J yields in low energy nuclear collisions at SPS and FAIR a baseline estimation

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J/ψyields in low energy nuclear collisions at SPS and

FAIR: a baseline estimation

S. Chatterjeea, P. P. Bhadurib,c,∗, S. Chattopadhyayb,c

aDepartment of Physics, Bose Institute, EN-80, Sector V, Kolkata-700091, India

bVariable Energy Cyclotron Centre, Bidhan Nagar, Kolkata-700064, India

cHomi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India

Abstract

The yield of J/ψ mesons, produced in proton-nucleus (p+A) and nucleus-

nucleus (A+A) collisions are estimated within a Glauber model ansatz for the

upcoming low energy heavy-ion collision experiments at SPS and FAIR. A data

driven parametrization is employed to incorporate the eﬀects of Cold Nuclear

Matter (CNM) on the J/ψ production cross-section.

Keywords: FAIR, SPS, Charmonium, Cold Nuclear Matter (CNM), Glauber

model

1. Introduction

The study of J/ψ production in relativistic nuclear collisions, is considered as

a promising diagnostic tool to characterize the hot and dense matter produced

in the collisions, since the seminal work by Matsui & Satz in 1986 [1]. The

suppression of the production yield of J/ψ mesons in heavy-ion collisions with

respect to proton-proton (p+p) and proton-nucleus (p+A) collisions was pro-

posed as an experimental signature of deconﬁnement transition and formation

of Quark-Gluon Plasma (QGP) [2]. Debye screening of the conﬁning potential

in a partonic medium was originally proposed as the only QGP eﬀect causing

dissociation of charmonium states. By now it is well known that suppression

∗Corresponding author

Email address: partha.bhaduri@vecc.gov.in (P. P. Bhaduri)

Preprint submitted to Elsevier October 21, 2022

arXiv:2210.10844v1 [hep-ph] 19 Oct 2022

to a large extent is also induced by the medium-induced imaginary potential

of the quarkonium system. In transport models of heavy-ion collisions, this is

dubbed in terms of the inelastic collisions with hard gluons leading to the ther-

mal broadening of the width of the in-medium quarkonium spectral function (see

Ref. [3] for a detailed review of the recent progress achieved in understanding

quarkonium under extreme conditions, from a theoretical perspective.)

Soon after the Matsui-Satz prediction, experimental investigations carried

out at SPS identiﬁed a considerable amount of J/ψ suppression already present

in p+A collisions [4, 5, 6, 5], when compared with the yield in p+p collisions. A

detailed survey on charmonium production at energies available at CERN-SPS

and BNL-RHIC can be found in Ref. [7]. In proton induced collisions, QGP

or in general formation of any secondary medium is traditionally not antici-

pated. However, the results from the recent experimental programs at the LHC

as well as at RHIC, have raised the question of whether there is a hydrody-

namic medium created in these so-called smaller systems [8, 9]. This change

of paradigm may have consequences for lower energies, in particular at large

charged particle multiplicity. As this article is focused on the low energy do-

main of the heavy-ion collisions, where the occurrence of the high multiplicity

events would be extremely rare, hence it might be justiﬁed to assume the ab-

sence of any secondary medium in proton induced collisions. The p+p collisions

might be considered to mimic the QCD vacuum. On the other hand, in p+A

reactions, the nascent J/ψ mesons during the pre-resonance or resonance stage

of evolution may interact with the nucleons present in the target nucleus, the

so-called primary medium, which might lead to their dissociation. Quantiﬁca-

tion of such Cold Nuclear Matter (CNM) eﬀects were traditionally attempted

within the Glauber model framework, by analyzing the target mass dependence

of the production cross-section of J/ψ mesons in p+A collisions [10]. An eﬀec-

tive “absorption” cross-section σeff

J/ψ measures the overall suppression present

in the data [4, 5, 6, 5]. Systematic analysis of the data collected in these p+A

reactions reveals a signiﬁcant dependence of the absorption cross-section on col-

lision energy with more dissociations at lower energies, as originally predicted

in Ref. [11]. Experimental conﬁrmation of this fact was subsequently performed

by the NA60 Collaboration at SPS [12]. The measurements revealed that in

158 GeV p+A collisions the J/ψ absorption cross-section directly extracted

from data is almost twice as large as that at 400 GeV. Estimation of the CNM

suppression with high precision is an essential prerequisite to correctly interpret-

ing the J/ψdata collected in nucleus-nucleus (A+A) collisions and to isolate the

genuine eﬀects of a hot and dense secondary medium. Extensive measurements

of J/ψ production in heavy-ion collisions were performed at SPS: in 158 A GeV

Pb-Pb collisions by the NA50 Collaboration [13] and subsequently in 158 A GeV

In-In collisions by the NA60 Collaboration [14]. The pertinent earlier signiﬁ-

cant experimental works at the SPS on the J/ψ production can be found in

Ref. [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. Within errors, the relative

J/ψ yield in In-In collisions has been found to be in line with suppression in-

duced by cold nuclear matter; an additional suppression of about 25 - 30 % is

observed in the most central Pb-Pb collisions. The conceptual origin of this

anomalous suppression is not yet clear, a variety of models with and without

plasma suppression eﬀects are available in the literature, none of which can pre-

cisely explain the data. The reader may note that the statistical regeneration

picture of charmonium production, a feature found essential at RHIC and LHC

energies, was also applied to the SPS heavy-ion data [27].

