11institutetext: Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie,
Orsay, France
Presented at DIS2022: XXIX International Workshop on Deep-Inelastic Scattering
and Related Subjects, Santiago de Compostela, Spain, May 2-6 2022.

# Charmonium production as a function of charged-particle multiplicity in pp
and p–Pb collisions with ALICE at the LHC

Theraa TORK  for the ALICE collaboration

###### Abstract

Heavy quarkonium production is an excellent tool to test both perturbative and
non-perturbative QCD, as perturbative QCD can describe the heavy quark
production process, while the formation of the quarkonium bound state involves
non-perturbative aspects. In ultrarelativistic heavy-ion collisions, a
deconfined state of QCD matter, made of free quarks and gluons, called quark-
gluon plasma (QGP) is expected to be formed. To probe such an environment, the
study of quarkonium production is an important tool as the heavy quarks are
produced during the initial stage of the collision and experience the entire
medium evolution. Surprisingly, in small colliding systems as pp and p–Pb,
QGP-like behaviours are observed when selecting high multiplicity events. The
physics interpretation of these behaviours remains unclear. However,
multiparton interaction is one of the main promising scenarios to explain such
observation. Studies of charmonium yields as a function of the event charged-
particle pseudorapidity density in pp and p–Pb collision allow one to probe
multiple parton interactions in an indirect way. These proceedings present the
measurements of quarkonium yields normalised to their average values as a
function of the charged-particle multiplicity in pp collisions at $\sqrt{s}$ =
13 TeV and in p–Pb collisions at $\sqrt{s_{\rm NN}}$ = 8.16 TeV, performed by
the ALICE experiment at the LHC. The corresponding results for the
$\psi\rm{(2S)}$-to-J/$\psi$ ratios as a function of charged-particle
multiplicity are also shown. In addition, J/$\psi$ pair production measurement
in pp collisions at $\sqrt{s}$ = 13 TeV is discussed.

##  1 Introduction

The early stages of a heavy-ion collision (A-A) include the formation of hot
and dense matter, known as quark-gluon plasma (QGP), consisting of freely
moving quarks and gluons. Quarkonia, i.e. charmonia (c$\Bar{\rm{c}}$) and
bottomonia (b$\Bar{\rm{b}}$), are expected to probe the whole evolution of the
QGP due to the early production of their constituent quarks. Moreover,
quarkonia are an excellent tool to test our current knowledge of QCD as heavy
quark production takes place during the hard processes of the collision,
whereas the quarkonium bound state formation is a soft process. Consequently,
quarkonium production is sensitive to both perturbative and non-perturbative
aspects of the QCD. The LHC data revealed several unexpected behaviours in
small systems (pp and p–Pb collisions) at high multiplicity, e.g, the non-zero
elliptic flow of identified hadrons through long-range angular correlation
measurementsin p–Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV [1] and the
enhanced production of multi-strange hadrons in pp collisions at $\sqrt{s}$ =
7 TeV [2]. These findings are quite surprising, as they are usually
interpreted as signatures of the QGP in A–A collisions. Multiparton
interactions (MPI) are one of the main scenarios proposed to explain these
observations in small systems. MPIs occur in events in which several parton-
parton interactions take place in a single hadron-hadron collision. Several
tools can be used to probe MPI with quarkonia, such as double quarkonium
production, or quarkonium production as a function of charged-particle
multiplicity. The former is a direct probe for MPI, as it is sensitive to
double hard parton scatterings. Moreover, it provides information on single
quarkonium production mechanisms [3]. However, a large integrated luminosity
is required to perform such analysis. On the other hand, the quarkonium
production as a function of charged-particle multiplicity is an indirect probe
for MPI. It is sensitive to the interplay between soft and hard QCD processes
in the event, as quarkonium production is a hard QCD process, whereas the
charged particles are usually produced during soft QCD processes.

