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Ring like correlation in relativistic heavy ion collision: an experimental probe using continuous wavelet transform approach

Continuous wavelet transform approach has been applied to the pseudo-rapidity distribution of shower particles produced in 16O-AgBr interactions at 60 AGeV and 32S-AgBr interactions at 200 AgeV. Multiscale analysis of wavelet pseudo-rapidity spectra has been performed in order to find out the presence of ring-like correlation, which could be either due to production of Cherenkov gluons or due to propagation of Mach Shock wave through excited nuclear matter. This approach fulfils the basic requirement of both effects that they lead to an overabundance of considered particles at some typical pseudo-rapidities. Comparison of experimental results with that obtained from analyzing events generated by FRITIOF code are not reproduced.


I. Introduction
The problem of presentation of high multiplicity events produced in high energy nucleusnucleus interactions is non-trivial. The presentation of each particle in 3-dimensional phase space corresponds to a dot. These dots form different pattern in phase-space which may be linked to different dynamics of multiparticle production. The distribution of these dots can be found for an ensemble of events and for a single event also. The average distribution over all events possesses fractal properties [1] at low energies. To study the properties of nuclear matter that may have undergo some qualitative changes, in hot and compressed condition collective effects are of prime importance.
It is also interesting to study phase-space pattern for a single event. But for a single event statistical fluctuation may dominate in the observed effects. Dense particle clusters are observed at different positions and at different scales of the considered phase-space. Analysis of these clusters on an event-by-event basis is informative.
The factorial moment method [2] was proposed to remove the background statistical fluctuation in global analysis. Recently a new type of mathematical approach have been developed, the so-called wavelet analysis, which has been applied successfully in different fields of science and engineering [3][4][5][6].The method is also fruitful in multiparticle data analysis as for a single event it can reveal the local characteristics of any pattern of particle distribution after eliminating the smooth polynomial trends at different scales. Thus one gets the opportunity to study strong dynamical fluctuation removing the statistical component.
We have considered 16 O-AgBr interactions at 60 AGeV and 32 S-AgBr interactions at 200 AGeV. The pseudo rapidity distribution of the pions produced in all events of these interactions is analysed using continuous wavelet based approach and also we have selected one high multiplicity event from each considered interaction for analysis. Our main aim is to detect some conspicuous peaks or irregularities, which may reveal the preferred emission polar angle in multiparticle production process. Production of large number of particles at some distinguished pseudo rapidity values may indicate the presence of ring-like structure if relativistic particles are considered for analysis. So in this regard we hope wavelet analysis will be fruitful to characterise the η distribution at different scale to localize multiparticle correlation that may involve different numbers of particles. We have also compared our experimental results with that obtained from analysing events, generated using FRITIOF code.
The rest of the paper is arranged as follows: in section II a brief description of the experiment has been given. Section III describes in detail the wavelet analysis method. In section IV we have discussed our findings followed by a conclusive section (section V).

II. Experimental Details
In the current analysis we have considered the interactions of the 16 O beam, moving at energy 60A GeV, and 32 S beam, moving at energy of 200 A GeV, with AgBr being the target present in a nuclear emulsion. Small stacks of ILFORD G5 emulsion plates were exposed to the above mentioned beam during EMU-08 experiments [16][17][18] at CERN. SPS accelerator used to accelerate the beams. The details of the experiment like: dimension of emulsion plate, beam flux have been given in our previous publication [19].   , which may be treated as a convenient substitute of the rapidity variable of a particle when the rest mass of the particle can be neglected in comparison to its energy or momentum, has been determined for each pion track for further analysis.

III. Wavelet Analysis Method
This is a practical mathematical tool which offers one to perform multiscale analysis of where " Ψ is a normalizing constant and given by the following integration:  The obvious reason for that is the Gaussian-like signal has been assumed. Another advantage of using > wavelet is that it attains feasible resolution both in scale and pseudorapidity domain simultaneously. Using this algorithm we will find out the wavelet pseudorapidity spectrums, which are nothing but the sum of wavelets representing the individual particles.

IV. Results and Discussions
Wavelet pseudo-rapidity spectra of all the events of the considered interactions will be presented first. In this approach one may find out the collective flow occurring in many events and not the unique behaviour of an individual event. In figure 2 we have presented the wavelet pseudo-rapidity spectra of the shower track distribution of 16  It would be interesting to analyse wavelet spectra of individual events of both the interactions using same approach as before to find any characteristic change in particle production of any particular event than in overall process. Two such spectra have been presented in figure 3, for the two highest multiplicity events: one from 16  From figure 3 we can say that most important scales are from 0.04 to 0.7, as the maximums corresponding to group of particle production are present in this scale region only. Figure.3 Wavelet pseudo-rapidity spectra for a single event i) for 16 The plots of E F vs. a have been shown in figure 4. Local maximums in these plots represent the dominant scales. Maximums for a<0.05 are insignificant as they results due to statistical reason. From figure 4 (i), the significant scales for O-event are restricted in the range 0.1<a<0.7 and that for S-event is 0.1<a<0.9. In these cases also FRITIOF events are found to be unable to reproduce the experimental findings.

V.Conclusions
Pseudo-rapidity distributions of pions coming out from 16 O-AgBr & 32 S-AgBr interactions at 60 AGeV & 200 AGeV respectively have been analyzed on the basis of continuous wavelet transformation. The following conclusions may be drawn from the analysis.
• The local maximums, which correspond to the irregularities, are revealed mainly in the scale region a≤0.8.
• The irregularities, found from the multiscale analysis of wavelet pseudorapidity spectra, reveals preferred pseudorapidity values suggests clustering effect in the particle production process.
• Overabundance of particle multiplicity at some distinguished pseudorapidity may be a signature of ring-like correlation.
• Events generated using FRITIOF code fails to reproduce the experimental behaviours exactly, which may be due to the fact that corresponding dynamical input has not been taken into account for developing the code.
The authors declare that there is no conflict of interest regarding the publication of this paper.