In nuclear collisions, no measurement on J/ψ production below top SPS en-

ergy (158 A GeV) has been attempted till date, owing to extremely low charm

production cross-sections. J/ψ measurements in low energy collisions demand

accelerators with unprecedented beam intensities and detectors with very high

rate capabilities. The Compressed Baryonic Matter (CBM) experiment, cur-

rently being constructed at the Facility for Anti-proton and Ion Research (FAIR)

accelerator complex in Darmstadt, Germany aims at the measurement of J/ψ

mesons via their decay into dileptons (both e+e−and µ+µ−channels) in pro-

ton and ion induced collisions [28]. The SIS100 accelerator at FAIR will deliver

accelerated proton beams with beam energy up to 30 GeV, while for heavy

ions (Z/A ∼0.4) the foreseen beam energy ranges between 3.43 - 12.04 A GeV

and for light ions (Z/A ∼0.5) 3.43 - 15.0 A GeV [29, 30], corresponding to

centre-of-mass energy √sNN ∼2.7 - 5.5 GeV. The foreseen unprecedented

beam intensities for both protons and heavy-ions at FAIR would enable the

detection of J/ψ mesons in p+A and nucleus-nucleus (A+A) collisions. At

FAIR, J/ψ production would occur close to its kinematic production threshold

(Eth

b∼12.5 GeV for an elementary NN reaction like: N+N→N+N+J/ψ).

The physics perspectives of the planned J/ψ measurements [31] include a strin-

gent test of the perturbative QCD (pQCD) based models of charmonia pro-

duction near threshold, the investigation of charm production and propagation

through dense baryonic medium and the possibility of discovering the predicted

sub-threshold charm production [32] in ion-ion collisions among the others.

Another complementary experiment to CBM is the NA60+ experiment at

CERN-SPS [33]. The NA60+ experiment plans to extend the existing study

on charmonia production by performing the J/ψ measurement via the di-muon

decay channel in the beam energy range 40 A to 160 A GeV, corresponding to

the center of mass energy range of √sNN ∼6 -17 GeV. Thus with the data from

CBM and NA60+, the dynamics of the J/ψ, likely to be produced in the early

stages of the collisions, can be probed over a large energy range, in a rather

unexplored energy domain. In addition to the unavailability of A+A data, no

systematic measurements have been performed so far on charmonium produc-

tion below 158 GeV in p+A collisions. This certainly calls for phenomenological

investigations on J/ψ production at low energies relevant for the upcoming ex-

perimental programs. A suitable estimation of J/ψ yields in this energy domain

would be extremely useful to optimize and reliably access the physics capabilities

of charmonium measurements of the corresponding experimental setups.

In the present article, we adopt the conventional geometrical Glauber formal-

ism for calculating the cross-section and yield of the J/ψ mesons, produced in

the early stages of p+A and A+A collisions at foreseen CBM and NA60+ ener-

gies. In literature, J/ψ production in elementary collisions is generally modelled

as a two step process: initially compact c¯cpairs produced via hard scattering are

treated with perturbative QCD (pQCD), whereas subsequent resonance binding

of the pair is non-perturbative in nature and treated phenomenologically. The

application of such two component models is based on QCD factorization, which

separates the initial c¯cproduction from the formation of the bound state. How-

ever at low collision energies, like those will be available at FAIR or CERN-SPS,

the validity of the QCD factorization is questionable. We thus employ here a

theory agnostic data driven parametrization to calculate the J/ψ production

in elementary p+pcollisions. The corresponding production cross-section in

p+Aand A+Acollisions are estimated employing the Glauber framework,

where the so called CNM suppression eﬀects are incorporated via an eﬀective

absorption cross-section. No additional medium eﬀect is incorporated in our

calculations, even for A+A collisions. Our estimations would thus serve as a

reference baseline for the upcoming measurements, with respect to which pos-

sible genuine secondary medium eﬀects on charmonium production if present,

can be isolated.

The article is organized in the following way. In section 2, for completeness,

we present a brief introduction to the Glauber model. J/ψ production in ele-

mentary proton-nucleon (p+N) collisions is discussed in section 3, while that in

p+A and A+A collisions within the present geometrical approach are provided

in section 4. Section 5 presents the projected J/ψ yield for diﬀerent collision

systems at diﬀerent energies, relevant for the upcoming experimental facilities.

We summarise our results in section 6.

2. Brief introduction to the Glauber model

In relativistic heavy-ion collisions, the Glauber model is common for a quan-

titative description of the geometrical conﬁguration of the colliding systems [34]

and related particle production. The model is based on the mean free path

concept with a minimal set of assumptions like the baryon-baryon interaction

cross-section remains unaltered throughout the passage of baryons of one nu-

cleus into another and the nucleons follow a straight-line trajectory along the

axis of collision. For two nuclei colliding at a certain impact parameter, the

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J/yieldsinlowenergynuclearcollisionsatSPSandFAIR:abaselineestimationS.Chatterjeea,P.P.Bhadurib,c,,S.Chattopadhyayb,caDepartmentofPhysics,BoseInstitute,EN-80,SectorV,Kolkata-700091,IndiabVariableEnergyCyclotronCentre,BidhanNagar,Kolkata-700064,IndiacHomiBhabhaNationalInstitute,AnushaktiNagar,Mumbai4...

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J yields in low energy nuclear collisions at SPS and FAIR a baseline estimation

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