Advances in High Energy Physics

Volume 2019, Article ID 3905376, 9 pages

https://doi.org/10.1155/2019/3905376

## Centrality Dependence of Multiplicity Fluctuations in Ion-Ion Collisions from the Beam Energy Scan at FAIR

Department of Physics, Aligarh Muslim University, Aligarh 202002, India

Correspondence should be addressed to Shakeel Ahmad; hc.nrec@damha.leekahs

Received 12 June 2019; Accepted 30 July 2019; Published 2 December 2019

Academic Editor: Fu-Hu Liu

Copyright © 2019 Anuj Chandra et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Multiplicity distributions and event-by-event multiplicity fluctuations in AuAu collisions at energies in future heavy-ion experiment at the Facility for Anti-proton and Ion Research (FAIR) are investigated. Events corresponding to FAIR energies are simulated in the frame work of Ultra Relativistic Quantum Molecular Dynamics (URQMD) model. It is observed that the mean and the width of multiplicity distributions monotonically increase with beam energy. The trend of variations of dispersion with mean number of participating nucleons for the centrality-bin width of 5% are in accord with the Central Limit Theorem. The multiplicity distributions in various centrality bins as well as for full event samples are observed to obey Koba, Nielsen and Olesen (KNO) scaling. The trends of variations of scaled variance with beam energy are also found to support the KNO scaling predictions for larger collision centrality. The findings also reveal that the statistical fluctuations in 5% centrality-bin width appear to be under control.

#### 1. Introduction

Any physical quantity measured in an experiment is subject to fluctuations. These fluctuations depend on the property of the system and are expected to provide important information about the nature of the system under study [1, 2]. As regards relativistic heavy-ion (AA) collisions, the system so created is a dense and hot fireball consisting of partonic and (or) hadronic matter [1, 2]. To investigate the existence of partonic matter in the early life of fireball is one of the main goals of AA collisions. Study of fluctuations in AA collisions would help to check the idea that fluctuations of a thermal system are directly related to various susceptibilities and could be an indicator for the possible phase transitions [1–3]. Fluctuations in experimental observables, such as charged particle multiplicity, particle ratios, mean transverse momentum, and other global observables are related to the thermodynamic properties of the system, like, entropy, specific heat, chemical potential, etc. [4–7]. Event-by-event (ebe) fluctuations of these quantities are regarded as an important mean to understand the particle production dynamics which, in turn, would lead to understand the nature of phase transition and the critical fluctuations at the QCD phase boundary. A non-monotonic behavior of the fluctuations as a function of collision centrality and energy of the colliding beam may signal the onset of confinement and may be used to probe the critical point in the QCD phase diagram [7]. The multiplicity of charged particles produced in heavy-ion collisions is the simplest and day-one observable, which provides a mean to investigate the dynamics of highly excited multi-hadron system. Studies involving multiplicity distributions (MDs) of the relativistic charged particles produced would allow finding the deviations from a simple superposition of multiple independent nucleon–nucleon () collisions. Such studies, if carried out in limited rapidity space are envisaged to provide useful information on dynamical fluctuations [8–11]. It has been stressed that moments of MDs in full and limited rapidity bins would lead to make some interesting remarks about the production mechanisms involved. Dependence of MDs and their moments on collision centrality is also expected to lead to some interesting conclusions because of the fact that in narrow centrality windows the geometrical fluctuations may be treated as under control, whereas, such windows, if correspond to most central collisions, may be of additional importance because of the extreme conditions of temperature and excitation energy [7]. An attempt is, therefore, made to study the multiplicity fluctuations in the narrow centrality windows in AuAu collisions for the Beam Energy Scan (BES) at FAIR energies (for 10, 20, 30 and 40A GeV) in the frame work of URQMD model, using the code, urqmd-v3.4 [12, 13]. The number of events simulated at these energies are 2.3, 2.3, 2.1, and 2.2M () respectively. The analysis is carried out in the pseudorapidity () and transverse momentum () intervals: and GeV/c respectively.

#### 2. The URQMD Model

Multiparticle production in relativistic collisions have been described earlier within the hydrodynamic approach [14]. At a later stage, the Regge theory [15] and multiperipheral models were developed [15, 16]. Although the difficulties attributed to the statistical models were overcome in these models, yet the inconvenience of this approach is the large number of free parameters which are to be fixed by comparison with the experiments. Subsequently various quark-parton models motivated by QCD were introduced and as a consequence a large variety of models for hadronic and heavy-ion collisions were proposed. These models may be classified into macroscopic (statistical and thermodynamic) models [17] and microscopic (string, transport, cascade, etc.) models, like URQMD, VENUS, RQMD, etc. The microscopic models describe the individual hadron-hadron collisions.

URQMD model is based on the covariant propagation of constituent quarks and di-quarks but has been accompanied by baryonic and mesonic degrees of freedom. At low energies, 5 GeV, the collisions are described in terms of interactions between hadrons and their excited states [17], whereas at higher energies (5 GeV), the quark and gluon degrees of freedom are considered and the concept of color string excitation is introduced with their subsequent fragmentation into hadrons [13]. In a transport model, AA collisions are considered as the superposition of all possible binary collisions. Every collision corresponding to the impact parameter, is considered, where represents the total cross section. The two colliding nuclei are described by Fermi gas model [17] and hence the initial momentum of each nucleon is taken at random between zero and Thomas-Fermi momentum. The interaction term includes more than 50 baryon and 45 meson species. The model can treat the intermediate fireball both in and out of a local thermal and chemical equilibria. The URQMD model, thus, provides an ideal framework to study heavy-ion collisions. Although, the phase transition from a hadronic to partonic phase are not explicitly included in the model, thus a clear suggestion about the location of critical point can not be made. The study, however, might help in the interpretation of the experimental data since it will permit subtraction of simple dynamical and geometrical effects from the expected Quark Gluon Plasma (QGP) signals [18].

#### 3. Results and Discussion

The URQMD model gives the value of impact parameter, *b* on ebe basis which allows to determine the collision centrality and mean number of participating nucleons, using the Glauber model [7, 19]. Values of number of participating nucleons, mean charged particle multiplicities and dispersion of MDs () for various collision centralities at the four energies are estimated and listed in Tables 1–4. The centrality selection is made from the MDs of charged particles for the minimum bias events in the considered and ranges. This is illustrated in Figure 1, where the multiplicity distribution of minimum bias events for = 40A GeV is displayed. The shaded regions show 10% centrality cross-section bins. Variations of and with for the centrality bin width = 2, 5 and 10% are presented in Figures 2 and 3. The statistical errors associated with these parameters are too small to be noticed in the figures. It may be noted from these figures that and increase smoothly with or collision centrality. The lines in Figure 2 are due to the best fits to the data obtained using the equation

whereas, in Figure 3 the lines are due to the least square fits to the data of the form