A combined relative uncertainty of
$1.9\%$ for the $\mathchar 28935\relax{(1S)}$ state, $1.8\%$ for the
$\mathchar 28935\relax{(2S)}$ state and $2.5\%$ for the $\mathchar
28935\relax{(3S)}$ state is assigned.

The efficiency of the global event requirements is found to be 100% in
simulation, and 99.4% in data, with negligible statistical uncertainty. The
difference, 0.6%, is assigned as systematic uncertainty.

The trigger efficiency uncertainty is computed using the same method as in the
7$\mathrm{\,Te\kern-1.00006ptV}$ and 8$\mathrm{\,Te\kern-1.00006ptV}$ analyses
[18]. The dimuon hardware-trigger efficiency is studied with events triggered
by the single-muon hardware trigger. The difference of this efficiency in data
and simulated samples divided by that in simulation is assigned as the
relative systematic uncertainty. The systematic uncertainty related to the
global event requirements applied in the single-muon trigger, as well as other
sources of uncertainties are assumed to be equal to those estimated in the
inclusive $b\bar{b}$ cross-section measurements at
7$\mathrm{\,Te\kern-1.00006ptV}$ and 13$\mathrm{\,Te\kern-1.00006ptV}$ [43].
In total, the systematic uncertainty coming from trigger efficiencies is
$3.9-9.8\%$ for the three $\mathchar 28935\relax$ states, depending on the
kinematic bin.

The tracking efficiencies in simulation are corrected with a data-driven
method using ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$ control samples. The number of SPD hits
distributions in simulated samples are weighted to improve the agreement with
data and an uncertainty of $0.8\%$ per track is assigned to account for a
different multiplicity between data and simulation. The tracking efficiencies
determined from simulated samples are corrected with the ratio of efficiencies
in data and simulation. The uncertainty due to the finite size of the control
samples is propagated to the final systematic uncertainty using a large number
of pseudoexperiments and is $0.1-6.6\%$ for the $\mathchar 28935\relax{(1S)}$
state, $0.2-6.4\%$ for the $\mathchar 28935\relax{(2S)}$ state and $0.2-6.5\%$
for the $\mathchar 28935\relax{(3S)}$ state, depending on the kinematic bin.
In total, the systematic uncertainty originating from the tracking efficiency
is $1.6-6.8\%$ for the $\mathchar 28935\relax{(1S)}$ state, $1.6-6.6\%$ for
the $\mathchar 28935\relax{(2S)}$ state and $1.6-6.7\%$ for the $\mathchar
28935\relax{(3S)}$ state, depending on the kinematic bin.

The muon identification efficiency is determined from simulation and
calibrated with data using a tag-and-probe method. The single-muon
identification efficiency is measured in intervals of $p$, $\eta$ and event
multiplicity. The statistical uncertainty due to the finite size of the
calibration sample is propagated to the final results using pseudoexperiments.
The uncertainty related to the kinematic binning scheme of the calibration
samples is studied by changing the bin size. The uncertainty due to the
kinematic correlations between the two muons, which is not considered in the
efficiency calculation, is studied with simulated samples. The correlation is
found to be negligible except for the most forward region, in which the two
muons from the $\mathchar 28935\relax$ decays have smaller opening angle. In
total, the systematic uncertainty assigned to the muon identification
efficiency is $0.1-7.9\%$ for the $\mathchar 28935\relax{(1S)}$ state,
$0.1-7.6\%$ for the $\mathchar 28935\relax{(2S)}$ state and $0.2-8.5\%$ for
the $\mathchar 28935\relax{(3S)}$ state, depending on the kinematic bin.

The systematic uncertainty on the signal efficiency of the vertex fit quality
requirement is studied by comparing data and simulation. A relative difference
of $0.2\%$ is assigned for the three $\mathchar 28935\relax$ states.

The kinematic distributions of $\mathchar 28935\relax$ mesons in simulation
and in data are slightly different within each kinematic bin due to the finite
bin size in $p_{\rm T}$ and $y$, causing differences in efficiencies. This
effect is studied by weighting the kinematic distributions of $\mathchar
28935\relax$ states in simulation to match the distributions in data. All
efficiencies are recalculated, and the relative differences of the total
efficiency between the new and the nominal results are assigned as systematic
uncertainties, which vary between $0.0-1.1\%$ for the $\mathchar
28935\relax{(1S)}$ state, $0.0-2.2\%$ for the $\mathchar 28935\relax{(2S)}$
state and $0.0-2.5\%$ for the $\mathchar 28935\relax{(3S)}$ state, depending
on the kinematic bin.

A systematic uncertainty of $1.0\%$ is assigned as a consequence of the
limited precision on the modelling of the final-state radiation in the
simulation, estimated as in the previous analysis [20].

The integrated luminosity is determined using the beam-gas imaging and van der
Meer scan methods [44]. A relative uncertainty of $3.9\%$ is assigned on the
luminosity and propagated to the cross-sections.

##  5 Results

###  5.1 Cross-sections

The double-differential cross-sections multiplied by dimuon branching
fractions for the $\mathchar 28935\relax{(1S)}$, $\mathchar 28935\relax{(2S)}$
and $\mathchar 28935\relax{(3S)}$ states are shown in Fig. 2. The
corresponding values are listed in Tables 2$-$4. By integrating the double-
differential results over $\mbox{$p_{\rm T}$}\;(y)$, the differential cross-
sections times dimuon branching fractions as functions of $y\;(\mbox{$p_{\rm
T}$})$ are shown in Fig. 3 for the three $\mathchar 28935\relax$ states, with
the theoretical predictions based on NRQCD [24] overlaid. The NRQCD
predictions are in agreement with the experimental data at high $p_{\rm T}$.

The total cross-sections multiplied by dimuon branching fractions for the
three states integrated over the ranges of $0<\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$ are measured to
be

$\displaystyle{\cal B}(\mathchar
28935\relax{(1S)}\rightarrow{\mu^{+}\mu^{-}})\times\sigma(\mathchar
28935\relax{(1S)},0<\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},2<y<4.5)$ $\displaystyle=4687\pm
10\pm 294~{}\rm\,pb,$ $\displaystyle{\cal B}(\mathchar
28935\relax{(2S)}\rightarrow{\mu^{+}\mu^{-}})\times\sigma(\mathchar
28935\relax{(2S)},0<\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},2<y<4.5)$
$\displaystyle=1134\pm\phantom{0}6\pm\phantom{0}71~{}\rm\,pb,$
$\displaystyle{\cal B}(\mathchar
28935\relax{(3S)}\rightarrow{\mu^{+}\mu^{-}})\times\sigma(\mathchar
28935\relax{(3S)},0<\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},2<y<4.5)$
$\displaystyle=\phantom{0}561\pm\phantom{0}4\pm\phantom{0}36~{}\rm\,pb,$

where the first uncertainty is statistical and the second is systematic. The
corresponding results as a function of $pp$ centre-of-mass energy are shown in
Fig. 4.

In this paper, results are obtained under the assumption of zero polarisation.
The effects of possible $\mathchar 28935\relax$ polarisation based on the LHCb
measurements [19] in $pp$ collisions at 7$\mathrm{\,Te\kern-1.00006ptV}$ and
8$\mathrm{\,Te\kern-1.00006ptV}$ are studied. The measurements show no large
transverse or longitudinal polarisation over the accessible phase-space
domain. The cross-sections increase up to $2.8\%$ for the three $\mathchar
28935\relax$ states when assuming the transverse polarisation of $\alpha=0.1$,
where $\alpha$ is the polarisation parameter in the helicity frame [45].

Figure 2: Double-differential cross-sections multiplied by dimuon branching
fractions as a function of $p_{\rm T}$ in intervals of $y$ for the (a)
$\mathchar 28935\relax{(1S)}$, (b) $\mathchar 28935\relax{(2S)}$ and (c)
$\mathchar 28935\relax{(3S)}$ mesons. Statistical and systematic uncertainties
are added in quadrature.