In these proceedings, the results from pp and p–Pb collisions for the self-
normalised quarkonium yields, measured at midrapidity ( $|y\rm{{}_{lab}}|$ ¡
0.9 ) or forward rapidity ( 2.5 ¡ $|y\rm{{}_{lab}}|$ ¡ 4.0), as a function of
the self-normalised charged-particle multiplicity, measured at midrapidity,
are discussed. The ratio of the self-normalised $\psi\rm{(2S)}$-to-J/$\psi$
yields as a function of charged-particle multiplicity, in both pp and p–Pb
collisions, are also shown. Finally, the measurement of the J/$\psi$ pair
production cross section in pp collisions is presented.

##  2 Experimental setup

ALICE (A Large Ion Collider Experiment) is a general purpose detector at the
LHC, devoted to heavy-ion physics. In addition, it has a rich program in small
collision systems, such as pp and p-Pb. ALICE is equipped with 18 different
sub-detectors, which can be classified into three main categories, according
to their usage in the analyses described below: (i) the muon spectrometer,
which reconstructs and identifies the muon tracks at large rapidity, (ii) the
central barrel detectors which reconstruct at midrapidity the primary vertex
and charged-particle tracks, as well as J/$\psi$ in the dielectron decay
channel, (iii) global detectors which contribute to triggering, background
rejection and charged-particle multiplicity measurements. More details about
the ALICE detector and its performance can be found in Ref.[4]

##  3 Results

###  3.1 J/$\psi$ pair production in pp collisions at $\sqrt{s}$ = 13 TeV

The inclusive J/$\psi$ pair production cross section per rapidity unit in pp
collisions at $\sqrt{s}$ = 13 TeV is presented in the top panel of Fig.1(a).
The results are compared with those for prompt J/$\psi$ production from the
LHCb experiment, performed in a slightly larger rapidity window[5]. A good
agreement is observed between the two measurements within uncertainties. The
derived double-to-single J/$\psi$ production cross section results are shown
in the bottom panel of the figure. The ALICE and LHCb results are also
consistent within the uncertainties.

(a) J/$\psi$ pair production

(b) J/$\psi$ self-normalised yields at midrapidity

Figure 1: (a) Inclusive J/$\psi$ pair production cross section (top panel),
and ratio of double-to-single inclusive J/$\psi$ production cross sections
(bottom panel), in pp collisions at $\sqrt{s}$ = 13 TeV. Results are compared
with LHCb measurements for prompt J/$\psi$ production [5]. (b) J/$\psi$ self-
normalised yields as a function of the self-normalised charged-particle
multiplicity [6]. Both quantities are measured at midrapidity. The results are
compared with several theoretical models [7, 8, 9, 10, 11, 12].

###  3.2 Quarkonium production as a function of charged-particle multiplicity
in pp collisions

The multiplicity dependence of the inclusive J/$\psi$ production, measured at
midrapidity, in pp collisions at $\sqrt{s}$ = 13 TeV was reported in Ref.[6].
In this work, the J/$\psi$ yields and the charged-particle multiplicity are
normalised to their respective average values obtained in the integrated
multiplicity interval. As presented in Fig.1(b), the self-normalised J/$\psi$
yields at midrapidity exhibit a faster than a linear increase with the
increasing charged-particle multiplicity at midrapidity. The trend of the data
is described quantitatively by the following models: the coherent particle
production model (CPP) [7], the color glass condensate model (CGC) [9], the
3-pomeron CGC model [8]. The percolation model [10] describes the trend of the
data at low multiplicity. The aforementioned models include initial and final
state effects, as well as MPI to describe the behavior of the J/$\psi$ yields
as a function of the event multiplicity. EPOS3 [12] and PYTHIA 8.2 [11] events
generators describe qualitatively a faster than a linear increase but not as
strong as in the data.

