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Inclusive $$\text {J}/\psi $$ production at midrapidity in pp collisions at $$\sqrt{s} = 13$$ TeV


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We report on the inclusive $$\text {J}/\psi $$ J / ψ production cross section measured at the CERN Large Hadron Collider in proton–proton collisions at a center-of-mass energy $$\sqrt{s}~=~13$$ s = 13 TeV. The $$\text {J}/\psi $$ J / ψ mesons are reconstructed in the $$\text {e}^{+}\text {e}^{-}$$ e + e - decay channel and the measurements are performed at midrapidity ( $$|y|<0.9$$ | y | < 0.9 ) in the transverse-momentum interval $$0<p_{\mathrm{T}} <40$$ 0 < p T < 40 GeV/ $$c$$ c , using a minimum-bias data sample corresponding to an integrated luminosity $$L_{\text {int}} = 32.2~\text {nb}^{-1}$$ L int = 32.2 nb - 1 and an Electromagnetic Calorimeter triggered data sample with $$L_{\text {int}} = 8.3~\mathrm {pb}^{-1}$$ L int = 8.3 pb - 1 . The $$p_{\mathrm{T}}$$ p T -integrated $$\text {J}/\psi $$ J / ψ production cross section at midrapidity, computed using the minimum-bias data sample, is $$\text {d}\sigma /\text {d}y|_{y=0} = 8.97\pm 0.24~(\text {stat})\pm 0.48~(\text {syst})\pm 0.15~(\text {lumi})~\mu \text {b}$$ d σ / d y | y = 0 = 8.97 ± 0.24 ( stat ) ± 0.48 ( syst ) ± 0.15 ( lumi ) μ b . An approximate logarithmic dependence with the collision energy is suggested by these results and available world data, in agreement with model predictions. The integrated and $$p_{\mathrm{T}}$$ p T -differential measurements are compared with measurements in pp collisions at lower energies and with several recent phenomenological calculations based on the non-relativistic QCD and Color Evaporation models.
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Eur. Phys. J. C (2021) 81:1121
Regular Article - Experimental Physics
Inclusive Jproduction at midrapidity in pp collisions
at s=13 TeV
ALICE Collaboration
CERN, 1211 Geneva 23, Switzerland
Received: 2 September 2021 / Accepted: 22 November 2021
© CERN for the benefit of the ALICE collaboration 2021
Abstract We report on the inclusive Jproduction
cross section measured at the CERN Large Hadron Col-
lider in proton–proton collisions at a center-of-mass energy
s=13 TeV. The Jmesons are reconstructed in the
e+edecay channel and the measurements are performed at
midrapidity (|y|<0.9) in the transverse-momentum inter-
val 0 <pT<40 GeV/c, using a minimum-bias data sample
corresponding to an integrated luminosity Lint =32.2nb
and an Electromagnetic Calorimeter triggered data sample
with Lint =8.3pb
1.ThepT-integrated Jproduction
cross section at midrapidity, computed using the minimum-
bias data sample, is dσ/dy|y=0=8.97 ±0.24 (stat)±
0.48 (syst)±0.15 (lumib. An approximate logarith-
mic dependence with the collision energy is suggested by
these results and available world data, in agreement with
model predictions. The integrated and pT-differential mea-
surements are compared with measurements in pp collisions
at lower energies and with several recent phenomenologi-
cal calculations based on the non-relativistic QCD and Color
Evaporation models.
1 Introduction
Quarkonium production in hadronic interactions is an excel-
lent case of study for understanding hadronization in quan-
tum chromodynamics (QCD), the theory of strong interac-
tions [1]. In particular, the production of the Jmeson,
a bound state of a charm and an anti-charm quark and the
lightest vector charmonium state, is the subject of many the-
oretical calculations. The cornerstone of all the theoretical
approaches is the factorization theorem, according to which
the Jproduction cross section can be factorized into a short
distance part describing the cc production and a long dis-
tance part describing the subsequent formation of the bound
state. In this way, the cc pair production cross section can be
computed perturbatively. The widely used Non-Relativistic
QCD (NRQCD) approach [2] describes the transition prob-
abilities of the pre-resonant cc pairs to bound states with a
set of long-distance matrix elements (LDME) fitted to exper-
imental data, assumed to be universal. Next-to-leading order
(NLO) calculations involving collinear parton densities are
able to describe production yields for transverse momen-
tum (pT) larger than the mass of the bound state [3,4],
but have difficulties describing the measured polarization
[5,6]. Calculations employing the kT-factorization approach
[7] can reach lower pTbut have similar difficulties when
compared to data [8]. The low-pTrange of quarkonium pro-
duction is modelled also within the Color Glass Condensate
effective theory coupled to leading order NRQCD calcula-
tions [9], which involves a saturation of the small Bjorken-x
gluon densities that dampens the heavy-quark pair produc-
tion yields. An alternative to the universal LDME approach
to hadronization used in the NRQCD framework is provided
by the Color Evaporation Model (CEM) [10,11] and its more
recent implementation using the kT-factorization approach,
the Improved CEM (ICEM) [12]. In the ICEM, the transi-
tion probability to a given bound state is proportional to the
cc pair production cross section integrated over an invariant-
mass range spanning between the mass of the bound state and
twice the mass of the lightest charmed meson. Finally, in the
Color Singlet Model (CSM) [1315], the pre-resonant cc pair
is produced directly in the color-singlet state with the same
quantum numbers as the bound state. Calculations within this
model at NLO precision are known to strongly underpredict
the measured production cross sections [16]. In this context,
apT-differential measurement of Jproduction cross sec-
tion covering a wide pTrange, starting from pT=0 and up
to high-pT, can discriminate between the different models of
quarkonium production.