Figure 3: Differential cross-sections multiplied by dimuon branching fractions
for the $\mathchar 28935\relax{(1S)}$ (black solid squares), $\mathchar
28935\relax{(2S)}$ (red upward triangles) and $\mathchar 28935\relax{(3S)}$
(blue downward triangles) states (top) versus $p_{\rm T}$ integrated over $y$
between 2.0 and 4.5 and (bottom) versus $y$ integrated over $p_{\rm T}$ from 0
to $15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Statistical and systematic
uncertainties are added in quadrature. Predictions from NRQCD [24] for the
$\mathchar 28935\relax{(1S)}$ (black grid shading), $\mathchar
28935\relax{(2S)}$ (red grid shading) and $\mathchar 28935\relax{(3S)}$ (blue
grid shading) states are overlaid in the top plot.

Figure 4: The production cross-sections multiplied by dimuon branching
fractions integrated over $0<\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$ versus centre-of-
mass energy of $pp$ collisions for the $\mathchar 28935\relax{(1S)}$ (black
solid squares), $\mathchar 28935\relax{(2S)}$ (red upward triangles) and
$\mathchar 28935\relax{(3S)}$ (blue downward triangles) states. Each set of
measurements is offset by a multiplicative factor $m$, which is shown on the
plot. Statistical and systematic uncertainties are added in quadrature.

###  5.2 Cross-section ratios

The ratios of the differential production cross-sections multiplied by dimuon
branching fractions between $\mathchar 28935\relax{(2S)}$ and $\mathchar
28935\relax{(1S)}$, $R_{2S/1S}$, and that between $\mathchar
28935\relax{(3S)}$ and $\mathchar 28935\relax{(1S)}$, $R_{3S/1S}$, are shown
in Fig. 5.

In these ratios, the statistical uncertainties of the cross-sections and those
due to the finite size of the simulated samples are assumed to be
uncorrelated. The systematic uncertainties related to the signal yields and
the efficiencies of the global event requirements, the trigger and the
tracking are assumed to be 100$\%$ correlated between the different states.

Figure 5:  Ratios of double-differential cross-sections times dimuon branching
fractions for (a) $\mathchar 28935\relax{(2S)}$ to $\mathchar
28935\relax{(1S)}$ and (b) $\mathchar 28935\relax{(3S)}$ to $\mathchar
28935\relax{(1S)}$. Ratios of differential cross-sections times dimuon
branching fractions (c) versus $p_{\rm T}$ integrated over $y$ and (d) versus
$y$ integrated over $p_{\rm T}$ for $\mathchar 28935\relax{(2S)}$ to
$\mathchar 28935\relax{(1S)}$ (black solid squares) and $\mathchar
28935\relax{(3S)}$ to $\mathchar 28935\relax{(1S)}$ (red upward triangles).
Statistical and systematic uncertainties are added in quadrature.

The cross-sections times dimuon branching fractions measured at a centre-of-
mass energy of $13\mathrm{\,Te\kern-1.00006ptV}$ presented in this paper are
compared with the measurements at $8\mathrm{\,Te\kern-1.00006ptV}$ [18]. The
ratios of double-differential cross-sections between 13 TeV and 8 TeV
measurements, $R_{13/8}$, are shown in Fig. 6. The corresponding values are
listed in Tables 5$-$7. The cross-section ratios between
$13\mathrm{\,Te\kern-1.00006ptV}$ and $8\mathrm{\,Te\kern-1.00006ptV}$ versus
$p_{\rm T}$ integrated over $y$, and versus $y$ integrated over $p_{\rm T}$
are shown in Fig. 7.

In the ratios, the systematic uncertainties originating from the fit model,
global event requirements and kinematic spectrum are assumed to be
uncorrelated. Those from trigger, muon identification, tracking correction and
luminosity are partially correlated. The systematic uncertainty from final-
state radiation is assumed to be $100\%$ correlated.

Figure 6: Ratios of double-differential cross-sections between 13 TeV and 8
TeV measurements versus $p_{\rm T}$ in intervals of $y$ for the (a) $\mathchar
28935\relax{(1S)}$, (b) $\mathchar 28935\relax{(2S)}$ and (c) $\mathchar
28935\relax{(3S)}$ states. Statistical and systematic uncertainties are added
in quadrature.

Figure 7: Ratios of differential cross-sections between 13 TeV and 8 TeV
measurements (top) versus $p_{\rm T}$ integrated over $y$ and (bottom) versus
$y$ integrated over $p_{\rm T}$ for the $\mathchar 28935\relax{(1S)}$ (black
solid squares), $\mathchar 28935\relax{(2S)}$ (red upward triangles) and
$\mathchar 28935\relax{(3S)}$ (blue downward triangles) states. Statistical
and systematic uncertainties are added in quadrature.

##  6 Conclusion

A study of the production of $\mathchar 28935\relax{(1S)}$, $\mathchar
28935\relax{(2S)}$ and $\mathchar 28935\relax{(3S)}$ mesons in proton-proton
collisions at the centre-of-mass energy
$\sqrt{s}=13\mathrm{\,Te\kern-1.00006ptV}$ is reported. The differential
cross-sections times dimuon branching fractions of $\mathchar 28935\relax$
mesons are measured as functions of $p_{\rm T}$ and $y$, in the kinematic
range $0<\mbox{$p_{\rm T}$}<30{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$2.0<y<4.5$. The production cross-section ratios of $\mathchar
28935\relax{(2S)}$ and $\mathchar 28935\relax{(3S)}$ mesons with respect to
the $\mathchar 28935\relax{(1S)}$ meson are given in intervals of $p_{\rm T}$
and $y$. The ratios of the production cross-sections with respect to those
measured at $\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$ are also presented.

The results of differential cross-sections times dimuon branching fractions as
a function of $p_{\rm T}$ integrated over $y$ between 2.0 and 4.5 are compared
with predictions based on NRQCD. These predictions provide a good description
of the experimental data at high $p_{\rm T}$ for all the three $\mathchar
28935\relax$ states.