The J/$\psi$ production at forward rapidity as a function of the charged-
particle multiplicity measured at midrapidity in pp collisions at $\sqrt{s}$ =
13 TeV has also been reported [13]. The J/$\psi$ self-normalised yields show
an increase compatible with a linear trend within uncertainties. This increase
is therefore less rapid than that of the J/$\psi$ yields measured at
midrapidity. The origin of the difference observed for these trends as a
function of multiplicity remains unclear, although the exercise consisting in
varying the rapidity range used to select the charged-particle multiplicity,
which is described in Ref.[6], suggests that it is not due to a possible bias
when the hard particle is produced in a jet.

In Ref.[14], the self-normalised forward $\psi\rm{(2S)}$ yields as a function
of the charged-particle multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV
are presented. The yields show an approximately linear increase with
multiplicity within the uncertainties, see Fig.2(a). The data are compatible
with PYTHIA 8.2 calculations [11], both with and without color reconnection
scenario (CR), within the uncertainties (see Ref.[14] for the comparison with
models). In Fig.2(b), the self-normalised $\psi\rm{(2S)}$-to-J/$\psi$ ratio is
shown as a function of charged-particle multiplicity. Measuring the excited-
to-ground charmonium state yield ratio allows disentangling possible final
state effects at play in pp collisions, as most of the other effects are
expected to cancel in the ratio. The data show a flat distribution as a
function of charged-particle multiplicity. PYTHIA 8.2 calculations suggest a
similar behavior for both $\psi\rm{(2S)}$ and J/$\psi$. The
$\psi\rm{(2S)}$-to-J/$\psi$ self-normalised yields are also compared with the
comover model calculations [15]. The comover model considers the possibility
for quarkonia to dissociate due to their interactions with the final state
particles that are comoving with them. The dissociation probability depends on
the size (binding radius) of the particle and the comover density. The comover
dissociation has a larger influence on $\psi\rm{(2S)}$ with respect to
J/$\psi$, due to its larger binding radius. In the multiplicity range where
the comover model calculations are available, data and model remain consistent
within uncertainties.

(a) $\psi(2S)$ self-normalised yield.

(b) $\psi(2S)$-to-J/$\psi$ self-normalised yield ratio.

Figure 2:  (a) Inclusive $\psi(2S)$ self-normalised yields, measured at
forward rapidity, as a function of the self-normalised charged-particle
multiplicity measured at midrapidity, in pp collisions at $\sqrt{s}=13$ TeV
and in p–Pb (Pb–p) collisions at $\sqrt{s_{\rm NN}}=8.16$ TeV at forward
(backward) rapidity[14]. (b) $\psi(2S)$-to-J/$\psi$ self-normalised yield
ratio, measured at forward rapidity, as a function of the self-normalised
charged-particle multiplicity, measured at midrapidity, in pp collisions at
$\sqrt{s}=13$ TeV [14]. Results are compared with predictions from comovers
model[10] and PYTHIA 8.2[11].

###  3.3 Quarkonium production as a function of charged-particle multiplicity
in p–Pb collisions

Several nuclear effects may influence the production of hadrons in p–Pb
collisions, as compared to pp collisions. The gluon shadowing [16] leads to
the suppression of quarkonium production in p–Pb collisions with respect to pp
collisions which is described by the modification of the parton distribution
functions in the nuclei (nPDF) with respect to isolated nucleons. The CGC
model [8] considers that at sufficiently high energies, the gluons interaction
probability increases due to their large density, reducing effectively their
total amount (gluon saturation). This scenario can influence both charged-
particle and quarkonium production rates. The fully coherent energy loss model
[17] suggests the emission of gluons, induced by the medium, coherently from
partons in the initial state and from the c$\Bar{c}$ pair in the final state.
On the other hand, the nuclear absorption [18] and the comovers models [15]
influence the production of heavy mesons due to the interaction with final
state particles. The nuclear absorption model predicts the breakup of
charmonia due to the interaction with the primordial nucleus. However, this
effect is neglected at the LHC energies, as the time needed to cross the
nucleus by the c$\Bar{\rm{c}}$ pair is much shorter than the charmonium
formation time.