In this paper, we present the integrated, and the pTand
rapidity (y) differential production cross sections of inclusive
Jproduction at midrapidity (|y|<0.9) in proton–proton
(pp) collisions at the center-of-mass energy s=13 TeV.
The inclusive Jyields include contributions from directly
produced J, feed-down from prompt decays of higher-
mass charmonium states, and non-prompt Jfrom the
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1121 Page 2 of 18 Eur. Phys. J. C (2021) 81:1121
decays of beauty hadrons. The pT-differential production
cross section of inclusive Jis measured in the 0 <pT<
15 GeV/cinterval using a minimum-bias triggered data sam-
ple and in the 15 <pT<40 GeV/cinterval using an
Electromagnetic Calorimeter triggered data sample. These
results complement existing measurements at midrapidity at
s=13 TeV performed by the CMS Collaboration [17],
which report the prompt Jproduction cross section for pT
>20 GeV/c. Previous measurements of the Jproduction
cross section in pp collisions performed by the ALICE Col-
laboration at midrapidity at lower energies were published in
Refs. [1820]. The inclusive Jproduction cross section in
pp collisions at s=13 TeV was published by the ALICE
Collaboration at forward rapidity in Ref. [21] and the prompt
and non-prompt production cross sections were reported by
the LHCb Collaboration in Ref. [22].
In the next sections, the ALICE detector and the data sam-
ple are described in Sect. 2, and the data analysis and the
determination of the systematic uncertainties are described
in Sects. 3and 4, respectively. The results are presented and
discussed together with recent model calculations in Sect. 5
and conclusions are drawn in Sect. 6.
2 The ALICE detector, data set and event selection
A detailed description of the ALICE detector and its perfor-
mance is provided in Refs. [23,24]. Here we mention only
the detector systems used for the reconstruction of the J
mesons decaying in the e+echannel at midrapidity. Unless
otherwise specified, the term electrons will be used through-
out the text to refer to both electrons and positrons.
The reconstruction of charged-particle tracks is performed
using the Inner Tracking System (ITS) [25] and the Time
Projection Chamber (TPC) [26], which are placed inside a
solenoidal magnet providing a uniform magnetic field of
B=0.5 T oriented along the beam direction. The ITS is
a silicon detector consisting of six cylindrical layers sur-
rounding the beam pipe at radii between 3.9 and 43.0cm.
The two innermost layers consist of silicon pixel detectors
(SPD), followed by two layers of silicon drift (SDD) and two
layers of silicon strip (SSD) detectors. The TPC is a cylin-
drical gas drift chamber which extends radially between 85
and 250 cm and longitudinally over 250 cm on each side
of the nominal interaction point. Both TPC and ITS have
full coverage in azimuth and provide tracking in the pseu-
dorapidity range |η|<0.9. Additionally, the measurement
of the specific energy loss (dE/dx) in the TPC active gas
volume is used for electron identification. The Electromag-
netic Calorimeter (EMCal) and the Di-jet Calorimeter (DCal)
[2729] are employed for triggering and electron identifica-
tion. The EMCal/DCal is a Shashlik-type lead-scintillator
sampling calorimeter located at a radius of 4.5 m from the
beam vacuum tube. The EMCal detector covers a pseudo-
rapidity range of |η|<0.7 over an azimuthal angle of
80<ϕ<187, and the DCal covers 0.22 <|η|<0.7
for 260<ϕ<320and |η|<0.7 for 320 <327.
The EMCal and DCal have identical granularity and intrinsic
energy resolution, and they form a two-arm electromagnetic
calorimeter, which in this paper will be referred to jointly as
In addition to these central barrel detectors, the V0 detec-
tors, composed of two scintillator arrays [30] placed along
the beam line on either side of the interaction point and cov-
ering the pseudorapidity intervals 3.7<η<1.7 and
2.8<η<5.1, respectively, are used for event triggering.
Together with the SPD detector, the V0 is also used to reject
background from beam-gas collisions and pileup events.
The measurement of the pT-integrated and pT-differential
production cross sections up to pT=15 GeV/c, the upper
limit being determined by the available integrated luminos-
ity, utilizes the minimum-bias (MB) trigger, defined as the
coincidence of signals in both V0 scintillator arrays. For
the pTinterval from 15 up to 40 GeV/c, the EMCal trig-
ger is employed to select events with high-pTelectrons. The
lower pTlimit is chosen such that the trigger efficiency does
not vary with pTabove this value, thus avoiding systematic
uncertainties related to trigger threshold effects. The EMCal
trigger is an online trigger which includes a Level 0 (L0) and
a Level 1 (L1) component [27]. The calorimeter is segmented
into towers and Trigger Region Units (TRUs), the latter being
composed of 384 towers each [27]. The L0 trigger is based
on the analog charge sum of 4 ×4 groups of adjacent tow-
ers evaluated within each TRU, in coincidence with the MB
trigger. The L1 trigger decision requires the L0 trigger and,
in addition, scans for 4 ×4 groups of adjacent towers across
the entire EMCal surface. The EMCal-triggered analysis pre-
sented in this paper uses the L1 trigger, and requires that at
least one of the charge sums of the 4 ×4 adjacent towers is
above 9 GeV.
This analysis includes all the data recorded by the ALICE
Collaboration during the LHC Run 2 data-taking campaigns
of 2016, 2017 and 2018 for pp collisions at s=13 TeV.
The maximum interaction rate for the dataset was 260 kHz,
with a maximum pileup probability in the same bunch cross-
ing of 0.5 ×103. The events selected for analysis were
required to have a reconstructed vertex within the interval
|zvtx|<10 cm to ensure a uniform detector acceptance.
