Advances in High Energy Physics

Volume 2017 (2017), Article ID 1453045, 14 pages

https://doi.org/10.1155/2017/1453045

## Experimental Results on Charge Fluctuations in Heavy-Ion Collisions

^{1}Nuclear Physics Division, Bhabha Atomic Research Center, Mumbai 400085, India^{2}Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794-3800, USA

Correspondence should be addressed to D. K. Mishra

Received 7 September 2016; Revised 29 November 2016; Accepted 30 November 2016; Published 17 January 2017

Academic Editor: Shi-Hai Dong

Copyright © 2017 D. K. Mishra 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. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We present a subset of experimental results on charge fluctuation from the heavy-ion collisions to search for phase transition and location of critical point in the QCD phase diagram. Measurements from the heavy-ion experiments at the SPS and RHIC energies observe that total charge fluctuations increase from central to peripheral collisions. The net-charge fluctuations in terms of dynamical fluctuation measure are studied as a function of collision energy () and centrality of the collisions. The product of and shows a monotonic decrease with collision energies, which indicates that at LHC energy the fluctuations have their origin in the QGP phase. The fluctuations in terms of higher moments of net-proton, net-electric charge, and net-kaon have been measured for various . Deviations are observed in both and for net-proton multiplicity distributions from the Skellam and hadron resonance gas model for GeV. Higher moment results of the net-electric charge and net-kaon do not observe any significant nonmonotonic behavior as a function of collision energy. We also discuss the extraction of the freeze-out parameters using particle ratios and experimentally measured higher moments of net-charge fluctuations. The extracted freeze-out parameters from experimentally measured moments and lattice calculations are found to be in agreement with the results obtained from the fit of particle ratios to the thermal model calculations.

#### 1. Introduction

The main goal of the high energy heavy-ion collisions is to study the phase structure of the quantum chromodynamic (QCD) phase diagram at finite temperature () and baryon chemical potential () [1–5]. Several theoretical models suggest that the QCD phase diagram may contain a first-order phase transition line between the hadron gas (HG) phase and Quark-Gluon phase which ends at the critical point towards high and lower [6–10]. Experimental programs have been performed at SPS and beam-energy scan (BES-I) program at RHIC to search for critical point and QGP-HG phase transition. In future, the upcoming program at RHIC (BES-II) [11], FAIR [12], NICA [13], and J-PARC [14] will also contribute to the physics at large . The location of the QCD critical point can be explored by systematically varying and . Experimentally, by changing the center of mass energy one can control and of the system and hence enables us to scan different sectors of the phase diagram.

One of the most striking signatures of such a QGP-HG phase transition could be a strong modification in the fluctuations of specific observables measured on an event-by-event basis [15, 16]. In principle, any observable that is not globally conserved fluctuates. Although most of these fluctuations are trivial and are of statistical origin, it is important to find out the dynamically relevant event-to-event fluctuation that enables the search for a possible critical point and a first-order coexistence region in the QCD phase diagram [17]. Over the past two decades quite a number of such observables have been suggested for clarifying the evolution of the system formed in heavy-ion collisions. These either refer to the signals from the plasma that are supposed to survive the phase transition or to the observables that experience strong fluctuation during the phase transition or close to the critical point. Most commonly measured event-by-event fluctuations in heavy-ion collision experiments are particle ratios (, , etc.), transverse energy , mean transverse momentum , and particle multiplicity fluctuations [18–21]. Predictions suggest that enhanced multiplicity fluctuations are connected to the production of QGP droplets, and suppression of fluctuation is connected to the nucleation process in a first-order QGP-HG phase transition. This may happen because of the rapid freeze-out just after the phase transition [15, 22]. An isothermal compressibility of the system can be considered to understand the sensitivity of the measured particle multiplicity to the phase transition [23]. The isothermal compressibility is defined as , where , and are the pressure, volume, and temperature of the system, respectively. In order to relate the compressibility to the measurements of multiplicity fluctuations, we assume that relativistic heavy-ion collisions can be described as a thermal system in the Grand Canonical Ensemble (GCE) [24]. The GCE is the most appropriate description as only part of the particles from the system around mid-rapidity are measured by the experiments. The energy and conserved quantum numbers in this region can be exchanged with the rest of the system that serves as a heat bath [25]. Several other studies have applied Canonical and Microcanonical ensembles to the multiplicity fluctuations too [26–28]. In the GCE, the isothermal compressibility is directly related to the variance of the particle multiplicity as follows:where is the particle multiplicity, is the mean of the multiplicity distribution, and is the Boltzmann constant [29]. Here, multiplicity fluctuation measurements are presented in terms of the scaled variance, , as [30]

In a continuous or second-order phase transition, the compressibility diverges at the critical point. Near the critical point, this divergence is described by a power law in the variable , where is the critical temperature. Hence, the relationship between multiplicity fluctuations and the compressibility can be exploited to search for a signature of critical behavior by looking for the expected power law scaling of the compressibility:where is the critical exponent for isothermal compressibility [29]. Recent studies [31, 32] show the behavior of the quark number susceptibility, , which is related to the value of the isothermal compressibility of the system. They predict that its value will increase by at least an order of magnitude close to the QCD critical point. As discussed above, the scaled variance is proportional to ; hence, the measurements of charged particle multiplicity are expected to be a sensitive probe for critical behavior.

If the system approaches close enough to the critical line for a long enough time period, then critical phenomena could be observed through the measurement of multiplicity fluctuations [8]. Subsequently, it may also be possible to determine the critical exponents of the system. Observation of critical behavior in heavy-ion collisions and the subsequent measurement of the critical exponents could determine the universality class in which QCD is grouped, providing essential constraints for the models [30].

