Event-by-Event Particle Ratio Fluctuations at LHC Energies

A Monte Carlo study of identified particle ratio fluctuations at LHC energies is carried out in the frame work of \hij model using the fluctuation variable $\nu_{dyn}$. The simulated events for Pb-Pb collisions at $\sqrt{s}_{NN}$ = 2.76 and 5.02 TeV and Xe-Xe collisions at $\sqrt{s}_{NN}$ = 5.44 TeV are analyzed. From this study, it is observed that the values of $[\pi,K]$, $[p,K]$ and $[\pi,p]$ follow the similar trends of energy dependence as observed in the most central collision data by NA49, STAR and ALICE experiments. It is also observed that $\nu_{dyn}$ for all the three combinations of particles for semi-central and central collisions, the model predicted values of $\nu_{dyn}[A,B]$ for Pb-Pb collisions at $\sqrt{s}_{NN}$ = 2.76 TeV agree fairly well with those observed in ALICE experiment. For peripheral collisions, however, the model predicted values of $\nu_{dyn}[\pi,K]$ are somewhat smaller, whereas for $[p,K]$ and $[\pi,p]$ it predicts larger values as compared to the corresponding experimental values. The possible reasons for the observed differences are discussed. The $\nu_{dyn}$ values scaled with charged particle density when plotted against $\langle$N$_{part}$$\rangle$, exhibit a flat behaviour, as expected from the independent particle emission sources. For $[p,K]$ and $[\pi,p]$ combinations, a departure from the flat trend is, however, observed in central collisions in the case of low p$_{T}$ window when effect of jet quenching or resonances are considered. Furthermore, the study of $\nu_{dyn}[A,B]$ dependence on particle density for various collision systems (including proton-proton collisions) suggests that at LHC energies $\nu_{dyn}$ values for a given particle pair is simply a function of charged particle density, irrespective of system size, beam energy and collision centrality.


Introduction
Fluctuations associated to a physical quantity measured in an experiment, in general, depend on the property of the system and are expected to provide useful clue about the nature of the system under study [1,2,3]. As regards the heavy-ion (AA) collisions, the system created is assumed to be a hot and dense fireball of hot partonic and (or) hadronic matter [1,2]. One of the main aims of studying AA collisions at relativistic energies is to search for the existence of partonic matter in the early stage of the created fireball. Fluctuations associated to a thermal system are supposed to be related to various susceptibilities [1,2,4] and would serve as an indicator of the possible phase transition. Moreover, the presence of large event-by-event (ebe) fluctuations, if observed, might be signal for the presence of distinct classes of events, one with and one without QGP formation [5,6,7]. Therefore, the search for the phase transition from hadronic matter to QGP still remains a topic of interest of high energy physicists [8,9,10].
Correlations and ebe fluctuations of dynamical nature are believed to be associated with the critical phenomena of phase transition and their studies would lead to the local and global differences between the events produced under similar initial conditions [11]. ebe fluctuations in hadronic and heavy-ion collisions have been investigated at widely different energies using several different approaches, for example, normalized factorial moments [12,13,14,15], multifractals [16,17], k-order rapidity spacing [18,19,20], erraticity [21,22,23], intensive and strongly intensive quantities (defined in term of multiplicity, transverse momentum, p T , etc.) [24,25,26].
Furthermore, ebe fluctuations in conserved quantities like strangeness, baryon number and electric charge have emerged as new tools to estimate the degree of equilibration and criticality of the measured systems [27,28,29,30,31]. The dynamical net charge fluctuations have been investigated by STAR and ALICE experiments [28,29] in terms of variable ν dyn [32], which is an excellent probe because of its robustness against detector efficiency losses [29]. The other measures of the net charge fluctuations, like the variance of charge V(Q), variance of charge ratio V(R), and the D-measure [29,31,33,34] prone to the measurement conditions [32,35].
It has, however, been pointed out [36] that large systematic uncertainties, like volume fluctuations due to impact parameter variations are associated in such measurements, while the multiplicity ratio fluctuations are sensitive to the density fluctuations instead of volume fluctuations [37]. Thus, the variable ν dyn , defined by considering the particle species pair, rather than defining it in terms of combinations of like and unlike charges, has been used as a tool to probe the properties of QGP [33,38]. Since it is speculated that the phase transition,  [42] and several others [33,36,38].