Beam-gas events and pileup collisions occurring within the
readout time of the SPD were rejected offline using timing
selections based on the V0 detector information. Pileup col-
lisions occurring within the same LHC bunch crossing were
rejected using offline algorithms which identify multiple ver-
tices [24]. The remaining fraction of pileup events surviving
the selections is negligible for both the MB and EMCal data
Eur. Phys. J. C (2021) 81:1121 Page 3 of 18 1121
The analyzed MB sample, satisfying all the quality selec-
tions, consists of about 2×109events, corresponding to an
integrated luminosity Lint =32.2nb
1±1.6% (syst),
and the EMCal-triggered sample consists of approximately
9×107events which corresponds to an integrated luminosity
Lint =8.3pb
1±2.0% (syst). The integrated luminosities
are obtained based on the MB trigger cross section (σMB),
measured in a van der Meer scan [31], separately for each
year, as described in Ref. [32]. For each of the used triggers,
MB and EMCal, the integrated luminosity is obtained as
Lint =NMB
σMB ×dstrig
dsMB ×LT
MB (1)
where NMB is the number of MB-triggered events in the
triggered sample, dstrig is the downscaling factor applied to
the considered trigger by the ALICE trigger processor and
trig is the trigger live time, i.e. the fraction of time where
the detector cluster1assigned to the trigger was available for
In this work we study the integrated, and the rapidity- and pT-
differential inclusive Jproduction at midrapidity (|y|<
0.9) reconstructing the Jfrom the e+edecay channel.
The MB sample analysis follows closely the one performed
in pp collisions at s=5.02 TeV [20].
3.1 Track selection
Electron-track candidates are reconstructed employing the
ITS and TPC. They are required to be within the accep-
tance of the central barrel (|η|<0.9), and to have a min-
imum transverse momentum of 1 GeV/c, which suppresses
the background with only a moderate Jefficiency loss.
The tracks are selected to have at least 2 hits in the ITS, one
of which having to be in one of the SPD layers, and share
at most one hit with other tracks. A minimum of 70 out of a
maximum of 159 clusters are required in the TPC.
In order to reject tracks originating from weak decays
and interactions with the detector material, a selection based
on the distance-of-closest approach (DCA) to the primary
vertex is applied to the tracks. For the MB analysis the tracks
are required to have a minimum DCA lower than 0.2 cm
in the transverse direction and 0.4 cm along the beam axis.
Such tight selection criterion is used in order to improve
the signal-to-background ratio and the signal significance. It
was checked with Monte Carlo (MC) simulations that these
1A detector cluster is a set of ALICE detectors readout with the same
set of triggers. All triggers assigned to a given cluster share the same
live-time, determined by the slowest detector in the cluster.
requirements do not lead to efficiency loss for the non-prompt
Jrelative to the prompt J. For the EMCal-triggered
event analysis, a looser selection on the DCA to the primary
vertex at 1 and 3 cm is applied to avoid rejecting non-prompt
Jfrom highly boosted beauty hadron decays.
The electrons are identified using the specific energy loss
dE/dxin the TPC gas. Their dE/dxis required to be within
a band of [−2,3]σrelative to the expectation for electrons
at the given track momentum, with σbeing the dE/dxres-
olution. The contamination from protons which occurs in
the momentum range p<1.5GeV/cand from pions for
momenta above 2 GeV/cis mitigated by rejecting tracks com-
patible with the proton or pion hypothesis within 3σ.
For the analysis of EMCal-triggered events, both the TPC
and the EMCal are used for electron identification. At least
one of the Jdecay-electron tracks, initially identified by
the TPC, is required to be matched to an EMCal cluster
(a group of adjacent towers belonging to the same elec-
tromagnetic shower). In order to ensure a constant trigger
efficiency on the selected events, the matched clusters are
selected to have a minimal energy of 14 GeV, a value that
is significantly higher than the applied online threshold of
9 GeV. Electrons are identified by applying a selection on
the energy-to-momentum ratio of the EMCal matched track
of 0.8<E/p<1.3 and on the dE/dxin the TPC of
[−2.25,3]σ. Due to the additional use of the EMCal for
electron identification with respect to the MB based anal-
ysis, no explicit hadron rejection was used for the EMCal
Secondary electrons from photon conversions, the main
background source for both analyses, are rejected using the
requirement of a hit in the SPD detector. This requirement
rejects most of the electrons from photon conversions occur-
ring beyond the SPD layers. An additional selection based
on track pairing, as described in detail in Ref. [20], is applied
to further reject conversion electrons, especially those from
photons converting in the beam pipe or in the SPD.
3.2 Signal extraction
The number of reconstructed Jmesons is extracted from
the invariant mass (mee) distribution of all possible opposite-
sign (OS) pairs constructed combining the selected electron
tracks within the same event (SE). Besides the Jsignal,
i.e. pairs of electrons originating from the decay of a common
Jmother, the invariant mass distribution contains a back-
ground with contributions from combinatorial and correlated
In the MB analysis, the combinatorial background, i.e.
pairs of electrons originating from uncorrelated processes, is
estimated using the event-mixing technique (ME), in which
pairs are built from opposite-sign electrons belonging to dif-
ferent events. The mixing is done considering events from the
1121 Page 4 of 18 Eur. Phys. J. C (2021) 81:1121
same run (a collection of events taken during a period of time
of up to a few hours) with a similar vertex position. The nor-
malized combinatorial background distribution Bcomb(mee)
is obtained as
OS (mee)×miNSE
LS (mi)
LS (mi)(2)
where NSE
OS and NME
LS are the number of same-event
like-sign (LS), mixed-event OS and mixed-event LS pairs,
respectively. Here, the mixed-event OS distribution is nor-
malized using the ratio of SE to ME like-sign pairs since these
are not expected to contain any significant correlated source.
