^{1}

^{1}

^{1}

^{2}

^{1}

^{2}

A continuous wavelet analysis is performed for pattern recognition of charged particle emission data in ^{28}Si-Ag/Br interaction at 14.5A GeV and in ^{32}S-Ag/Br interaction at 200A GeV. Making use of the event-wise local maxima present in the scalograms, we try to identify the collective behavior in multiparticle production, if there is any. For the first time, the wavelet results are compared with a model prediction based on the ultrarelativistic quantum molecular dynamics (UrQMD), where we adopt a charge reassignment algorithm to modify the UrQMD events to mimic the Bose-Einstein type of correlation among identical mesons—a feature known to be the most dominating factor responsible for local cluster formation. Statistically significant deviations between the experiment and the simulation are interpreted in terms of nontrivial dynamics of multiparticle production.

The primary objective of studying high-energy heavy-ion interactions is to compress and heat up the nuclear matter beyond the critical values of certain thermodynamic parameters in such a way that the boundaries of individual nucleons melt down to form a thermally and chemically equilibrated color deconfined state of quark-gluon plasma (QGP) [

The wavelet analysis technique has found its application in many branches of physics [^{28}Si-Ag/Br events at an incident energy of 14.5A GeV and ^{32}S-Ag/Br events at an incident energy of 200A GeV. Nuclear emulsion technique has been used to collect the experimental data. Several works on the wavelet analysis of multiparticle production at

Ilford G5 nuclear photoemulsion pellicles of size 16 cm × 10 cm × 600 ^{28}Si beam at an incident energy of 14.5A GeV from the alternating gradient synchrotron (AGS) of the Brookhaven National Laboratory (BNL). Similarly pellicles of size 18 cm × 7 cm × 600 ^{32}S beam at an incident energy of 200A GeV from the super proton synchrotron (SPS) at CERN. The primary interactions (also called events/stars) within the emulsion plates are found by following individual projectile tracks, that is, tracks caused by the ^{28}Si and ^{32}S nuclei, along the forward as well as along the backward direction. The process known as line scanning was performed with Leitz microscopes under a total magnification of 300x. On the other hand, Koristka microscopes were utilized for the track counting and angle measurement purposes, for which a total magnification of 1500x was used. The secondary charged particles coming out of an event are categorized in the following way.

The shower tracks—caused by the singly charged produced particles most of which are

The grey and black tracks—resulting from the fragments of the target (Ag/Br) nuclei. Their numbers are denoted, respectively, by

The projectile fragments—caused by the spectator parts of the incident projectile (Si/S) nuclei. In an event, their number is denoted by

^{28}Si-Ag/Br events and 200

^{32}S-Ag/Br events are selected for further analysis, which is confined only to the angular distribution of the shower tracks. The average shower track multiplicity

^{28}Si-sample, and

^{32}S-sample. The pseudorapidity

^{28}Si-sample are the peak density

^{32}S-sample they are

To eliminate the background noise, we compare the experiment with the UrQMD (version 3.3p1) model [

It is well known that the Bose-Einstein correlation (BEC), an identical particle effect, dominates the origin of cluster formation. Due to the correlated emission of like sign and/or opposite sign mesons, the particle yield with small relative momenta may be enhanced, which is one of the reasons of large local densities in the final state particles in any high-energy interaction. The effect is quantum statistical in nature and it is not incorporated in the framework of a transport model like the UrQMD. Recently, a new algorithm has been developed [

In the first step, we arbitrarily choose a meson from an event, and irrespective of its original charge, assign a charge “sign”

In the next step, we calculate the distances in the four momenta

Then, we start to generate uniformly distributed random numbers

Now, we go back to our first step and again randomly choose a meson from the pool of the left over mesons for which the charge reassignment has not yet been done. Obviously, the weight factors

The algorithm is then repeated until all mesons belonging to each charge variety in the event are used up, and then we move to the next event.

We use the UrQMD code in its default setting and generate the minimum bias event samples in the laboratory frame, separately for the Ag and the Br targets and, respectively, for the ^{28}Si and ^{32}S projectiles. For each projectile, the Ag and Br event samples are then mixed up. While doing so, the proportional abundances of these nuclei in the G5 emulsion [

The wavelet method is used to analyze nonstationary as well as inhomogeneous signals that can be any ordered set of numerically recorded information on some processes, objects, functions, and so forth. A wavelet construction is based on a dilation

(a) First derivative and (b) second derivative (Mexican hat wavelet) of Gaussian function.