$\mbox{$p_{\rm T}$}\left[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}\right]$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
0$-$1 | $94.75\pm 2.44\pm 6.27$ | $89.26\pm 1.65\pm 5.65$ | $82.21\pm 1.65\pm 5.63$ | $70.76\pm 1.55\pm 6.10$ | $49.85\pm 1.74\pm 5.94$
1$-$2 | $233.67\pm 3.83\pm 15.52$ | $236.95\pm 2.72\pm 14.94$ | $216.85\pm 2.61\pm 14.87$ | $177.87\pm 2.47\pm 16.12$ | $124.19\pm 2.68\pm 14.27$
2$-$3 | $313.67\pm 4.40\pm 20.72$ | $303.07\pm 3.14\pm 18.95$ | $274.80\pm 2.89\pm 18.39$ | $240.07\pm 2.88\pm 20.28$ | $151.23\pm 2.94\pm 20.38$
3$-$4 | $330.78\pm 4.51\pm 22.11$ | $313.85\pm 3.22\pm 19.58$ | $281.00\pm 2.90\pm 18.17$ | $240.17\pm 2.84\pm 18.96$ | $156.12\pm 3.04\pm 20.26$
4$-$5 | $308.47\pm 4.36\pm 20.08$ | $285.77\pm 3.09\pm 18.01$ | $251.96\pm 2.70\pm 16.26$ | $215.22\pm 2.71\pm 17.63$ | $147.40\pm 3.00\pm 18.69$
5$-$6 | $261.01\pm 4.05\pm 17.44$ | $242.35\pm 2.86\pm 15.04$ | $211.58\pm 2.50\pm 13.80$ | $176.79\pm 2.43\pm 13.91$ | $118.96\pm 2.68\pm 16.00$
6$-$7 | $219.98\pm 3.74\pm 13.90$ | $194.56\pm 2.51\pm 12.11$ | $172.49\pm 2.20\pm 11.10$ | $138.96\pm 2.16\pm 11.22$ | $92.48\pm 2.41\pm 12.40$
7$-$8 | $175.08\pm 3.34\pm 11.48$ | $156.34\pm 2.18\pm 9.76$ | $136.22\pm 1.90\pm 8.62$ | $107.01\pm 1.87\pm 8.15$ | $67.50\pm 2.05\pm 8.26$
8$-$9 | $134.33\pm 2.86\pm 8.69$ | $119.99\pm 1.86\pm 7.49$ | $103.59\pm 1.58\pm 6.65$ | $79.26\pm 1.57\pm 6.62$ | $51.49\pm 1.85\pm 6.58$
9$-$10 | $101.78\pm 2.46\pm 6.58$ | $89.18\pm 1.54\pm 5.63$ | $76.04\pm 1.34\pm 4.98$ | $59.62\pm 1.33\pm 5.06$ | $38.61\pm 1.59\pm 5.52$
10$-$11 | $81.97\pm 2.14\pm 5.57$ | $72.34\pm 1.34\pm 4.54$ | $59.17\pm 1.16\pm 3.92$ | $44.99\pm 1.13\pm 3.88$ | $26.02\pm 1.30\pm 3.16$
11$-$12 | $60.06\pm 1.78\pm 4.12$ | $53.65\pm 1.14\pm 3.38$ | $44.40\pm 0.99\pm 2.96$ | $34.43\pm 0.97\pm 2.98$ | $21.94\pm 1.17\pm 2.79$
12$-$13 | $46.88\pm 1.54\pm 3.25$ | $39.55\pm 0.98\pm 2.50$ | $31.71\pm 0.83\pm 2.12$ | $24.76\pm 0.82\pm 2.24$ | $13.07\pm 0.93\pm 1.69$
13$-$14 | $34.64\pm 1.30\pm 2.44$ | $28.00\pm 0.79\pm 1.78$ | $23.81\pm 0.71\pm 1.61$ | $18.20\pm 0.70\pm 1.67$ | $9.77\pm 0.53\pm 1.24$
14$-$15 | $26.20\pm 1.10\pm 1.85$ | $22.15\pm 0.68\pm 1.42$ | $17.87\pm 0.61\pm 1.23$ | $14.18\pm 0.60\pm 1.30$
15$-$16 | $20.81\pm 0.97\pm 1.49$ | $16.20\pm 0.58\pm 1.05$ | $13.14\pm 0.51\pm 0.91$ | $10.07\pm 0.51\pm 1.01$ | $3.48\pm 0.20\pm 0.44$
16$-$17 | $17.64\pm 0.87\pm 1.27$ | $13.17\pm 0.53\pm 0.87$ | $10.41\pm 0.46\pm 0.75$ | $7.76\pm 0.46\pm 0.81$
17$-$18 | $12.29\pm 0.65\pm 0.89$ | $10.13\pm 0.45\pm 0.68$ | $8.35\pm 0.41\pm 0.61$ | $5.83\pm 0.39\pm 0.62$
18$-$19 | $8.50\pm 0.53\pm 0.63$ | $8.33\pm 0.42\pm 0.58$ | $5.82\pm 0.35\pm 0.44$ | $4.88\pm 0.37\pm 0.54$
19$-$20 | $7.57\pm 0.50\pm 0.58$ | $6.19\pm 0.34\pm 0.43$ | $5.15\pm 0.32\pm 0.39$ | $3.90\pm 0.31\pm 0.43$
20$-$21 | $5.04\pm 0.29\pm 0.37$ | $4.47\pm 0.21\pm 0.31$ | $3.53\pm 0.18\pm 0.27$ | $1.48\pm 0.09\pm 0.17$ | $0.54\pm 0.06\pm 0.07$
21$-$22
22$-$23 | $3.52\pm 0.24\pm 0.27$ | $2.86\pm 0.17\pm 0.21$ | $2.06\pm 0.14\pm 0.17$
23$-$24
24$-$25 | $2.06\pm 0.17\pm 0.16$ | $1.60\pm 0.12\pm 0.12$ | $1.49\pm 0.12\pm 0.13$
25$-$26 | $0.48\pm 0.05\pm 0.06$
26$-$27 | $1.40\pm 0.10\pm 0.11$ | $1.16\pm 0.10\pm 0.10$ | $0.67\pm 0.06\pm 0.06$
27$-$28
28$-$29 | $0.82\pm 0.09\pm 0.07$
29$-$30
Table 2: Double-differential cross-sections times dimuon branching fraction in
different bins of $p_{\rm T}$ and $y$ for $\mathchar 28935\relax{(1S)}$ (in
$\rm\,pb$). The first uncertainty is statistical and the second is systematic.

$\mbox{$p_{\rm T}$}\left[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}\right]$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
0$-$1 | $19.09\pm 1.26\pm 1.29$ | $17.48\pm 0.87\pm 1.11$ | $16.64\pm 0.92\pm 1.14$ | $14.71\pm 0.83\pm 1.26$ | $8.43\pm 0.79\pm 1.02$
1$-$2 | $51.52\pm 2.06\pm 3.43$ | $47.02\pm 1.45\pm 2.96$ | $40.56\pm 1.42\pm 2.77$ | $36.04\pm 1.33\pm 3.25$ | $25.69\pm 1.38\pm 3.04$
2$-$3 | $65.75\pm 2.33\pm 4.33$ | $58.61\pm 1.65\pm 3.66$ | $57.16\pm 1.63\pm 3.85$ | $47.30\pm 1.52\pm 4.04$ | $31.50\pm 1.49\pm 4.31$
3$-$4 | $71.64\pm 2.44\pm 4.76$ | $66.47\pm 1.78\pm 4.14$ | $62.67\pm 1.65\pm 4.06$ | $53.90\pm 1.59\pm 4.38$ | $30.28\pm 1.52\pm 4.01$
4$-$5 | $68.54\pm 2.36\pm 4.43$ | $64.62\pm 1.75\pm 4.06$ | $57.78\pm 1.53\pm 3.72$ | $48.37\pm 1.50\pm 4.04$ | $35.79\pm 1.65\pm 4.62$
5$-$6 | $61.05\pm 2.23\pm 4.05$ | $61.03\pm 1.68\pm 3.78$ | $52.15\pm 1.45\pm 3.39$ | $41.41\pm 1.37\pm 3.31$ | $29.36\pm 1.54\pm 3.96$
6$-$7 | $59.77\pm 2.22\pm 3.78$ | $49.55\pm 1.50\pm 3.08$ | $43.04\pm 1.29\pm 2.76$ | $36.43\pm 1.26\pm 2.98$ | $23.17\pm 1.39\pm 3.17$
7$-$8 | $46.04\pm 1.94\pm 3.03$ | $42.95\pm 1.32\pm 2.68$ | $37.01\pm 1.12\pm 2.34$ | $29.84\pm 1.14\pm 2.33$ | $19.00\pm 1.25\pm 2.35$
8$-$9 | $37.33\pm 1.76\pm 2.43$ | $34.72\pm 1.14\pm 2.16$ | $29.41\pm 0.95\pm 1.88$ | $23.17\pm 0.97\pm 1.99$ | $14.44\pm 1.10\pm 1.91$
9$-$10 | $30.18\pm 1.52\pm 1.98$ | $27.93\pm 0.98\pm 1.76$ | $23.81\pm 0.81\pm 1.57$ | $19.29\pm 0.84\pm 1.64$ | $10.82\pm 0.92\pm 1.57$
10$-$11 | $23.97\pm 1.32\pm 1.66$ | $21.65\pm 0.83\pm 1.37$ | $18.12\pm 0.71\pm 1.20$ | $14.81\pm 0.71\pm 1.27$ | $10.55\pm 0.91\pm 1.33$
11$-$12 | $19.99\pm 1.17\pm 1.41$ | $16.51\pm 0.69\pm 1.04$ | $14.06\pm 0.60\pm 0.94$ | $10.44\pm 0.59\pm 0.93$ | $6.32\pm 0.76\pm 0.81$
12$-$13 | $16.85\pm 1.03\pm 1.19$ | $14.30\pm 0.61\pm 0.90$ | $10.38\pm 0.51\pm 0.71$ | $8.30\pm 0.52\pm 0.75$ | $4.46\pm 0.64\pm 0.57$
13$-$14 | $12.67\pm 0.94\pm 0.92$ | $10.57\pm 0.53\pm 0.67$ | $7.96\pm 0.44\pm 0.54$ | $6.55\pm 0.44\pm 0.62$ | $4.16\pm 0.40\pm 0.53$
14$-$15 | $9.61\pm 0.75\pm 0.71$ | $8.29\pm 0.46\pm 0.53$ | $7.27\pm 0.41\pm 0.51$ | $5.07\pm 0.39\pm 0.47$
15$-$16 | $7.93\pm 0.66\pm 0.58$ | $6.76\pm 0.40\pm 0.44$ | $5.58\pm 0.35\pm 0.39$ | $3.43\pm 0.34\pm 0.35$ | $1.55\pm 0.15\pm 0.19$
16$-$17 | $5.82\pm 0.55\pm 0.43$ | $4.85\pm 0.34\pm 0.32$ | $4.14\pm 0.31\pm 0.30$ | $2.39\pm 0.27\pm 0.25$
17$-$18 | $4.77\pm 0.48\pm 0.37$ | $3.43\pm 0.28\pm 0.23$ | $3.26\pm 0.27\pm 0.24$ | $2.44\pm 0.27\pm 0.27$
18$-$19 | $4.07\pm 0.42\pm 0.31$ | $3.53\pm 0.28\pm 0.24$ | $2.38\pm 0.23\pm 0.18$ | $1.64\pm 0.23\pm 0.18$
19$-$20 | $3.84\pm 0.39\pm 0.31$ | $2.88\pm 0.25\pm 0.20$ | $1.95\pm 0.22\pm 0.15$ | $1.58\pm 0.20\pm 0.19$
20$-$21 | $2.05\pm 0.20\pm 0.16$ | $1.89\pm 0.14\pm 0.13$ | $1.65\pm 0.13\pm 0.13$ | $0.83\pm 0.07\pm 0.09$ | $0.27\pm 0.05\pm 0.04$
21$-$22
22$-$23 | $1.77\pm 0.18\pm 0.14$ | $1.10\pm 0.11\pm 0.08$ | $0.78\pm 0.09\pm 0.06$
23$-$24
24$-$25 | $0.85\pm 0.12\pm 0.07$ | $0.78\pm 0.09\pm 0.06$ | $0.63\pm 0.08\pm 0.05$
25$-$26 | $0.30\pm 0.05\pm 0.04$
26$-$27 | $0.47\pm 0.06\pm 0.04$ | $0.61\pm 0.08\pm 0.05$ | $0.31\pm 0.04\pm 0.03$
27$-$28
28$-$29 | $0.49\pm 0.07\pm 0.04$
29$-$30
Table 3: Double-differential cross-sections times dimuon branching fraction in
different bins of $p_{\rm T}$ and $y$ for $\mathchar 28935\relax{(2S)}$ (in
$\rm\,pb$). The first uncertainty is statistical and the second is systematic.