The summation extends over all the mass bins mibetween
0 and 5 GeV/c2to minimize the statistical uncertainty on
the background matching. The correlated background in the
mass region relevant for this analysis originates mainly from
semi-leptonic decays of heavy-flavor hadrons [33]. In order
to extract the number of reconstructed J,NJ, the com-
binatorial background-subtracted invariant mass distribution
is fitted with a two-component function: one empirical func-
tion to describe the correlated background shape, which is a
second order polynomial at low pair pT(pee
T<1GeV/c) and
an exponential at high-pT(pee
T>1GeV/c), plus a template
shape obtained from MC simulations, described in Sect. 3.3,
for the Jsignal.
For the analysis of the EMCal-triggered event sample, due
to the relatively large contribution from correlated sources at
high pT, the event mixing technique is not used. Instead, a fit
of the invariant mass distribution is performed using the MC
template for the signal and a third-order polynomial function
to describe both the combinatorial and correlated background
In both analyses, the contribution from ψ(2S)decaying in
the dielectron channel is not included in the fit as the expected
number of such pairs is 1% of the Jraw yield and it is
statistically not significant in the analyzed data samples. The
number of Jis obtained by counting the number of e+e
pairs in the mass range 2.92 mee 3.16 GeV/c2remain-
ing after subtracting the background. The SE-OS dielectron
invariant mass distribution for a few of the pTintervals is
shown in Fig. 1, together with the estimated signal and back-
ground components.
3.3 Corrections
The double differential Jproduction cross section is cal-
culated as
BR(Je+e)×A××y×pT×Lint. ,
where NJis the number of reconstructed Jinagiven
interval of rapidity yand transverse momentum pT,
BR(Je+e)is the decay branching ratio into the
dielectron channel [34], A×is the average acceptance
and efficiency factor and Lint is the integrated luminosity of
the data sample.
The correction for acceptance and efficiency is the prod-
uct of the kinematical acceptance factor, the reconstruc-
tion efficiency, which includes both tracking and particle-
identification (PID) efficiency, and the fraction of signal in
the signal counting mass window. For the EMCal-triggered
events analysis, the efficiency for the EMCal cluster recon-
struction is also considered. The efficiency related to the
EMCal trigger is estimated using a parameterized simula-
tion of the L1 trigger which includes decalibration and noise
based on measured data, and takes into account the time-
dependent detector conditions. With the exception of the PID
efficiency, all the corrections are obtained based on a MC sim-
ulation of unpolarized Jmesons embedded in inelastic pp
collisions simulated using PYTHIA 6.4 [35] with the Peru-
gia 2011 tune [36]. The prompt Jare generated with a flat
rapidity distribution and a pTspectrum obtained from a phe-
nomenological interpolation of Jmeasurements at RHIC,
CDF and the LHC at lower energies [37]. For the non-prompt
b pairs are generated using the PYTHIA Perugia 2011
tune. The Jdecays are simulated using PHOTOS [38],
which includes the radiative component of the Jdecay.
The generated particles are transported through the ALICE
detector setup using the GEANT3 package [39].
The PID efficiency is determined with a data-driven
method by using a clean sample of electrons from tagged
photon conversion processes, passing the same quality crite-
ria as the electrons selected for the Jreconstruction. The
PID selection efficiency for single electrons is propagated to
the Jlevel using a simulation of the Jdecay. The accep-
tance times efficiency correction factor for the MB sample
analysis varies with pTbetween 7.6% and 16% while in the
case of the EMCal-triggered sample analysis it increases with
Due to the finite size of the pTintervals, there is a mild
dependence of the correction factors on the shape of the inclu-
sive JpTdistribution used in the simulation. This is mit-
igated iteratively by using the corrected JpT-differential
production cross section to reweight the acceptance times
efficiency correction factor and obtain an updated corrected
cross section. The procedure is stopped when the differ-
ence between the input and output corrected pT-differential
production cross section drops below 1%, which typically
occurs within 1 to 2 iterations, depending on the pTinterval.
Additionally, to check if the default MC used in the analy-
sis could introduce a bias on the EMCal trigger efficiency,
due to the enhancement of J, another MC simulation,
based on a di-jet production generated by PYTHIA8 [40],
Eur. Phys. J. C (2021) 81:1121 Page 5 of 18 1121
2.5 3 3.5
=13 TeVsALICE pp
= 8.3 pb
= 32.2 nb
|<0.9y, |
(MB)c < 2 GeV/
p1 <
(EMCal)c < 20 GeV/
p15 <
2.5 3 3.5
(MB)c < 7 GeV/
p5 <
MB: Signal
Correlated bkg.
Combinatorial bkg.
2.5 3 3.5
(EMCal)c < 30 GeV/
p25 <
Total bkg.
c (GeV/
ccounts per 40 MeV/
Fig. 1 Invariant-mass distributions for SE e+epairs in two pee
vals from the MB event analysis (left panels) and two pee
from the EMCal-triggered event analysis (right panels). The signal and
background components obtained from the fit procedure are shown sep-
arately. For the top-right panel, the distributions are scaled for conve-
nience by a factor of 2
at s=13 TeV, is used as a cross-check. As a result, the
default MC and the di-jet MC lead to a compatible EMCal
trigger efficiency.
4 Systematic uncertainties
There are several sources of systematic uncertainties affect-
ing this analysis, namely the ITS-TPC tracking, the electron
identification, the signal extraction procedure, the Jinput
kinematic distributions used in MC simulations, the determi-
nation of the integrated luminosity and the branching ratio of
the dielectron decay channel. A summary of these is given
in Table 1.