At LHC energies, the particle ratio fluctuations has been investigated by ALICE experiment at √ s N N = 2.76 TeV only [43,44,45]. It has been reported [43] that ν dyn for [π, K] and [p, K] combinations acquires positive values irrespective of the centrality class, whereas, for [π, p] combination, the variable changes sign from positive to negative toward more peripheral collisions, indicating the difference in the production mechanisms involved of these pairs. The observed trend of energy dependence of ν dyn with beam energy [43] suggests that the production dynamics changes significantly from that reported at lower energies. It has also been pointed out [43] that further investigations involving fluctuations with charge and species specific pairs be carried out to characterize the production dynamics and understand the observed sign changes. It was, therefore, considered to undertake the study of particle ratio fluctuations by analysing the data on Pb-Pb collisions at √ s N N = 2.76 and 5.02 TeV and Xe-Xe collisions at √ s N N = 5.44 TeV in the framework of HIJING model. Using the HIJING the effect of jet quenching and resonance production can also be looked into.

Formalism
The particle ratio fluctuations may be studied in terms of the yields of the ratio of particle types A and B. The particle ratio A/B is estimated by counting the particle types A and B produced in each event. Using the relative widths of the particle ratio distributions of the data and the corresponding mixed events the observable σ dyn is defined as [38,46]: where σ data and σ mixed respectively denote the relative widths (standard deviation/mean) of the ratio A/B for the data and mixed events. Yet another variable ν dyn , which is commonly accepted for studying the particle ratio fluctuations has been proposed [32]. ν dyn [A, B] quantifies the deviation of the fluctuations in the number of particle species A and B from that expected from Poissonian statistics [46]. This variable does not involve particle ratios directly but is related to σ dyn [42,46].
The ν dyn [A, B] is defined as [38,43,45,46]: where N A and N B respectively denote the event multiplicities of particle types A and B within the given kinematical limits, while the quantities within ... represent their mean values. It should be mentioned here that the particle type A or B includes the particle and its anti-particle.   [48,51,52,53,54,55]. Besides this, the basic property of HIJING model is that it considers the nucleus-nucleus collisions as a superposition of nucleon-nucleon collisions. However, the mechanism for final state interactions among the low p T particles is not included in the HIJING model.
Due to which the phenomena such as collectivity and equilibrium can not be addressed. Therefore, HIJING is mainly designed to explore the range of possible initial conditions that may occur in high energy heavy-ion collisions.
Furthermore, HIJING also takes into account other important physics processes like jet quenching [56], multiple scattering and nuclear shadowing to study the nuclear effects [48]. To study the dependence of moderate and high p T observables on an assumed energy loss of partons traversing the produced dense matter, a jet quenching approach is incorporated in the HIJING model [48].
In high energy heavy-ion collisions, the interaction of high p T jets in the produced transient dense medium is treated as one of the signals of phase transition [56].
Therefore, the rapid-variation of µ D (Debye Screening) near the phase transition point could lead to a variation of jet quenching phenomenon, that could be used as a diagnostic tool of the QGP phase transition [48]. window. However, if both decay products lie within the acceptance cone, mean charged particle multiplicity will increase but the net charge does not change [58].
Hadron production in HIJING involves a cocktail of resonances that may also give a rough estimate of the strength of correlations between charged and neutral kaons [59]. Present study is an attempt to explore the effect of fluctuations in understanding the dissipative properties of a color defined medium using the jet quenching, resonance production and jet/minijet contributions incorporated in HIJING model [60]. It was found that [61,62,63,64] the HIJING predicted values of charged particle density when jet quenching and contributions from resonance  Table 1. The analysis is carried out by considering only those charged particles which have pseudorapidity (η) and transverse momentum (p T ) in the range, |η| < 0.8 and 0.2 < p T < 1.5 GeV/c respectively. ALICE experiment has also used same η-cut but instead of p T they have considered the charged particles with momentum, 0.2 < p < 1.5 GeV/c. It may be mentioned here that for the η range considered in ALICE experiment and also in the present study, for p T < 5.0 GeV/c, p T ≃ 0.9p. In order to examine the effect of jet quenching, a higher p T range, 0.2 < p T < 5.0 GeV/c, is also considered where this effect is expected to be more visible. The centrality of an event is estimated by applying VZERO-A and VZERO-C detector η cuts of the ALICE experiment [65,66,67], i.e., by considering the charged particles which have their η values in the range, 2.8 < η < 5.1 or −3.7 < η < −1.7. For this multiplicity distributions of charged particles having their η values within these limits are examined and quantiled to fix the minimum and maximum limits for a centrality class.