$\mbox{$p_{\rm T}$}\left[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}\right]$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
0$-$1 | $7.37\pm 0.91\pm 0.51$ | $7.54\pm 0.66\pm 0.50$ | $7.41\pm 0.78\pm 0.52$ | $6.12\pm 0.64\pm 0.55$ | $4.94\pm 0.67\pm 0.62$
1$-$2 | $22.47\pm 1.58\pm 1.54$ | $19.32\pm 1.10\pm 1.26$ | $16.34\pm 1.13\pm 1.16$ | $15.91\pm 1.05\pm 1.48$ | $10.74\pm 0.96\pm 1.35$
2$-$3 | $27.76\pm 1.75\pm 1.90$ | $28.45\pm 1.32\pm 1.84$ | $25.14\pm 1.32\pm 1.74$ | $21.13\pm 1.21\pm 1.85$ | $13.83\pm 1.12\pm 1.92$
3$-$4 | $29.69\pm 1.81\pm 2.04$ | $32.38\pm 1.42\pm 2.09$ | $27.69\pm 1.31\pm 1.86$ | $22.49\pm 1.24\pm 1.88$ | $15.97\pm 1.22\pm 2.17$
4$-$5 | $32.80\pm 1.85\pm 2.20$ | $32.05\pm 1.42\pm 2.09$ | $24.71\pm 1.19\pm 1.65$ | $22.72\pm 1.19\pm 1.94$ | $14.63\pm 1.21\pm 1.91$
5$-$6 | $32.21\pm 1.81\pm 2.21$ | $30.17\pm 1.34\pm 1.94$ | $26.25\pm 1.16\pm 1.77$ | $20.10\pm 1.10\pm 1.69$ | $13.96\pm 1.18\pm 1.96$
6$-$7 | $27.96\pm 1.74\pm 1.82$ | $26.21\pm 1.23\pm 1.69$ | $22.66\pm 1.06\pm 1.51$ | $18.97\pm 1.03\pm 1.61$ | $13.34\pm 1.16\pm 1.87$
7$-$8 | $25.34\pm 1.62\pm 1.71$ | $20.59\pm 1.05\pm 1.33$ | $20.17\pm 0.90\pm 1.32$ | $16.09\pm 0.93\pm 1.28$ | $10.90\pm 1.05\pm 1.38$
8$-$9 | $21.21\pm 1.45\pm 1.42$ | $17.63\pm 0.92\pm 1.14$ | $16.74\pm 0.78\pm 1.11$ | $11.39\pm 0.77\pm 1.01$ | $8.73\pm 0.96\pm 1.14$
9$-$10 | $18.24\pm 1.27\pm 1.22$ | $15.46\pm 0.81\pm 1.01$ | $13.48\pm 0.67\pm 0.92$ | $9.65\pm 0.65\pm 0.85$ | $6.29\pm 0.86\pm 0.94$
10$-$11 | $14.77\pm 1.17\pm 1.04$ | $11.39\pm 0.67\pm 0.74$ | $9.99\pm 0.57\pm 0.69$ | $7.96\pm 0.57\pm 0.70$ | $4.96\pm 0.69\pm 0.62$
11$-$12 | $11.48\pm 0.99\pm 0.82$ | $10.66\pm 0.59\pm 0.70$ | $9.00\pm 0.52\pm 0.62$ | $5.57\pm 0.46\pm 0.49$ | $4.04\pm 0.69\pm 0.52$
12$-$13 | $8.45\pm 0.84\pm 0.61$ | $8.69\pm 0.53\pm 0.57$ | $7.29\pm 0.44\pm 0.51$ | $5.45\pm 0.43\pm 0.49$ | $3.39\pm 0.59\pm 0.46$
13$-$14 | $5.67\pm 0.69\pm 0.41$ | $7.15\pm 0.45\pm 0.47$ | $5.63\pm 0.38\pm 0.40$ | $4.55\pm 0.40\pm 0.43$ | $2.03\pm 0.32\pm 0.26$
14$-$15 | $5.70\pm 0.64\pm 0.42$ | $5.28\pm 0.38\pm 0.35$ | $3.68\pm 0.31\pm 0.26$ | $3.49\pm 0.35\pm 0.34$
15$-$16 | $5.11\pm 0.57\pm 0.38$ | $4.47\pm 0.35\pm 0.30$ | $3.56\pm 0.30\pm 0.26$ | $2.37\pm 0.29\pm 0.24$ | $0.85\pm 0.14\pm 0.11$
16$-$17 | $5.17\pm 0.53\pm 0.39$ | $3.08\pm 0.29\pm 0.21$ | $2.87\pm 0.27\pm 0.21$ | $1.82\pm 0.25\pm 0.20$
17$-$18 | $3.22\pm 0.44\pm 0.25$ | $2.81\pm 0.26\pm 0.19$ | $2.03\pm 0.23\pm 0.15$ | $1.54\pm 0.23\pm 0.16$
18$-$19 | $3.09\pm 0.38\pm 0.25$ | $2.46\pm 0.24\pm 0.17$ | $1.67\pm 0.21\pm 0.13$ | $1.23\pm 0.22\pm 0.14$
19$-$20 | $2.34\pm 0.33\pm 0.19$ | $1.65\pm 0.19\pm 0.12$ | $1.34\pm 0.19\pm 0.11$ | $0.85\pm 0.16\pm 0.10$
20$-$21 | $1.29\pm 0.17\pm 0.10$ | $1.35\pm 0.12\pm 0.09$ | $1.17\pm 0.11\pm 0.09$ | $0.60\pm 0.06\pm 0.07$ | $0.21\pm 0.05\pm 0.03$
21$-$22
22$-$23 | $0.89\pm 0.14\pm 0.07$ | $1.06\pm 0.11\pm 0.08$ | $0.83\pm 0.10\pm 0.07$
23$-$24
24$-$25 | $0.77\pm 0.11\pm 0.06$ | $0.46\pm 0.07\pm 0.03$ | $0.51\pm 0.07\pm 0.04$
25$-$26 | $0.16\pm 0.04\pm 0.02$
26$-$27 | $0.44\pm 0.06\pm 0.04$ | $0.41\pm 0.07\pm 0.03$ | $0.23\pm 0.04\pm 0.02$
27$-$28
28$-$29 | $0.32\pm 0.06\pm 0.03$
29$-$30
Table 4: Double-differential cross-sections times dimuon branching fraction in
different bins of $p_{\rm T}$ and $y$ for $\mathchar 28935\relax{(3S)}$ (in
$\rm\,pb$). The first uncertainty is statistical and the second is systematic.