The uncertainty of the ITS-TPC tracking efficiency is one
of the dominant sources of systematic uncertainty and has
two contributions: one due to the TPC-ITS matching and
one related to the track-quality requirements. The former is
obtained from the residual difference observed for the ITS-
TPC single-track matching between data and MC simulations
[41], which is further propagated to Jdielectron pairs. It
varies between 2.8% and 5.4%, depending on pT. The uncer-
tainty related to the track-quality requirements is estimated
by repeating the analysis with variations of the selection crite-
ria and taking the root mean square (RMS) of the distribution
of the results as systematic uncertainty. This uncertainty also
depends on pTand is equal to 3.7% for pT<5GeV/cand
approximately 2% for pT>5GeV/c. In Table 1, both con-
tributions are added in quadrature and provided as ranges for
the pT- and y-differential results.
As described in Sect. 3.3, the particle identification effi-
ciency is determined via a data-driven procedure using a sam-
ple of identified electrons from tagged photon conversions.
For the MB data sample, the uncertainty of this procedure
is estimated by repeating the analysis with a looser and a
tighter hadron (pion and proton combined) rejection crite-
ria and taking the largest deviation from the results obtained
with the standard PID selection divided by 12. In addition,
the statistical uncertainty of the pure electron sample used
for the determination of the efficiency, which becomes non-
negligible at high pT, is propagated to the total uncertainty for
the PID. The total PID systematic uncertainty is larger than
1% only for pT>7GeV/c, reaching 4% in the pTinterval
10 <pT<15 GeV/c. For the EMCal-triggered analysis,
the particle identification systematic uncertainty has contri-
butions from the electron identification in both the TPC and
the EMCal. The values are estimated by varying the dE/dx
range for the electron selection in the TPC, the E/pselection
range in the EMCal, and the minimum energy of the matched
clusters. The total PID uncertainty, obtained in an analogous
way as for the MB sample, increases with pTfrom 2.8% to
For pTup to 15 GeV/c, the systematic uncertainties asso-
ciated to the Jsignal extraction procedure is dominated
by the Jinvariant mass signal shape template used to cal-
culate the fraction of reconstructed Jmesons within the
1121 Page 6 of 18 Eur. Phys. J. C (2021) 81:1121
Tabl e 1 Summary of contributions to systematic uncertainties of the measured Jproduction cross section (in percentage)
Source (pT,y)-integrated y-differential pT-differential (MB) pT-differential (EMCal)
0<pT<15 (GeV/c)15<pT<40 (GeV/c)
Tracking 4.9 4.9 4.7–6.5 5.7
PID 0.6 0.6 0.0–4.1 2.8–5.4
Signal shape 1.9 1.9 1.4–2.2 1.0–4.0
Background fit 0.3 0.3–0.4 0.2–1.2 1.0–6.0
MC input 1.0 1.0 0.0–0.9 0.9
EMCal trigger Not used Not used Not used 0.5
Luminosity 1.6 1.6 1.6 2.0
Branching ratio 0.5 0.5 0.5 0.5
Total uncorrelated 0.3 0.3–0.4 0.2–1.2 1.0–6.0
Total correlated 5.4 5.4 5.2–7.4 6.5–8.8
Global 1.7 1.7 1.7 2.0
Total (w/o global) 5.4 5.4 5.3–7.5 7.0–11.0
signal counting mass window. This uncertainty amounts to
1.9% and is evaluated by repeating the extraction of the cor-
rected yield with different invariant mass intervals used for
the signal counting and taking the RMS of the variations as a
systematic uncertainty. An additional source of uncertainty,
due to the fit of the correlated background, is determined
by varying the fit mass range and is typically below 1%.
For pT>15 GeV/c, the systematic uncertainty associated to
the Jsignal extraction are evaluated similarly to the MB
analysis, however, the components associated to the signal
shape and the background fit have similarly large contribu-
tions. This is one of the main sources of uncertainty in this
pTrange. The total uncertainty of the signal extraction varies
with pTbetween about 2 and 7%.
The uncertainty on the EMCal trigger efficiency is studied
varying the contribution from random noise (evaluated using
energy resolution measurements in data) applied to the 4×4
groups of adjacent towers. It was also studied using the di-
jet production generated by PYTHIA8 at s=13 TeV
mentioned in Sect. 3.3. The latter study showed a difference
in the EMCal trigger efficiency of 0.5%, which is assigned
as a systematic uncertainty.
Since the Jefficiency has a dependence on pT, the par-
ticular Jkinematic distribution used in the MC simulation,
from which efficiencies are derived, can have an impact on
the average efficiency computed for finite pTintervals. As
described in Sect. 3.3, this is mitigated via an iterative proce-
dure and the remaining uncertainty is related to the precision
of the measured Jspectrum. This uncertainty is estimated
by fitting the measured pTspectrum with a power law func-
tion and allowing the fitted parameters to vary according to
the covariance matrix. For each of such a variation, the aver-
age efficiency in a given kinematic interval is recomputed
and the RMS of the distribution obtained from the varia-
tion of efficiency with respect to the central value is taken
as a systematic uncertainty. This amounts to 1% for the pT-
integrated case and is smaller for all of the considered pT
The uncertainty of the integrated luminosity arising from
the vdM-scan based measurements amounts to 1.6% for both
the MB and EMCal-triggered data samples, and is deter-
mined as described in Ref. [32]. For the EMCal-triggered
data sample only, an additional uncertainty of 1.1% arising
from the precision of the trigger downscaling is assigned. The
uncertainty on the Jdecay branching ratio to the dielec-
tron channel amounts to 0.53% as reported by the Particle
Data Group [34].
The uncertainties of the integrated luminosity and branch-
ing ratio are treated as global systematic uncertainties. All the
other uncertainties are considered as point to point correlated,
with the exception of the one due to the background fit which
is considered to be fully uncorrelated. The systematic uncer-
tainties are thus dominated by correlated sources. The total
correlated, uncorrelated and global uncertainties obtained as
the sum in quadrature of the corresponding sources are given
in Table 1.