In Figure ^{28}Si-Ag/Br events at an incident energy of 14.5A GeV at different scales (four different ^{32}S-Ag/Br event sample at 200A GeV/c are presented in Figure ^{32}S-sample than in the ^{28}Si-sample. There are at least 6 prominent peaks within ^{28}Si case. The other peaks, one to the right and three to the left side of the central region, can be related, respectively, to the projectile and the target fragmentations.

^{28}Si-Ag/Br interaction at 14.5A GeV for different values of the scale parameter

^{32}S-Ag/Br interaction at 200A GeV for different values of the scale parameter

The wavelet spectra can be generated for individual events at many different scales that can be used to simultaneously study the location and scale dependence of ^{28}Si-Ag/Br event ^{32}S-Ag/Br one ^{28}Si-Ag/Br diagram, we recognize that two large groups of particles are present, one centered around ^{32}S-Ag/Br diagram again, there are two large groups, one at

Wavelet pseudorapidity spectra for a single event (a) in ^{28}Si-Ag/Br interaction at 14.5A GeV: event multiplicity 146, and (b) in ^{32}S-Ag/Br interaction at 200A GeV: event multiplicity 379.

Identification of the peculiarities in particle distribution in individual events from the 2-d energy spectrum ^{28}Si-Ag/Br event and the other for the ^{32}S-Ag/Br event considered above, are plotted in Figure ^{28}Si-Ag/Br event a peak at ^{32}S-Ag/Br event there are a couple of maxima and minima. The maxima are located at ^{28}Si-Ag/Br events are graphically seen. The experiments as usual are plotted together with the simulations. Except in Figure ^{32}S-Ag/Br events are plotted. In this case also no significant difference between the experiment and the corresponding simulation is seen.

Scalogram for a single event: (a) ^{28}Si-Ag/Br interaction at 14.5A GeV: event multiplicity 146, and (b) ^{32}S-Ag/Br interaction at 200A GeV: event multiplicity 379. The same events for which the wavelet pseudorapidity spectra are shown in Figure

Distributions of the local maxima (left panel) and minima (right panel) of the scalograms for ^{28}Si-Ag/Br interaction at 14.5A GeV.

Same as Figure ^{32}S-Ag/Br interaction at 200A GeV.

The wavelet analysis is not complete unless we study the distributions of the locations ^{28}Si-Ag/Br sample (both experiment and simulation) are graphically presented at different cumulative scale windows. The common features of these diagrams are that at the lowest ^{32}S-Ag/Br sample on the other hand behaves a little differently. The distributions are shown in Figure ^{28}Si-Ag/Br and ^{32}S-Ag/Br samples are once again graphically shown, where we choose differential scale intervals to draw the histograms. For both sets of data, the basic features are more or less the same. As expected at the smallest scale ^{32}S-Ag/Br interaction are slightly wider than those for the ^{28}Si-Ag/Br interaction. It seems that the inclusion of BEC into the UrQMD in both interactions increases the heights of the local peaks to a small extent.

^{28}Si-Ag/Br interaction at 14.5A GeV—(a) the experiment, (b) the UrQMD, and (c) the UrQMD + BEC. The distributions in different scale windows are so shifted as to avoid mutual overlapping.

The same as Figure ^{32}S-Ag/Br interaction at 200A GeV.

^{28}Si-Ag/Br interaction at 14.5A GeV—(a) the experiment, (b) the UrQMD, and (c) the UrQMD + BEC. The distributions for different scale windows are so shifted as to avoid mutual overlapping.

The same as Figure ^{32}S-Ag/Br interaction at 200A GeV.

Pseudorapidity distributions of singly charged particles coming out with relativistic speeds from the ^{28}Si-Ag/Br and ^{32}S-Ag/Br interactions, respectively, at 14.5A GeV and 200A GeV, are analyzed by using the continuous wavelet transform technique. Compared to similar other such emulsion investigations [

For background noise elimination, the experiments are compared with a set of ordinary UrQMD simulated data, and also with the same set of UrQMD output that is modified by a mimicry of the Bose-Einstein type of correlation. The observed discrepancies between the experiment and the corresponding simulation should, therefore, result from nontrivial dynamics like collective flow of hadronic matter.

Irregularities in the wavelet pseudorapidity spectra, not reproducible by the simulation, are observed in individual ^{28}Si event sample under consideration. The differences with all probability are not a result of ordinary correlations among identical bosons. They should be interpreted in terms of certain nontrivial dynamical reason(s), which are not very much clear from the present analysis.

The present study can be extended to the azimuthal angle distribution of the

Provash Mali acknowledges financial support from the University Grants Commission, Government of India; Project no. 40-510/2011 (SR). Soumya Sarkar is supported by the INSPIRE fellowship of the Department of Science & Technology, Government of India.