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Event by Event analysis of Maximum Pseudo-rapidity Gap Fluctuation in High energy Nucleus-nucleus Collisions

A study of Event by Event analysis of maximum Pseudo-rapidity Gap Fluctuation in heavy-ion collisions in terms of the scaled variance {\omega} has been carried out for relativistic AA collisions with multiplicity cut (N>10) using nuclear emulsion data at 4.5 AGeV/c. The values of scaled variance are found to be greater than zero indicating the presence of strong fluctuation of maximum rap gap values in the multiparticle production process. The event by event fluctuations are found to decrease with the increase of average multiplicity of the interactions. Experimental analysis has been compared with the results obtained from the analysis of events simulated by generating random numbers (MC-RAND events) and also by Ultra Relativistic Quantum Molecular Dynamics (UrQMD) model. UrQMD model simulated values of event by event fluctuations of maximum rapidity gap are less than the corresponding experimental values.


Introduction
High energy nucleus-nucleus collisions deals with the production of copious amounts of various particles and multiplicity of such particles are extremely important to investigate the detailed characteristics of particle production process. The goal of the current heavy-ion collision physics is to study the properties of the phase transition between the quark-gluon plasma (QGP) phase and the ordinary hadronic phase. Fluctuation measurements in heavyion collisions have a good chance of being the signals of the QGP formation. The study and analysis of fluctuations are an essential method to characterize a physical system.
Fluctuations of different observables of the final-state particles act as a probe to study the phase transition [1][2][3][4]. Fluctuation in particle multiplicity and momentum distribution has been found to be very useful to explore the thermalization and statistical behaviour of the produced particles [5][6][7][8][9]. Multiplicity fluctuation can tell us whether a global thermalization has been achieved [10]. In nucleus-nucleus collisions, transverse energy is an extensive global variable. Transverse energy is also an indicator of the energy density achieved in the collisions. Studies of transverse energy fluctuations are very important [11][12] as energy density is directly related to the formation of QGP. Charge fluctuations [13][14][15] are sensitive to the unit charge of the underlying system. Quarks have fractional electric and baryonic charges. Therefore, the fluctuations of those charges in a QGP and a hadronic matter are clearly distinguishable. All these are interesting and deserve careful study. There has been evidence for occurrence of multiplicity fluctuations in the pseudo-rapidity distributions [16].
The existence of such fluctuations would give information on the substructure in space-time of collision region. Large fluctuations in pseudo-rapidity window have been observed in cosmic ray events and in hadron-hadron, nucleus-nucleus and hadron-nucleus interactions at accelerator energies [17][18]. They have been interpreted in terms of several models: as a possible indication of hadronic phase transition, as Cherenkov radiation or simply originating from a cascade mechanism. The rapid development in the field of pion multiplicity fluctuations in recent years is related to the large amount of high multiplicity data from well-known heavy ion experiments at CERN-SPS and BNL-RHIC. Although some progress has been made in understanding the fluctuation phenomena, a lot of questions remain unanswered. 3 In the recent years studies of event by event fluctuations have gained immense popularity among the scientists. The study of event-by-event fluctuations in high-energy heavy-ion collisions may provide us more information about the multiparticle production dynamics [19][20][21][22]. Event-by-event analysis is potentially a powerful technique to study relativistic heavy-ion collisions, as the magnitude of fluctuations of various quantities around their mean values is controlled by the dynamics of the system. It is believed that a detailed study of each event produced in high-energy nucleus-nucleus collision, may reveal new phenomena occurred in some rare events for which favourable conditions may have been created. High-energy nucleus-nucleus collisions produce a large number of particles. The study of a single event with large statistics can reveal very different physics than the analysis of averages over a large statistical ensemble. Event-by-event fluctuations may provide us information about the heat capacity [21,[23][24][25], possible equilibration of the system [26][27][28][29][30][31][32][33][34] or about the phase transition [25,35]. An important characteristic of muliparticle production that deserves special attention is the maximum pseudo-rapidity gap. Maximum pseudo-rapidity gap (Δη max in an event has been defined as the difference of maximum and minimum pseudo-rapidity values of the two produced shower particles in an event.
From the maximum pseudo-rapidity gap values one can get information for the particle production process. Diffractive processes are expected to contribute mainly due to the larger values of pseudo-rapidity gaps [36]. Maximum pseudo-rapidity gap values are important to study long range correlations suppressing the contributions from resonance and mini-jets [37].
So far investigations of fluctuations of rapidity gaps have been carried out by different groups [38][39][40][41] to extract the dynamical signal of particle production process. None so far have studied the event by event fluctuations of maximum pseudo-rapidity gap (Δη max .
This study may also be a potential source of information towards the hidden dynamics of particle production process.
Our aim in this paper is to carry out a detailed analysis of the event-by-event fluctuations of maximum pseudo-rapidity gap in terms of the scaled variance for 16 O-AgBr, 28 Si-AgBr and 32 S-AgBr interactions at an incident momentum of 4.5 AGeV/c. Experimental analysis has been compared with the results obtained from the analysis of events simulated by 4 generating random numbers (MC-RAND events) and also by Ultra Relativistic Quantum Molecular Dynamics (UrQMD) model.