5 Results
The inclusive pT-differential Jproduction cross section in
pp collisions at s=13 TeV at midrapidity, obtained from
the combined analysis of the MB-triggered ( pT<15 GeV/c)
and EMCal-triggered (15 <pT<40 GeV/c) samples is
shown in the upper panels of Fig. 2. Statistical uncertain-
ties are shown as error bars, while the boxes around the
data points represent the correlated and uncorrelated system-
atic uncertainties added in quadrature, excluding the global
Eur. Phys. J. C (2021) 81:1121 Page 7 of 18 1121
0 5 10 15 20 25 30 35
)c (GeV/
1.6% ±
= 32.2 nb
2.0% ±
= 8.3 pb
<4y 2.5<
= 3.2 pb
= 13 TeVs
, pp
ALICE, inclusive J/
5 10152025303540
)c (GeV/
data / mid-y fit
)c (GeV/
= 32.2 nb
L = 13 TeV, s x
= 5.6 nb
L = 7 TeV, s x
2.1% ±
= 19.5 nb
L = 5.02 TeV, s x
|<0.9y, |
Inclusive J/
)c (GeV/
data / 13 TeV fit
Fig. 2 Inclusive Jproduction cross section at midrapidity (|y|<
0.9) in pp collisions at s=13 TeV compared with the ALICE
forward-rapidity measurement at s=13 TeV [21] (left panel) and
the scaled ALICE midrapidity measurements at s=5.02 TeV [20]
and s=7TeV[18] (right panel). The error bars represent sta-
tistical uncertainties while the boxes around the data points represent
the total systematic uncertainty, excluding the global uncertainty from
the luminosity and branching ratio. The lower panels show the ratio
between the measurements at different rapidity and energies, and the
power law fit, discussed in the text, to the Jproduction cross section
(red dashed line) at midrapidity at s=13 TeV. The boxes in the
lower panels include the systematic uncertainty of the data points and
the uncertainty of the integral of the fit function in the given pTinterval
added in quadrature
uncertainty from luminosity determination and branching
ratio. The x-axis extent of the boxes illustrates the size of
the pTinterval with the data points placed in the center. A
simple power law function of the type
with A,p0and nbeing free parameters, is used to fit the
measured distribution. Since the systematic uncertainties are
largely correlated, only the statistical ones are used in the fit.
Duetothelarge pTintervals, the fit is performed by consid-
ering the mean value of the function in the pTinterval rather
than its value at the center of the interval. The values obtained
for the fitted parameters are A=2.15 ±0.18 μb/(GeV/c)2,
p0=4.09 ±0.22 GeV/cand n=3.04 ±0.09. The fit func-
tion, shown in Fig. 2as a dashed red line, provides a good
description of the data points measured with both MB and
EMCal data samples, and illustrates the consistency between
the two analyses.
In the left panel of Fig. 2, the production cross section
measured at midrapidity is compared with the forward rapid-
ity measurement at the same energy [21]. The bottom panel
shows the ratio between the forward rapidity data points
and the mean cross section at midrapidity obtained by inte-
grating the fit function described above in the pTintervals
of the forward-rapidity measurement. The displayed uncer-
tainty boxes include the systematic uncertainty of the for-
ward rapidity measurement and the uncertainty of the func-
tion mean, added in quadrature. A monotonic drop of this
ratio can be observed towards high pT, indicating a harder
JpTdistribution at midrapidity.
The right panel of Fig. 2shows a comparison with midra-
pidity measurements performed by the ALICE Collaboration
in pp collisions at the lower collision energies of s=7TeV
[18] and 5.02 TeV [20]. In the bottom panel, the ratio between
the lower energy measurements and the fitted 13 TeV results
is shown. The displayed uncertainty boxes include the sys-
tematic uncertainty of the lower energy data points and the
uncertainty of the fit function mean, added in quadrature.
Although the uncertainties of the measurement at 7 TeV
are large, the data indicates an increase of the production
cross section with increasing collision energy. In addition,
the monotonic drop of the ratio between the 5.02 TeV and
13 TeV measurements indicates a hardening of the pTspec-
trum with increasing collision energy, as also observed from
the energy dependence of the inclusive Javerage pTdis-
cussed in Ref. [20].
The measured inclusive Jproduction cross section is
compared with several phenomenological calculations of
the prompt Jproduction in the left panel of Fig. 3.In
addition, to illustrate the impact of the unaccounted feed-
down from beauty decays in the theory predictions, a cal-
culation of the non-prompt Jproduction by Cacciari
et al., using the Fixed-Order Next-to-Leading-Logarithms
approach (FONLL) [45], is shown in the same panel. Accord-
1121 Page 8 of 18 Eur. Phys. J. C (2021) 81:1121
0 5 10 15 20 25 30 35 40
)c (GeV/
prompt J/
from b
= 13 TeV sALICE pp
|<0.9y, |
Inclusive J/
= 32.2 nb
= 8.3 pb
0 5 10 15 20 25 30 35
inclusive J/
from b, FONLL, added)
= 13 TeV sALICE pp
|<0.9y, |
Inclusive J/
= 32.2 nb
= 8.3 pb
0 5 10 15 20 25 30 35 40
)c (GeV/
model / 13 TeV fit
Fig. 3 Inclusive Jproduction cross section compared with calcu-
lations for the prompt Jproduction cross section using ICEM [42],
NLO NRQCD [3,4,43], LO NRQCD + CGC [44] and for the non-
prompt Jfrom beauty-hadron feed-down using FONLL [45](left
panel). Inclusive Jproduction cross section compared with the cor-
responding calculations obtained as the sum of the prompt Jcom-
ponent shown in the left panel and the non-prompt contribution from
FONLL (right panel). The bottom panel shows the ratios between the
model calculations and a fit to the data points. The bands illustrate the
theoretical uncertainties centered around the ratio between the model
calculation and the power-law fit to the data (see text for details)
ing to the FONLL calculations, the non-prompt contribu-
tion to the inclusive Jyield is approximately 10% at low-
pTand grows to approximately 50% at pT=40GeV/c.In
the right panel of Fig. 3, the measured inclusive production
cross section is compared to predictions for inclusive J
production obtained as the sum of the prompt Jcalcu-
lations listed above and the beauty feed-down contribution
calculated using FONLL. The bottom panel shows the ratio
between each theoretical calculation and the fit to the data.