$\mbox{$p_{\rm T}$}\left[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}\right]$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
0$-$1 | $1.231\pm 0.081$ | $1.200\pm 0.071$ | $1.257\pm 0.081$ | $1.346\pm 0.109$ | $1.578\pm 0.188$
1$-$2 | $1.187\pm 0.072$ | $1.256\pm 0.070$ | $1.330\pm 0.082$ | $1.354\pm 0.113$ | $1.568\pm 0.174$
2$-$3 | $1.256\pm 0.075$ | $1.241\pm 0.069$ | $1.325\pm 0.080$ | $1.484\pm 0.114$ | $1.575\pm 0.203$
3$-$4 | $1.299\pm 0.078$ | $1.282\pm 0.070$ | $1.379\pm 0.080$ | $1.512\pm 0.109$ | $1.704\pm 0.211$
4$-$5 | $1.345\pm 0.079$ | $1.334\pm 0.074$ | $1.420\pm 0.082$ | $1.555\pm 0.116$ | $1.919\pm 0.235$
5$-$6 | $1.393\pm 0.085$ | $1.368\pm 0.076$ | $1.455\pm 0.085$ | $1.616\pm 0.117$ | $1.894\pm 0.245$
6$-$7 | $1.484\pm 0.087$ | $1.408\pm 0.078$ | $1.540\pm 0.089$ | $1.654\pm 0.124$ | $1.993\pm 0.258$
7$-$8 | $1.544\pm 0.095$ | $1.483\pm 0.083$ | $1.591\pm 0.091$ | $1.700\pm 0.120$ | $1.912\pm 0.231$
8$-$9 | $1.566\pm 0.096$ | $1.504\pm 0.086$ | $1.649\pm 0.096$ | $1.709\pm 0.133$ | $2.171\pm 0.279$
9$-$10 | $1.561\pm 0.098$ | $1.484\pm 0.086$ | $1.616\pm 0.098$ | $1.822\pm 0.147$ | $2.453\pm 0.353$
10$-$11 | $1.633\pm 0.112$ | $1.637\pm 0.097$ | $1.723\pm 0.106$ | $1.899\pm 0.160$ | $2.592\pm 0.343$
11$-$12 | $1.614\pm 0.112$ | $1.644\pm 0.098$ | $1.759\pm 0.113$ | $1.941\pm 0.165$ | $3.396\pm 0.476$
12$-$13 | $1.702\pm 0.122$ | $1.648\pm 0.102$ | $1.752\pm 0.115$ | $1.959\pm 0.179$ | $2.712\pm 0.421$
13$-$14 | $1.691\pm 0.130$ | $1.540\pm 0.099$ | $1.777\pm 0.123$ | $2.026\pm 0.194$ | $3.973\pm 0.589$
14$-$15 | $1.660\pm 0.136$ | $1.651\pm 0.109$ | $1.812\pm 0.130$ | $2.188\pm 0.217$
15$-$16 | $1.763\pm 0.150$ | $1.573\pm 0.110$ | $1.805\pm 0.136$ | $2.219\pm 0.243$ | $4.978\pm 0.794$
16$-$17 | $2.018\pm 0.174$ | $1.790\pm 0.132$ | $1.865\pm 0.151$ | $2.168\pm 0.260$
17$-$18 | $1.834\pm 0.170$ | $1.790\pm 0.138$ | $2.131\pm 0.183$ | $2.332\pm 0.296$
18$-$19 | $1.529\pm 0.150$ | $1.984\pm 0.166$ | $1.877\pm 0.180$ | $2.679\pm 0.376$
19$-$20 | $1.874\pm 0.197$ | $1.854\pm 0.164$ | $2.044\pm 0.205$ | $2.598\pm 0.369$
20$-$21 | $1.853\pm 0.176$ | $1.912\pm 0.157$ | $2.088\pm 0.196$ | $2.865\pm 0.369$ |
21$-$22 |
22$-$23 | $2.119\pm 0.230$ | $2.071\pm 0.191$ | $2.212\pm 0.244$ |
23$-$24 |
24$-$25 | $1.664\pm 0.210$ | $1.863\pm 0.216$ | $2.652\pm 0.335$ |
25$-$26 |  |
26$-$27 | $2.340\pm 0.274$ | $2.059\pm 0.262$ | $2.205\pm 0.289$ |  |
27$-$28 |  |
28$-$29 | $2.096\pm 0.326$ |  |
29$-$30 |  |
Table 5: The cross-section ratios between 13 TeV and 8 TeV in different bins
of $p_{\rm T}$ and $y$ for $\mathchar 28935\relax{(1S)}$.