Experimental Details
The present analysis is based on the interactions of 16 O, 28 Si and 32 S projectiles at an incident momentum of 4.5 AGeV/c with AgBr as target present in nuclear emulsion. The data were obtained by exposing the stacks of NIKFI-BR2 emulsion pellicles of dimension 20cm 10 cm  600  m horizontally to 4.5 AGeV/c 16 O, 28 Si and 32 S projectile beams at Dubna Synchrophasotron. In order to get the required data for the present analysis NIKFI-BR2 emulsion pellicles of dimension 20cm 10 cm  600  m were irradiated by the 16  angles. 5 According to the terminology of nuclear emulsion, particles emitted from an interaction (called an event or a star) are classified into four categories, namely the shower particles, the grey particles, the black particles and the projectile fragments [43]. Characteristics of these particles are given below.

Shower particles:
The tracks of particles having ionization I less or equal to 1.4I 0 are called shower tracks. I 0 is the minimum ionization of a singly charged particle. The shower particles are mostly pions (about more than 90%) with a small admixture of kaons and hyperons (less than 10%). These shower particles are produced in a forward cone. The velocities of these particles are greater than 0.7c where c is the velocity of light in free space. Because of such a high velocity, these particles are not generally confined within the emulsion pellicle. Energies of these shower particles lie in the GeV range. In an emulsion experiment, the pseudo-rapidity is a convenient choice for the basic variable in terms of which the particle emission data can be analyzed. It is an approximation of the dimensionless boost parameter rapidity (additive under Lorentz boost) of a particle.

Analysis and Results
As we are dealing with interactions at 4.5AGeV/c, problems may be caused by lower We have utilized the framework of independent emission hypothesis based on the following assumptions in order to generate the MC-RAND events as did in our previous publication [44]. (iii) The pseudo-rapidity distribution of the simulated events should reproduce the pseudorapidity distribution of the experimental data. 9 To generate the MC-RAND events, the multiplicity and pseudo-rapidity distribution of the experimental data has been given as the input. The pseudo-rapidity values of the simulated events have been generated by generating random numbers. The MC-RAND events have the identical pseudo-rapidity and multiplicity distribution as the experimental data [47].
Consequently, the average multiplicities of the shower tracks for the MC-RAND events will be equal to those of the experimental events. We have generated Monte Carlo-simulated (MC-RAND) events for 16 O-AgBr, 28 Si-AgBr and 32 S-AgBr interactions in the pseudo-rapidity phase space. Table 1 and table 2  For more details about this model, readers are requested to consult [45][46].

Discussion of Systematic Errors
Before going to the conclusion of our analysis, it would be relevant to present a discussion on systematic errors of the data. Detailed analysis on systematic errors for the same data set has been presented in our earlier publication [48][49]. From our previous papers [48][49], we find that the efficiency of identifying the shower particles contribute to the systematic error of the analysis. We have shown that [48][49] applying the along the track scanning procedure with the help of two independent observers helps us to increase the scanning efficiency to more than 99% and hence to minimize the systematic errors to less than 1%. It 11 has been mentioned in [48][49] that along the track scanning method gives reliable event samples because of its high detection efficiency. In nuclear emulsion detector tracks of   e e pair origi ati g fro γ -conversion may cause problem in the identification of pions [48][49]. These tracks are produced at a distance from the interaction point after travelling through certain radiation lengths. In order to exclude such tracks lying close to shower tracks near vertex, special care was taken while performing angular measurements. Usually all the shower tracks in the forward direction were followed more than 100-200 μm from the interaction vertex for angular measurement. The tracks due to   e e pair can be easily recognized from the grain density measurement, which is initially much larger than the grain density of a single shower track. It may also be mentioned that the tracks of an electron and positron when followed downstream in nuclear emulsion showed considerable amount of Coulomb scattering as compared to the energetic charged pions. Such   e e pairs were eliminated from the data and consequently they contribute almost nothing (~0.01%) to the systematic errors [44,[48][49].
It has been mentioned earlier that the shower particles are mostly pions (more than 90%) Applying the UrQMD model it has been seen that [48][49] for 16 O-AgBr, 28 Si-AgBr and 32 S-AgBr interactions, above 90% of the produced particles are  -mesons, (3-5) % of the produced particles are kaons and (1-2) % of the produced particles are  -mesons, hyperons and  mesons. In our earlier publication [48][49] 28 Si-AgBr and 32 S-AgBr interactions respectively [48][49]. The contribution to the systematic errors due to the presence of other mesons and hyperons with the pions in the shower particles has been calculated to be (7.60.05 to 8.91.07) % for these interactions. The total contribution of systematic errors in our analysis does not exceed 10% [49].

Conclusions
The study of event-by-event maximum pseudo-rapidity gap fluctuations in terms of the scaled variance has been carried out for 16 O-AgBr, 28 Si-AgBr, 32 Table 1 represents the average multiplicities of the shower particles for all the interactions in case of the experimental and the UrQMD data for the full sample of events.  Table 2 represents the average shower particle multiplicities for 16 O-AgBr, 28 Si-AgBr and 32 S-AgBr interactions at 4.5AGeV/c in case of experimental, MC-RAND and UrQMD data after applying the multiplicity cut (N > .
17 Table 3 Interactions  Table 3 represents the values of event by event maximum pseudo-rapidity gap fluctuation in high energy nucleus-nucleus insteractions.