The colored bands represent the theoretical uncertainties for
each model, centered around the model to data ratio. These
uncertainties are typically due to the variation of the renor-
malization and factorization scales, and of the charm quark
Several phenomenological approaches are used for the
calculation of the Jyields shown in Fig. 3. The green
and blue dashed lines represent NLO NRQCD calculations
from Ma et al. [4] and Butenschoen et al. [3], respectively,
using collinear gluon parton distribution functions (PDFs).
Although the calculation of the short distance terms is very
similar, the predictions of these two approaches differ due
to the LDME sets which are obtained in separate fits of
the Tevatron and HERA data with different low-pTcut-
offs. In addition, the calculation from Ref. [3] does not
include the feed-down from higher mass charmonium states.
The brown solid line represents a calculation obtained with
the MC generator PEGASUS [43] developed by Lipatov et
al. which employs a kT-factorization approach using pT-
dependent gluon distribution functions and NRQCD matrix
elements combined with LDMEs extracted from an NLO
high-transverse momentum analysis [8]. Using the KMR
[46] technique to construct the unintegrated gluon PDFs, this
calculation can extend down to JpT=0. A different
model to calculate the low pTJproduction cross sec-
tion, by Ma and Venugopalan [44] (green solid line) is based
on a Color-Glass Condensate (CGC) approach coupled to
a Leading Order (LO) NRQCD calculation which includes
a soft-gluon resummation. The calculations obtained using
the ICEM model by Cheung and Vogt [42] within the kT-
factorization approach are shown by the violet solid line. In
this calculation, LDMEs are not used, however one normal-
ization parameter per charmonium state is used to account
for long distance effects [47]. The feed down from the higher
mass charmonium states is taken into account in this model.
As shown in the right panel of Fig. 3, all the models pro-
vide a reasonable description of the inclusive Jproduc-
tion cross section within the theoretical uncertainties over
the entire pTrange covered by this measurement. In par-
ticular, both the ICEM and NRQCD + CGC calculations
show very good agreement with the data in the low-pTrange.
Eur. Phys. J. C (2021) 81:1121 Page 9 of 18 1121
10 1 10
, pp
Inclusive J/
=13 TeVs
|<0.9,yALICE, |
=2.76, 5.02, 7 TeVs|<0.9,yALICE, |
|<0.6yCDF, |
|<0.35yPHENIX, |
|<1ySTAR, |
et al.ICEM, Cheung
et al.NRQCD + CGC, Ma
1.6% ±
= 32.2 nb
= 3.2 pb
NRQCD + CGC (prompt J/
from b)
ICEM (inclusive J/
= 13 TeV, inclusive J/sALICE pp
Fig. 4 Inclusive pT-integrated Jproduction cross section as a func-
tion of collision energy (left panel) and rapidity (right panel) compared
with the ICEM [42] and NRQCD + CGC [44] model calculations. The
midrapidity pT-integrated production cross section values are measured
by the PHENIX [48], STAR [49], CDF [50] and ALICE [1820]col-
laborations. The forward-rapidity production cross section shown in the
right panel is reported by ALICE in Ref. [21]
The NRQCD calculation from Lipatov, which uses the kT-
factorization approach, also provides a good description of
the data for pT>2GeV/c, while it overestimates the mea-
sured cross section at lower pT. However, this is a significant
progress compared to traditional collinear approaches which
tend to diverge towards pT=0.
The measured pT-integrated inclusive Jproduction
cross section at midrapidity, obtained by performing the anal-
ysis on the MB data sample without any explicit selection on
the JpT(pT>0), is
dy=8.97 ±0.24 (stat.) ±0.48 (syst.) ±0.15 (lumi)
±0.05 (BR) μb.
The systematic uncertainty includes all the systematic
sources mentioned in Table 1added in quadrature, with the
exception of the global ones which are given separately. The
fraction of the total cross section covered by the EMCal-
triggered event analysis results (pT>15 GeV/c)isestimated
to be less than 0.5% and is not used in this measurement.
A comparison of this measurement with previous midrapid-
ity measurements in pp collisions at lower energies from
PHENIX [48], STAR [49], CDF [50] and ALICE [1820]
is shown in the left panel of Fig. 4. An approximate log-
arithmic increase of the cross sections with the energy is
observed. The collision energy-dependent measurements are
also compared with the calculations from the ICEM [42] and
the NRQCD + CGC [44] models. Both calculations provide
a good description of the energy dependent trend within large
theoretical uncertainties, dominated by the low-pTregion of
the spectrum.
The right panel of Fig. 4shows the rapidity-differential
inclusive Jproduction cross section which includes three
data points measured in this analysis around midrapidity
and the previously published ALICE measurement at for-
ward rapidity [21]. While no rapidity dependence is observed
in the central rapidity range, a steep decrease towards for-
ward rapidity is seen. The two model calculations employed,
using ICEM [42] and the NRQCD + CGC [44], combined
with non-prompt contributions calculated with FONLL [45],
exhibit rather different rapidity dependences. However, both
are compatible with the data owing to the large theoretical
uncertainties, which are at present much larger than the exper-
imental uncertainties.