$\mbox{$p_{\rm T}$}\left[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}\right]$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
0$-$1 | $1.177\pm 0.114$ | $1.106\pm 0.086$ | $1.177\pm 0.100$ | $1.318\pm 0.128$ | $1.194\pm 0.185$
1$-$2 | $1.182\pm 0.086$ | $1.150\pm 0.073$ | $1.155\pm 0.082$ | $1.260\pm 0.115$ | $1.560\pm 0.201$
2$-$3 | $1.187\pm 0.082$ | $1.105\pm 0.068$ | $1.267\pm 0.085$ | $1.329\pm 0.112$ | $1.454\pm 0.203$
3$-$4 | $1.198\pm 0.083$ | $1.177\pm 0.071$ | $1.348\pm 0.086$ | $1.433\pm 0.116$ | $1.426\pm 0.196$
4$-$5 | $1.251\pm 0.085$ | $1.243\pm 0.076$ | $1.390\pm 0.087$ | $1.460\pm 0.121$ | $1.864\pm 0.252$
5$-$6 | $1.299\pm 0.092$ | $1.363\pm 0.084$ | $1.436\pm 0.093$ | $1.524\pm 0.124$ | $1.777\pm 0.249$
6$-$7 | $1.472\pm 0.106$ | $1.330\pm 0.084$ | $1.433\pm 0.093$ | $1.636\pm 0.138$ | $1.847\pm 0.268$
7$-$8 | $1.379\pm 0.102$ | $1.446\pm 0.092$ | $1.559\pm 0.101$ | $1.699\pm 0.140$ | $1.878\pm 0.260$
8$-$9 | $1.390\pm 0.108$ | $1.473\pm 0.097$ | $1.605\pm 0.106$ | $1.689\pm 0.152$ | $1.978\pm 0.308$
9$-$10 | $1.485\pm 0.120$ | $1.518\pm 0.102$ | $1.667\pm 0.115$ | $1.834\pm 0.167$ | $2.173\pm 0.370$
10$-$11 | $1.470\pm 0.130$ | $1.553\pm 0.110$ | $1.589\pm 0.115$ | $1.913\pm 0.184$ | $2.899\pm 0.473$
11$-$12 | $1.526\pm 0.142$ | $1.538\pm 0.111$ | $1.694\pm 0.132$ | $1.775\pm 0.185$ | $2.848\pm 0.545$
12$-$13 | $1.709\pm 0.162$ | $1.707\pm 0.126$ | $1.627\pm 0.132$ | $1.845\pm 0.203$ | $3.014\pm 0.675$
13$-$14 | $1.612\pm 0.173$ | $1.662\pm 0.133$ | $1.625\pm 0.144$ | $1.974\pm 0.233$ | $4.958\pm 0.959$
14$-$15 | $1.607\pm 0.186$ | $1.671\pm 0.143$ | $1.986\pm 0.175$ | $1.995\pm 0.257$
15$-$16 | $1.681\pm 0.201$ | $1.666\pm 0.147$ | $1.964\pm 0.192$ | $1.863\pm 0.268$ | $4.896\pm 1.034$
16$-$17 | $1.541\pm 0.196$ | $1.639\pm 0.161$ | $1.897\pm 0.201$ | $1.754\pm 0.294$
17$-$18 | $1.819\pm 0.253$ | $1.442\pm 0.155$ | $1.894\pm 0.221$ | $2.348\pm 0.402$
18$-$19 | $1.768\pm 0.246$ | $1.918\pm 0.210$ | $1.713\pm 0.215$ | $2.098\pm 0.414$
19$-$20 | $2.158\pm 0.307$ | $2.073\pm 0.243$ | $2.110\pm 0.317$ | $2.507\pm 0.494$
20$-$21 | $1.529\pm 0.208$ | $1.749\pm 0.184$ | $2.396\pm 0.284$ | $3.504\pm 0.536$ |
21$-$22 |
22$-$23 | $2.323\pm 0.349$ | $1.720\pm 0.229$ | $1.914\pm 0.304$ |
23$-$24 |
24$-$25 | $1.353\pm 0.244$ | $1.923\pm 0.288$ | $2.269\pm 0.387$ |
25$-$26 |  |
26$-$27 | $1.710\pm 0.312$ | $2.088\pm 0.364$ | $2.294\pm 0.420$ |  |
27$-$28 |  |
28$-$29 | $2.538\pm 0.517$ |  |
29$-$30 |  |
Table 6: The cross-section ratios between 13 TeV and 8 TeV in different bins
of $p_{\rm T}$ and $y$ for $\mathchar 28935\relax{(2S)}$.

$\mbox{$p_{\rm T}$}\left[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}\right]$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
0$-$1 | $1.117\pm 0.167$ | $1.145\pm 0.126$ | $1.362\pm 0.174$ | $1.265\pm 0.173$ | $1.681\pm 0.328$
1$-$2 | $1.372\pm 0.135$ | $1.143\pm 0.095$ | $1.138\pm 0.109$ | $1.364\pm 0.152$ | $1.566\pm 0.251$
2$-$3 | $1.294\pm 0.119$ | $1.275\pm 0.096$ | $1.389\pm 0.116$ | $1.397\pm 0.139$ | $1.399\pm 0.223$
3$-$4 | $1.193\pm 0.107$ | $1.349\pm 0.099$ | $1.386\pm 0.108$ | $1.409\pm 0.136$ | $1.702\pm 0.264$
4$-$5 | $1.443\pm 0.124$ | $1.403\pm 0.103$ | $1.299\pm 0.101$ | $1.475\pm 0.141$ | $1.633\pm 0.260$
5$-$6 | $1.601\pm 0.139$ | $1.477\pm 0.109$ | $1.539\pm 0.118$ | $1.514\pm 0.148$ | $1.896\pm 0.308$
6$-$7 | $1.495\pm 0.135$ | $1.524\pm 0.115$ | $1.539\pm 0.119$ | $1.676\pm 0.165$ | $2.131\pm 0.351$
7$-$8 | $1.618\pm 0.149$ | $1.376\pm 0.108$ | $1.643\pm 0.125$ | $1.680\pm 0.160$ | $2.198\pm 0.355$
8$-$9 | $1.593\pm 0.152$ | $1.438\pm 0.116$ | $1.704\pm 0.132$ | $1.565\pm 0.169$ | $2.494\pm 0.447$
9$-$10 | $1.724\pm 0.170$ | $1.607\pm 0.130$ | $1.689\pm 0.138$ | $1.609\pm 0.176$ | $2.538\pm 0.533$
10$-$11 | $1.797\pm 0.199$ | $1.431\pm 0.125$ | $1.566\pm 0.136$ | $1.645\pm 0.186$ | $2.253\pm 0.474$
11$-$12 | $1.755\pm 0.210$ | $1.687\pm 0.143$ | $1.808\pm 0.166$ | $1.610\pm 0.196$ | $2.930\pm 0.689$
12$-$13 | $1.451\pm 0.184$ | $1.639\pm 0.146$ | $1.870\pm 0.172$ | $1.933\pm 0.239$ | $3.684\pm 0.985$
13$-$14 | $1.177\pm 0.174$ | $1.727\pm 0.158$ | $1.852\pm 0.189$ | $2.167\pm 0.291$ | $3.385\pm 0.851$
14$-$15 | $1.478\pm 0.218$ | $1.580\pm 0.163$ | $1.574\pm 0.175$ | $2.100\pm 0.311$
15$-$16 | $1.680\pm 0.245$ | $1.848\pm 0.199$ | $1.980\pm 0.231$ | $1.941\pm 0.328$ | $4.640\pm 1.254$
16$-$17 | $2.348\pm 0.337$ | $1.587\pm 0.189$ | $1.888\pm 0.232$ | $2.167\pm 0.419$
17$-$18 | $1.809\pm 0.315$ | $1.824\pm 0.227$ | $1.827\pm 0.262$ | $1.913\pm 0.377$
18$-$19 | $1.958\pm 0.319$ | $2.109\pm 0.274$ | $1.937\pm 0.304$ | $1.977\pm 0.460$
19$-$20 | $1.987\pm 0.357$ | $1.696\pm 0.244$ | $2.075\pm 0.369$ | $2.116\pm 0.536$
20$-$21 | $1.532\pm 0.254$ | $1.846\pm 0.234$ | $2.536\pm 0.348$ | $3.255\pm 0.582$ |
21$-$22 |
22$-$23 | $1.744\pm 0.346$ | $2.294\pm 0.313$ | $2.580\pm 0.412$ |
23$-$24 |
24$-$25 | $2.257\pm 0.466$ | $1.510\pm 0.285$ | $2.408\pm 0.461$ |
25$-$26 |  |
26$-$27 | $1.700\pm 0.316$ | $2.215\pm 0.459$ | $2.339\pm 0.495$ |  |
27$-$28 |  |
28$-$29 | $2.629\pm 0.654$ |  |
29$-$30 |  |
Table 7: The cross-section ratios between 13 TeV and 8 TeV in different bins
of $p_{\rm T}$ and $y$ for $\mathchar 28935\relax{(3S)}$.

## Acknowledgements

We thank Kuang-Ta Chao, Yu Feng, Yan-Qing Ma, Hua-Sheng Shao and Jian-Xiong
Wang for frequent and interesting discussions on the production of $\mathchar
28935\relax$ mesons. We express our gratitude to our colleagues in the CERN
accelerator departments for the excellent performance of the LHC. We thank the
technical and administrative staff at the LHCb institutes. We acknowledge
support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and
FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG
(Germany); INFN (Italy); NWO (The Netherlands); MNiSW and NCN (Poland);
MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain); SNSF and SER
(Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). We
acknowledge the computing resources that are provided by CERN, IN2P3 (France),
KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain),
GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland),
IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are
indebted to the communities behind the multiple open-source software packages
on which we depend. Individual groups or members have received support from
AvH Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC
(European Union), ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes
(France), 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), Herchel Smith Fund, the Royal Society, the
English-Speaking Union and the Leverhulme Trust (United Kingdom).

