Central nucleus-nucleus collisions at relativistic energies with a new method based on Random Matrix Theory

Abstract

Using the method based on Random Matrix Theory (RMT), the results for the nearest-neighbor distributions obtained from the experimental data on 12 C-C collisions at 4.2 AGeV/c have been discussed and compared with the simulated data on 12 C-C collisions at 4.2 AGeV/c produced with the aid of the Dubna Cascade Model. The results show that the correlation of secondary particles decreases with an increasing number of charged particles N ch . These observed changes in the nearest-neighbor distributions of charged particles could be associated with the centrality variation of the collisions.

Study of <sup>12</sup>CC Collisions at 4.5 A GeV to Define Centrality

“…Indeed, one can find a good agreement between the results obtained in this way and a standard analysis based on the method of effective mass spectra and two-pair correlation function often used in high energy physics [18]. The purpose of the present review is to discuss a novel criterion for the centrality of collision, using a rigorous mathematical framework of the RMT [18][19][20][21][22]. Section 2 briefly reviews how to detect the manifestation of correlations with the aid of nearest-neighbor spacing energy distribution (NND) from the data obtained in light nuclei collisions in Dubna Experiments.…”

“…In general [18][19][20][21][22], this procedure does not involve any uncertainty or spurious contributions and deals with a direct processing of physical data.…”

“…Evidently, the absence of an unambiguous criterion for the centrality may significantly affect the interpretation of experimental results and, therefore, hide a true signal on the onset of a new phase of the hadronic matter. In a preliminary report [15] it is suggested that tools from Random Matrix Theory (RMT) [16][17][18][19][20][21][22] might be useful in illuminating the presence of correlations in the spectral (momentum) distribution of secondary particles produced in nucleusnucleus collisions at high energy [18][19][20][21][22]. It is noteworthy that during the last twenty years the RMT grew into the powerful new statistical theory of fluctuations in a variety of physical problems [19][20][21][22].…”

“…In various fields, the Dyson-Mehta statistical measures are most often used to quantify a system's correlations and to determine what information the fluctuations contain. These measures do not depend on the background of measurements and used in the context of RMT give universal forms depending only on the fundamental symmetries preserved [19][20][21][22]. Their only requirement is that local mean densities (or secular behaviors) be understood and their effects be removed.…”

“…The astonishing thing is that the fluctuating properties quite different systems are determined only by over-all symmetries of system [17]. This fact provides the basis for application of the RMT tools for analysis of nucleus-nucleus collision data at high energies [15][16][17][18][19][20][21][22].…”