The values of mean number of participating nucleons, N part and mean charged particle density, dN ch /dη for different centrality classes are listed in Tables 2-4.
Variations of dN ch /dη with N part for these events are plotted in Fig.1. The values of N part and dN ch /dη reported earlier [65,66,67] are also given in these tables and displayed in the figure. It is interesting to note from Tables 2-4 and Fig.1 that HIJING-default predicts somewhat higher values of N part and dN ch /dη for various centrality classes as compared to those observed in experiments [65,66]. It may also be noted from the tables and the figure that the values of dN ch /dη are higher when jet quenching is turned on, which might be due to the enhanced production of low p T particles. This may be understood as when a partonic jet is quenched in the dense medium, it would fragment into large number of partons which, in turn, result in the production of low p T charged particles [68]. It may also be noted that the effect of jet quenching is rather more pronounced in central collisions, as compared to that in peripheral collisions. Enhancement in the dN ch /dη values due to resonances may also be seen in the figure.
Variations of mean multiplicities of charged pions, kaons, protons and antiprotons with N part are shown in Fig.2. It is observed that mean multiplicities of π ± , K ± and pp increase with increasing N part in almost identical fashion. It is also noted that the contributions to the particle multiplicities due to the jet quenching and resonance decays are maximum in most central collisions, which gradually decrease with N part and tend to vanish for N part values corresponding to centrality ∼ 50% and above. The reasons for the enhancement in particle multiplicities have been discussed in the previous section.  [41] and ALICE experiment [43] are also presented in the figure. Kinematical ranges used in these experiments are mentioned in the figure.
The statistical errors associated to ν dyn are too small to be visible in the figure.
These errors are determined using the sub-sample method [40]: The data set is divided into 30 sub-samples and the values ν dyn [A, B] i are calculated for each sub-sample independently. Using these values of ν dyn , the mean and dispersion are estimated as; The statistical error associated is then calculated as; The following observations may be made from the figure: GeV an increasing trend in ν dyn [π, K] is seen with decreasing beam energy.
Such a difference in ν dyn [π, K] values observed in NA49 [40] and STAR [41] experiments has been argued to be due to the difference in measurement methods adopted in the two experiments. The observed positive values of ν dyn [π, K] in experiments from √ s N N = 7.7 GeV to 2.76 TeV as well as predicted by UrQMD, HSD [41] and HIJING in the present study are either due to the dominance of variance of K and π or because of the presence of an anti-correlation ( N π N K < 0) between the K and π.
• ν dyn [p, K] values, as reported by STAR [41] and ALICE [43], may be observed to show an increasing trend with beam energy. At  iments has been argued to be due to increasing rate of pair production as compared to the rate of ∆ resonance production with increasing beam energy.
Variation of ν dyn with N part for the three combinations of particle species are shown in Fig.4. It is observed that ν dyn is maximum for the smallest value of N part , i.e., for peripheral collisions. It decreases quickly as N part becomes larger and thereafter acquire nearly constant positive values for N part ≥ 100.
In order to examine the effect of jet quenching, a parallel analysis of the data considering the p T range 0.2 < p T < 5.0 GeV/c is also carried out, because this effect is expected to be more visible on higher p T range. The values of ν dyn for this p T range are plotted against N part in Fig.5 Although ν dyn is robust against detector efficiency losses, yet it has some intrinsic multiplicity dependence [43,71]. In order to reduce the effect of multiplicities, the ν dyn values for all three combinations of particles are scaled by mean charged particle density, dN ch /dη . This removes the 1/N ch dependence of ν dyn [32,42]. Shown in Fig.8 are dependence of ν dyn [A, B] on the mean charged particle density for the three particle type pairs and three tunes of HIJING at the three incident energies. These plots are obtained for the p T range, 0.2 < p T < 1.5 GeV/c. Similar plots for 0.2 < p T < 5.0 GeV/c are presented in Fig.9. In order to examine   Res-on JQ-off 3.7         GeV/c.