The multiplicity dependence of the J/$\psi$ self-normalised yields in p–Pb
collisions at $\sqrt{s\rm{{}_{NN}}}$ = 8.16 TeV is reported in Ref.[19]. In
this analysis, J/$\psi$ mesons are reconstructed at forward and backward
rapidity in the nucleon-nucleon center-of-mass frame, while the charged-
particle multiplicity is measured at midrapidity. The results show an increase
of the yields with increasing multiplicity at both forward and backward
rapidity. This increase is weaker for the yields reconstructed at forward
rapidity with respect to the ones reconstructed at backward rapidity. The
trend of the yields are consistent with EPOS3 calculations [12]. The self-
normalised yields of the $\psi\rm{(2S)}$ as a function of the self-normalised
charged-particle multiplicity in p–Pb collisions are presented in Fig.2(a) and
compared to pp collisions. The $\psi\rm{(2S)}$ yield increases as a function
of multiplicity at both forward and backward rapidity in p–Pb collisions. This
increase is compatible with a linear increase, depicted as a dashed line in
the figure, within uncertainties. The $\psi\rm{(2S)}$ self-normalised yields
exhibit a similar behaviour in pp and p–Pb collisions within uncertainties. In
Fig.3(a), the self-normalised yields of $\psi\rm{(2S)}$, measured at forward
rapidity, are compared with the percolation coupled to comover model [15, 10]
and using EPS09 nPDF parameterizations [16]. The model includes the influence
of percolation, where the initial state partons are represented as strings
with a certain transverse size and can interact with each other. In a dense
environment, these strings can overlap, reducing the effective number of
strings, and leading to an effective reduction in the quarkonium production.
As described before, the comover model is based on the probability for
quarkonia to dissociate due to their interactions with final state particles.
The percolation + comover + EPS09 model is compatible with the data within
uncertainties (the large model uncertainties are dominated by the EPS09 ones).
The $\psi(2S)$-to-J/$\psi$ self-normalised yield ratio at forward rapidity as
a function of the charged-particle multiplicity at midrapidity is presented in
Fig.3(b) [14]. The result shows a distribution compatible with unity within
uncertainties. The measurements are compared to the comovers model
calculations [15]. Within the large experimental uncertainties, the results
remain consistent with the comover scenario, which suggests a slightly
stronger suppression of the $\psi\rm{(2S)}$ with respect to J/$\psi$ in the
high multiplicity region.

(a) Self-normalised $\psi\rm{(2S)}$ yield

(b) Self-normalised $\psi(2S)$-to-J/$\psi$ ratio

Figure 3: (a) The self-normalised $\psi(2S)$ yield and (b) the self-normalised
$\psi(2S)$-to-J/$\psi$ yield ratio, measured at forward rapidity, as a
function of the charged-particle multiplicity, measured at midrapidity, in
p–Pb collisions at $\sqrt{s\rm{{}_{NN}}}$ = 8.16 TeV [14]. The
$\psi(2S)$-to-J/$\psi$ yield ratios are compared to the percolation + comover
+ EPS09 model within the large uncertainties [15, 10, 16], while the
$\psi(2S)$ yields are compared to the comover model [15].

##  4 Summary

The J/$\psi$ pair production in pp collisions at $\sqrt{s}$ = 13 TeV is
presented. The result shows a good agreement within uncertainties with similar
measurements performed by the LHCb experiment. The J/$\psi$ and $\psi(2S)$
self-normalised yields show an increase as a function of the charged-particle
multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV and p–Pb collisions at
$\sqrt{s\rm{{}_{NN}}}$ = 8.16 TeV. The trend of the data is described by
several models which include initial and final state effects, as well as MPI.
In the measurement of the $\psi(2S)$-to-J/$\psi$ production ratios, a similar
behaviour for the two states is observed as a function of multiplicity, within
uncertainties. The experimental precision on the excited state measurements
together with the model uncertainties do not allow one to disentangle possible
final state effects at play. The LHC Run 3 will provide higher luminosity,
leading to more precise multiplicity-differential measurements, bringing
further constraints to MPI modeling.

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