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LHCb collaboration

R. Aaij43, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, J. Albrecht10,
F. Alessio40, M. Alexander53, A. Alfonso Albero38, S. Ali43, G. Alkhazov31, P.
Alvarez Cartelle55, A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L.
An3, L. Anderlini18, G. Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B.
Appleby56, F. Archilli43, P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M.
Artuso61, E. Aslanides6, M. Atzeni42, G. Auriemma26, S. Bachmann12, J.J.
Back50, C. Baesso62, S. Baker55, V. Balagura7,b, W. Baldini17, A. Baranov35,
R.J. Barlow56, S. Barsuk7, W. Barter56, F. Baryshnikov32, V. Batozskaya29, V.
Battista41, A. Bay41, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61,
L.J. Bel43, N. Beliy63, V. Bellee41, N. Belloli21,i, K. Belous37, I.
Belyaev32,40, E. Ben-Haim8, G. Bencivenni19, S. Benson43, S. Beranek9, A.
Berezhnoy33, R. Bernet42, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt42, F. Betti15,40, M.O. Bettler49, M. van Beuzekom43, Ia.
Bezshyiko42, S. Bifani47, P. Billoir8, A. Birnkraut10, A. Bizzeti18,u, M.
Bjørn57, T. Blake50, F. Blanc41, S. Blusk61, V. Bocci26, T. Boettcher58, A.
Bondar36,w, N. Bondar31, S. Borghi56,40, M. Borisyak35, M. Borsato39, F.
Bossu7, M. Boubdir9, T.J.V. Bowcock54, E. Bowen42, C. Bozzi17,40, S. Braun12,
M. Brodski40, J. Brodzicka27, D. Brundu16, E. Buchanan48, C. Burr56, A.
Bursche16, J. Buytaert40, W. Byczynski40, S. Cadeddu16, H. Cai64, R.
Calabrese17,g, R. Calladine47, M. Calvi21,i, M. Calvo Gomez38,m, A.
Camboni38,m, P. Campana19, D.H. Campora Perez40, L. Capriotti56, A.
Carbone15,e, G. Carboni25, R. Cardinale20,h, A. Cardini16, P. Carniti21,i, L.
Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina21, M. Cattaneo40, G.
Cavallero20,h, R. Cenci24,t, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier40, G. Chatzikonstantinidis47, M. Chefdeville4, S. Chen16, S.-G.
Chitic40, V. Chobanova39, M. Chrzaszcz40, A. Chubykin31, P. Ciambrone19, X.
Cid Vidal39, G. Ciezarek40, P.E.L. Clarke52, M. Clemencic40, H.V. Cliff49, J.
Closier40, V. Coco40, J. Cogan6, E. Cogneras5, V. Cogoni16,f, L. Cojocariu30,
P. Collins40, T. Colombo40, A. Comerma-Montells12, A. Contu16, G. Coombs40, S.
Coquereau38, G. Corti40, M. Corvo17,g, C.M. Costa Sobral50, B. Couturier40,
G.A. Cowan52, D.C. Craik58, A. Crocombe50, M. Cruz Torres1, R. Currie52, C.
D’Ambrosio40, F. Da Cunha Marinho2, C.L. Da Silva73, E. Dall’Occo43, J.
Dalseno48, A. Davis3, O. De Aguiar Francisco40, K. De Bruyn40, S. De Capua56,
M. De Cian12, J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone19,
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Demmer10, A. Dendek28, D. Derkach35, O. Deschamps5, F. Dettori54, B. Dey65, A.
Di Canto40, P. Di Nezza19, S. Didenko69, H. Dijkstra40, F. Dordei40, M.
Dorigo40, A. Dosil Suárez39, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L.
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Fernandez Prieto39, F. Ferrari15, L. Ferreira Lopes41, F. Ferreira Rodrigues2,
M. Ferro-Luzzi40, S. Filippov34, R.A. Fini14, M. Fiorini17,g, M. Firlej28, C.
Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, M. Fontana16,40, F.
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Gao3, L.M. Garcia Martin71, J. García Pardiñas39, J. Garra Tico49, L.
Garrido38, D. Gascon38, C. Gaspar40, L. Gavardi10, G. Gazzoni5, D. Gerick12,
E. Gersabeck56, M. Gersabeck56, T. Gershon50, Ph. Ghez4, S. Gianì41, V.
Gibson49, O.G. Girard41, L. Giubega30, K. Gizdov52, V.V. Gligorov8, D.
Golubkov32, A. Golutvin55,69, A. Gomes1,a, I.V. Gorelov33, C. Gotti21,i, E.
Govorkova43, J.P. Grabowski12, R. Graciani Diaz38, L.A. Granado Cardoso40, E.
Graugés38, E. Graverini42, G. Graziani18, A. Grecu30, R. Greim43, P.
Griffith16, L. Grillo56, L. Gruber40, B.R. Gruberg Cazon57, O. Grünberg67, E.
Gushchin34, Yu. Guz37, T. Gys40, C. Göbel62, T. Hadavizadeh57, C.
Hadjivasiliou5, G. Haefeli41, C. Haen40, S.C. Haines49, B. Hamilton60, X.
Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N. Harnew57, S.T. Harnew48, C.
Hasse40, M. Hatch40, J. He63, M. Hecker55, K. Heinicke10, A. Heister9, K.
Hennessy54, L. Henry71, E. van Herwijnen40, M. Heß67, A. Hicheur2, D. Hill57,
P.H. Hopchev41, W. Hu65, W. Huang63, Z.C. Huard59, W. Hulsbergen43, T.
Humair55, M. Hushchyn35, D. Hutchcroft54, P. Ibis10, M. Idzik28, P. Ilten47,
R. Jacobsson40, J. Jalocha57, E. Jans43, A. Jawahery60, F. Jiang3, M. John57,
D. Johnson40, C.R. Jones49, C. Joram40, B. Jost40, N. Jurik57, S. Kandybei45,
M. Karacson40, J.M. Kariuki48, S. Karodia53, N. Kazeev35, M. Kecke12, F.
Keizer49, M. Kelsey61, M. Kenzie49, T. Ketel44, E. Khairullin35, B. Khanji12,
C. Khurewathanakul41, K.E. Kim61, T. Kirn9, S. Klaver19, K. Klimaszewski29, T.
Klimkovich11, S. Koliiev46, M. Kolpin12, R. Kopecna12, P. Koppenburg43, S.
Kotriakhova31, M. Kozeiha5, L. Kravchuk34, M. Kreps50, F. Kress55, P.
Krokovny36,w, W. Krupa28, W. Krzemien29, W. Kucewicz27,l, M. Kucharczyk27, V.
Kudryavtsev36,w, A.K. Kuonen41, T. Kvaratskheliya32,40, D. Lacarrere40, G.
Lafferty56, A. Lai16, G. Lanfranchi19, C. Langenbruch9, T. Latham50, C.
Lazzeroni47, R. Le Gac6, A. Leflat33,40, J. Lefrançois7, R. Lefèvre5, F.
Lemaitre40, O. Leroy6, T. Lesiak27, B. Leverington12, P.-R. Li63, T. Li3, Y.
Li7, Z. Li61, X. Liang61, T. Likhomanenko68, R. Lindner40, F. Lionetto42, V.
Lisovskyi7, X. Liu3, D. Loh50, A. Loi16, I. Longstaff53, J.H. Lopes2, D.
Lucchesi23,o, M. Lucio Martinez39, A. Lupato23, E. Luppi17,g, O. Lupton40, A.
Lusiani24, X. Lyu63, F. Machefert7, F. Maciuc30, V. Macko41, P. Mackowiak10,
S. Maddrell-Mander48, O. Maev31,40, K. Maguire56, D. Maisuzenko31, M.W.
Majewski28, S. Malde57, B. Malecki27, A. Malinin68, T. Maltsev36,w, G.
Manca16,f, G. Mancinelli6, D. Marangotto22,q, J. Maratas5,v, J.F. Marchand4,