6 Conclusions
The integrated, and the pT- and y-differential inclusive J
production cross sections at midrapidity (|y|<0.9) in pp
collisions at s=13 TeV are presented in the pTrange
0<pT<40 GeV/c, exceeding the pTrange of all the
previous measurements reported by the ALICE Collabora-
tion. The measurement up to 15 GeV/cis performed using a
minimum-bias triggered data sample and the one at high-pT
is performed using an EMCal-triggered data sample, both
collected by ALICE during the LHC Run 2.
The data are compared with the ALICE lower collision
energy measurements at midrapidity [18,20] and with the
1121 Page 10 of 18 Eur. Phys. J. C (2021) 81:1121
ALICE forward-rapidity results [21]. An approximate loga-
rithmic dependence of the integrated Jproduction cross
section with collision energy is suggested by the data, in
agreement with the available predictions. The pT-differential
cross section measured in this analysis shows a significant
hardening with respect to both the forward-rapidity measure-
ment at s=13 TeV and the midrapidity measurement at
s=5.02 TeV.
Several calculations within the NRQCD framework [3,4,
43,44] and one using the ICEM approach [42] are compared
with the measured inclusive Jproduction cross section.
In particular, the ICEM, the NRQCD model based on the
CGC approach and a new NRQCD calculation using the kT-
factorization approach provide a prediction for the Jpro-
duction cross section down to pT=0. All models provide a
good description of the measured inclusive Jproduction
cross section, although with large theoretical uncertainties.
Acknowledgements We wish to thank Mathias Butenschoen, Vin-
cent Cheung, Bernd A. Kniehl, Artem V. Lipatov, Yan-Qing Ma, Raju
Venugopalan and Ramona Vogt for kindly providing their calculations.
The ALICE Collaboration would like to thank all its engineers and
technicians for their invaluable contributions to the construction of
the experiment and the CERN accelerator teams for the outstanding
performance of the LHC complex. The ALICE Collaboration grate-
fully acknowledges the resources and support provided by all Grid
centres and the Worldwide LHC Computing Grid (WLCG) collabo-
ration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detec-
tor: A. I. Alikhanyan National Science Laboratory (Yerevan Physics
Institute) Foundation (ANSL), State Committee of Science and World
Federation of Scientists (WFS), Armenia; Austrian Academy of Sci-
ences, Austrian Science Fund (FWF): [M 2467-N36] and Nationals-
tiftung für Forschung, Technologie und Entwicklung, Austria; Ministry
of Communications and High Technologies, National Nuclear Research
Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico
e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep),
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil;
Ministry of Education of China (MOEC) , Ministry of Science and
Technology of China (MSTC) and National Natural Science Founda-
tion of China (NSFC), China; Ministry of Science and Education and
Croatian Science Foundation, Croatia; Centro de Aplicaciones Tec-
nológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Min-
istry of Education, Youth and Sports of the Czech Republic, Czech
Republic; The Danish Council for Independent Research | Natural Sci-
ences, the VILLUM FONDEN and Danish National Research Founda-
tion (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland;
Commissariat à l’Energie Atomique (CEA) and Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3) and Centre
National de la Recherche Scientifique (CNRS), France; Bundesmin-
isterium für Bildung und Forschung (BMBF) and GSI Helmholtzzen-
trum für Schwerionenforschung GmbH, Germany; General Secretariat
for Research and Technology, Ministry of Education, Research and
Religions, Greece; National Research, Development and Innovation
Office, Hungary; Department of Atomic Energy Government of India
(DAE), Department of Science and Technology, Government of India
(DST), University Grants Commission, Government of India (UGC)
and Council of Scientific and Industrial Research (CSIR), India; Indone-
sian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucle-
are (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Edu-
cation, Culture, Sports, Science and Technology (MEXT) and Japan
Society for the Promotion of Science (JSPS) KAKENHI, Japan; Con-
sejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo
de Cooperación Internacional en Ciencia y Tecnología (FONCICYT)
and Dirección General de Asuntos del Personal Academico (DGAPA),
Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek
(NWO), Netherlands; The Research Council of Norway,Norway; Com-
mission on Science and Technology for Sustainable Development in the
South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú,
Peru; Ministry of Education and Science, National Science Centre and
WUT ID-UB, Poland; Korea Institute of Science and Technology Infor-
mation and National Research Foundation of Korea (NRF), Republic
of Korea; Ministry of Education and Scientific Research, Institute of
Atomic Physics and Ministry of Research and Innovation and Insti-
tute of Atomic Physics, Romania; Joint Institute for Nuclear Research
(JINR), Ministry of Education and Science of the Russian Federation,
National Research Centre Kurchatov Institute, Russian Science Foun-
dation and Russian Foundation for Basic Research, Russia; Ministry of
Education, Science, Research and Sport of the Slovak Republic, Slo-
vakia; National Research Foundation of South Africa, South Africa;
Swedish Research Council (VR) and Knut and Alice Wallenberg Foun-
dation (KAW), Sweden; European Organization for Nuclear Research,
Switzerland; Suranaree University of Technology (SUT), National Sci-
ence and Technology Development Agency (NSDTA) and Office of the
Higher Education Commission under NRU project of Thailand, Thai-
land; Turkish Energy, Nuclear and Mineral Research Agency (TEN-
MAK), Turkey; National Academy of Sciences of Ukraine, Ukraine;
Science and Technology Facilities Council (STFC), United Kingdom;
National Science Foundation of the United States of America (NSF) and
United States Department of Energy, Office of Nuclear Physics (DOE
NP), United States of America. In addition, individual groups and mem-
bers have received support from Horizon 2020 and Marie Skłodowska
Curie Actions, European Union.
Data Availability Statement This manuscript has associated data in a
data repository. [Authors’ comment: Manuscript has associated data in
a HEPData repository at]
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