Centrality in Relativistic Nuclear Collisions and the Random Matrix Approach

Abstract

Using the random matrix approach, results for nearest-neighbor distributions obtained from experimental data on 12 𝐶 + 12 𝐶 collisions at 4.2 𝐴 GeV/𝑐 and simulations produced with the aid of an ultra-relativistic quantum molecular dynamics model are studied. Comparison reveals that the observed changes in the nearest-neighbor distributions for different multiplicities can be associated with the onset of a region of central 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.…”

“…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.…”

“…Evidently, that the energy of secondary particles produced in nucleus-nucleus collisions at high energies is given by continuous distributions. Since in each event only a finite number of particles are emitted, the discreteness naturally comes in the analysis of data [19,22]. The average number of particles per unit of energy can change with increase (decrease) the absolute value of the energy and its direction in each event.…”

“…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].…”