U. Marconi15, C. Marin Benito38, M. Marinangeli41, P. Marino41, J. Marks12, G.
Martellotti26, M. Martin6, M. Martinelli41, D. Martinez Santos39, F. Martinez
Vidal71, A. Massafferri1, R. Matev40, A. Mathad50, Z. Mathe40, C. Matteuzzi21,
A. Mauri42, E. Maurice7,b, B. Maurin41, A. Mazurov47, M. McCann55,40, A.
McNab56, R. McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N.
Meinert67, D. Melnychuk29, M. Merk43, A. Merli22,q, E. Michielin23, D.A.
Milanes66, E. Millard50, M.-N. Minard4, L. Minzoni17,g, D.S. Mitzel12, A.
Mogini8, J. Molina Rodriguez1,y, T. Mombächer10, I.A. Monroy66, S. Monteil5,
M. Morandin23, G. Morello19, M.J. Morello24,t, O. Morgunova68, J. Moron28,
A.B. Morris6, R. Mountain61, F. Muheim52, M. Mulder43, D. Müller40, J.
Müller10, K. Müller42, V. Müller10, P. Naik48, T. Nakada41, R. Nandakumar51,
A. Nandi57, I. Nasteva2, M. Needham52, N. Neri22, S. Neubert12, N. Neufeld40,
M. Neuner12, T.D. Nguyen41, C. Nguyen-Mau41,n, S. Nieswand9, R. Niet10, N.
Nikitin33, A. Nogay68, D.P. O’Hanlon15, A. Oblakowska-Mucha28, V. Obraztsov37,
S. Ogilvy19, R. Oldeman16,f, C.J.G. Onderwater72, A. Ossowska27, J.M. Otalora
Goicochea2, P. Owen42, A. Oyanguren71, P.R. Pais41, A. Palano14, M.
Palutan19,40, G. Panshin70, A. Papanestis51, M. Pappagallo52, L.L.
Pappalardo17,g, W. Parker60, C. Parkes56, G. Passaleva18,40, A. Pastore14, M.
Patel55, C. Patrignani15,e, A. Pearce40, A. Pellegrino43, G. Penso26, M. Pepe
Altarelli40, S. Perazzini40, D. Pereima32, P. Perret5, L. Pescatore41, K.
Petridis48, A. Petrolini20,h, A. Petrov68, M. Petruzzo22,q, B. Pietrzyk4, G.
Pietrzyk41, M. Pikies27, D. Pinci26, F. Pisani40, A. Pistone20,h, A. Piucci12,
V. Placinta30, S. Playfer52, M. Plo Casasus39, F. Polci8, M. Poli Lener19, A.
Poluektov50, N. Polukhina69, I. Polyakov61, E. Polycarpo2, G.J. Pomery48, S.
Ponce40, A. Popov37, D. Popov11,40, S. Poslavskii37, C. Potterat2, E. Price48,
J. Prisciandaro39, C. Prouve48, V. Pugatch46, A. Puig Navarro42, H. Pullen57,
G. Punzi24,p, W. Qian63, J. Qin63, R. Quagliani8, B. Quintana5, B. Rachwal28,
J.H. Rademacker48, M. Rama24, M. Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†,
F. Ratnikov35,x, G. Raven44, M. Ravonel Salzgeber40, M. Reboud4, F. Redi41, S.
Reichert10, A.C. dos Reis1, C. Remon Alepuz71, V. Renaudin7, S. Ricciardi51,
S. Richards48, K. Rinnert54, P. Robbe7, A. Robert8, A.B. Rodrigues41, E.
Rodrigues59, J.A. Rodriguez Lopez66, A. Rogozhnikov35, S. Roiser40, A.
Rollings57, V. Romanovskiy37, A. Romero Vidal39,40, M. Rotondo19, M.S.
Rudolph61, T. Ruf40, J. Ruiz Vidal71, J.J. Saborido Silva39, N. Sagidova31, B.
Saitta16,f, V. Salustino Guimaraes62, C. Sanchez Mayordomo71, B. Sanmartin
Sedes39, R. Santacesaria26, C. Santamarina Rios39, M. Santimaria19, E.
Santovetti25,j, G. Sarpis56, A. Sarti19,k, C. Satriano26,s, A. Satta25, D.M.
Saunders48, D. Savrina32,33, S. Schael9, M. Schellenberg10, M. Schiller53, H.
Schindler40, M. Schmelling11, T. Schmelzer10, B. Schmidt40, O. Schneider41, A.
Schopper40, H.F. Schreiner59, M. Schubiger41, M.H. Schune7,40, R. Schwemmer40,
B. Sciascia19, A. Sciubba26,k, A. Semennikov32, E.S. Sepulveda8, A. Sergi47,
N. Serra42, J. Serrano6, L. Sestini23, P. Seyfert40, M. Shapkin37, Y.
Shcheglov31,†, T. Shears54, L. Shekhtman36,w, V. Shevchenko68, B.G. Siddi17,
R. Silva Coutinho42, L. Silva de Oliveira2, G. Simi23,o, S. Simone14,d, N.
Skidmore12, T. Skwarnicki61, I.T. Smith52, M. Smith55, l. Soares Lavra1, M.D.
Sokoloff59, F.J.P. Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, F.
Stagni40, M. Stahl12, S. Stahl40, P. Stefko41, S. Stefkova55, O. Steinkamp42,
S. Stemmle12, O. Stenyakin37, M. Stepanova31, H. Stevens10, S. Stone61, B.
Storaci42, S. Stracka24,p, M.E. Stramaglia41, M. Straticiuc30, U. Straumann42,
S. Strokov70, J. Sun3, L. Sun64, K. Swientek28, V. Syropoulos44, T. Szumlak28,
M. Szymanski63, S. T’Jampens4, Z. Tang3, A. Tayduganov6, T. Tekampe10, G.
Tellarini17, F. Teubert40, E. Thomas40, J. van Tilburg43, M.J. Tilley55, V.
Tisserand5, M. Tobin41, S. Tolk40, L. Tomassetti17,g, D. Tonelli24, R.
Tourinho Jadallah Aoude1, E. Tournefier4, M. Traill53, M.T. Tran41, M.
Tresch42, A. Trisovic49, A. Tsaregorodtsev6, A. Tully49, N. Tuning43,40, A.
Ukleja29, A. Usachov7, A. Ustyuzhanin35, U. Uwer12, C. Vacca16,f, A. Vagner70,
V. Vagnoni15, A. Valassi40, S. Valat40, G. Valenti15, R. Vazquez Gomez40, P.
Vazquez Regueiro39, S. Vecchi17, M. van Veghel43, J.J. Velthuis48, M.
Veltri18,r, G. Veneziano57, A. Venkateswaran61, T.A. Verlage9, M. Vernet5, M.
Vesterinen57, J.V. Viana Barbosa40, D. Vieira63, M. Vieites Diaz39, H.
Viemann67, X. Vilasis-Cardona38,m, A. Vitkovskiy43, M. Vitti49, V. Volkov33,
A. Vollhardt42, B. Voneki40, A. Vorobyev31, V. Vorobyev36,w, C. Voß9, J.A. de
Vries43, C. Vázquez Sierra43, R. Waldi67, J. Walsh24, J. Wang61, M. Wang3, Y.
Wang65, D.R. Ward49, H.M. Wark54, N.K. Watson47, D. Websdale55, A. Weiden42,
C. Weisser58, M. Whitehead9, J. Wicht50, G. Wilkinson57, M. Wilkinson61,
M.R.J. Williams56, M. Williams58, T. Williams47, F.F. Wilson51,40, J.
Wimberley60, M. Winn7, J. Wishahi10, W. Wislicki29, M. Witek27, G. Wormser7,
S.A. Wotton49, K. Wyllie40, Y. Xie65, M. Xu65, Q. Xu63, Z. Xu3, Z. Xu4, Z.
Yang3, Z. Yang60, Y. Yao61, H. Yin65, J. Yu65, X. Yuan61, O. Yushchenko37,
K.A. Zarebski47, M. Zavertyaev11,c, L. Zhang3, Y. Zhang7, A. Zhelezov12, Y.
Zheng63, X. Zhu3, V. Zhukov9,33, J.B. Zonneveld52, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National University of Science and Technology MISIS, Moscow, Russia,
associated to 32
70National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
71Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
72Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43
73Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
xNational Research University Higher School of Economics, Moscow, Russia
yEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
†Deceased