The fluctuations of conserved quantities are predicted to be one of the most sensitive signals of the QGP formation and phase transition, which may provide complementary understanding of strong interactions, apart from other QGP signatures [15, 33]. It has been argued that entropy conserving hadronization of plasma of quarks and gluons should produce a final state characterized by a dramatic reduction of the net-charge fluctuations in QGP phase as compared to that of a hadron gas. Further, prediction relies on the notion that quark-quark correlations can be neglected, and hadronization of gluons produces pairs of positive and negative particles not contributing to the net-charge fluctuations. It has also been suggested that the excitation function of conserved numbers like net-baryon, net-charge, and net-strangeness fluctuations should show a nonmonotonic behavior, as a possible signature of QCD critical end point (CEP) [1, 34, 35]. In the thermodynamic limit, the correlation length () diverges at CEP [1]. The experimentally measured moments of the net-baryon, net-charge, and net-strangeness distributions are related to the higher power of of the system and hence these moments can be used to look for signals of a phase transition and critical point [36, 37]. Also, the comparison of experimentally measured cumulants with the lattice calculations enables us to extract the freeze-out parameters, that is, freeze-out temperature () and of the system produced in heavy-ion collisions [38, 39]. In recent years, lots of efforts have been put on both theoretical and experimental fronts to study the fluctuation of conserved quantities.

This review is organized as follows. In the following section, we discuss the total charge fluctuations from various experiments. In Section 3, the results on net-charge fluctuation are presented, which include dynamical fluctuation measure , higher moments of net-proton, net-electric charge, and net-kaon fluctuations. Towards end of Section 3, extraction of freeze-out parameters using higher moments is discussed. Finally, in Section 4, we summarize our observations.

#### 2. Total Charge Fluctuation

In a thermodynamical system of strongly interacting matter formed in the heavy-ion collisions, the fluctuations of particle multiplicities, mean transverse momentum (), transverse energy (), and other global observables are related to the fundamental properties of the system, such as specific heat, chemical potential, and compressibility. These observables either refer to signals from the plasma that are supposed to survive the phase transition or to observables that experience strong fluctuations during the phase transition or close to the critical point. The existence of a critical point at the QCD phase transition has been associated with the large event-by-event fluctuations of above observables. As far as observables are concerned, electric charge fluctuations have been measured over a wide range of collision energies, from CERN SPS to RHIC and LHC energies. Enhanced fluctuations in neutral to charged pions have been predicted as a signature of the formation of Disoriented Chiral Condensates (DCC) [40, 41]. The relative fluctuation which can be extracted from experimental data has contributions from both statistical and dynamical sources. In order to extract the dynamical part associated with new physics from the observed fluctuations, one has to understand the contributions from statistical and other known sources. Some of the known sources of fluctuations contributing to the observed experimental value of scaled variance () include finite particle multiplicity, effect of limited acceptance of the detectors, impact parameter fluctuations, fluctuations in the number of primary collisions, effects of rescattering of secondaries, resonance decays, and Bose-Einstein correlations [42].

The relative fluctuation is defined as where is the charged particle multiplicity and is also known as scaled variance. If the multiplicity distribution is Poissonian, the scaled variance is 1.0. Figure 1 shows the comparison of the relative fluctuation of the charge particle multiplicity as a function of collision centrality which is related to number of participants () in Pb + Pb collisions at 158 AGeV [40]. The error on calculated in the model is mainly due to the error on the mean number of charged particles in nucleon-nucleon interactions, the error in the number of participants calculated, and the uncertainty in the calculated transverse energy [40]. The experimental data are compared with the model calculations. It is observed that the relative fluctuations increase from central to peripheral collisions. The observed charge particles multiplicity fluctuations have been found to well agree with the results obtained from a simple participant model [45]. In the participant model, the particle multiplicity may be expressed as where is the number of participants in the collision and is the number of particles produced by the th participant within the detector acceptance. The mean value of is the ratio of the average multiplicity measured in the detector acceptance to the average number of participants, . Hence, fluctuation in the particle multiplicity will have contributions due to fluctuations in , () and also due to the fluctuations in the number of particles produced per participant (). The multiplicity fluctuation in the participant model can be expressed as [40] Another experiment at SPS also performed similar study shown in Figure 2 [43]. The scaled variance (), where is the variance of the distribution and is the multiplicity of the particles. The scaled variance of positive, negative, and total charged particles as a function of centrality is shown in Figure 2. The experimental data is compared with the model calculations. The results from different models (HIJING [46], HSD [47], UrQMD [48], and VENUS [49]) are almost independent of centrality and behave like a Poisson expectation. However, the experimental data points indicate strong dependence on centrality. The scaled variance increases from central to peripheral collisions. The measured centrality dependence can be reproduced in superposition models with the assumption of contributions from target participants to the particle production in the forward hemisphere [43, 44]. Figure 3 shows the centrality () dependence of scaled variance at = 62.4 and 200 GeV in Au + Au collisions at RHIC [30]. The shaded regions represent the systematic uncertainties from the reference range. The statistical uncertainties are shown along with the data points. Here, represents the estimate of the remaining dynamical multiplicity fluctuations. For all centralities, the scaled variance lies above the Poisson expectation of 1.0. At these energies, also the scaled variance increases from central to peripheral collisions. Hence, similar centrality dependence has been observed by the experiments at the SPS and RHIC energies. The absence of large dynamical fluctuation in excess of the participant superposition model indicates that there is no evidence of critical behavior related to the compressibility observable.