Advances in High Energy Physics

Volume 2015 (2015), Article ID 614090, 9 pages

http://dx.doi.org/10.1155/2015/614090

## On Productions of Net-Baryons in Central Au-Au Collisions at RHIC Energies

Institute of Theoretical Physics, Shanxi University, Taiyuan, Shanxi 030006, China

Received 22 May 2015; Revised 17 June 2015; Accepted 18 June 2015

Academic Editor: Sally Seidel

Copyright © 2015 Ya-Hui Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

The transverse momentum and rapidity distributions of net-baryons (baryons minus antibaryons) produced in central gold-gold (Au-Au) collisions at 62.4 and 200 GeV are analyzed in the framework of a multisource thermal model. Each source in the model is described by the Tsallis statistics to extract the effective temperature and entropy index from the transverse momentum distribution. The two parameters are used as input to describe the rapidity distribution and to extract the rapidity shift and contribution ratio. Then, the four types of parameters are used to structure some scatter plots of the considered particles in some three-dimensional (3D) spaces at the stage of kinetic freeze-out, which are expected to show different characteristics for different particles and processes. The related methodology can be used in the analyses of particle production and event holography, which are useful for us to better understand the interacting mechanisms.

#### 1. Introduction

In high energy nucleus-nucleus collisions, due to the fast speed and the great mass of the projectile and target nuclei, the collisions can form new substances such as pions, kaons, antiprotons, which do not obviously exist in the nuclei [1, 2]. In the area filled with new and rich phenomena, there are many issues which are difficult to deal with, and the collisions still stay at the phenomenological stage in understanding [3]. To restore the original process of the collisions by analyzing various properties of final-state particles is a major aspect in high energy nuclear physics [4].

The relativistic heavy ion collider (RHIC) located in the United States and the large hadron collider (LHC) located in Switzerland are the main sources of experimental data of heavy-ion collisions [5–7]. They play very significant roles in the studies of high energy nucleus-nucleus collisions. The transverse momentum and rapidity distributions of different final-state particles can be measured from the experiments. The two distributions are related to the excitation degree of the interacting system and the penetrating power of the projectile nucleus, respectively. From the two distributions, we can extract some other distributions and correlations. Scientists worked in fields of high energy and nuclear physics are very interested in experiments performed in the colliders.

Since the 1980s or earlier days, many phenomenological models have been proposed to explain the large number of experimental data in high energy particle-particle, particle-nucleus, and nucleus-nucleus collisions [4]. In these models, except for the standard (Boltzmann, Fermi-Dirac, and Bose-Einstein) and other distributions, the Tsallis statistics can describe the thermal source (fireball) and transverse momentum distributions [8–10]. An effective temperature parameter which reflects the excitation degree of interacting system and an entropy index (nonextensive parameter) which describes the degree of nonequilibrium of interacting system are used in the Tsallis statistics. Particularly, the Tsallis statistics describes the temperature fluctuations in two- or three-standard distributions.

Among abundant experimental data, the transverse momentum and (pseudo)rapidity distributions of identified particles are very important. From the two distributions, we can extract some parameters such as the (effective) temperature, entropy index, rapidity shift, and contribution ratio in the framework of a multisource thermal model [11–14]. These parameters can be then used to extract some scatter plots of the considered particles in some three-dimensional (3D) spaces. These scatter plots are expected to show different characteristics for different particles and processes. We then propose a new method for studies of particle production and event holography. In addition, baryon transport is a fundamental aspect of high energy nucleus-nucleus collisions as it pertains to the initial scatterings where the Quark-Gluon Plasma (QGP) is formed. It is a process that is not very well understood and so further theoretical studies are needed.

In this paper, in the framework of a multisource thermal model [11–14] in which each source is described by the Tsallis (transverse) momentum distribution [8–10, 15, 16], we analyze the transverse momentum and rapidity distributions of net-baryons (baryons minus antibaryons) produced in central gold-gold (Au-Au) collisions at the center-of-mass energies of 62.4 GeV and 200 GeV. Based on the descriptions of the two distributions, some scatter plots of the considered particles in some 3D spaces are structured to show partly the event picture in the whole phase space. A methodology related to particle production and event holography is presented to better understand the interacting mechanisms.

#### 2. The Model and Method

According to the multisource thermal model [11–14], in high energy nucleus-nucleus collisions, the target nucleus and the projectile nucleus penetrate each other. We can assume that many emission sources are formed in the interacting system. In a given frame of reference such as the center-of-mass reference frame, these sources with different rapidity shifts in the rapidity space can be divided into four parts: a leading target nucleon cylinder (LT) in rapidity interval , a leading projectile nucleon cylinder (LP) in rapidity interval , a target cylinder (TC) in rapidity interval , and a projectile cylinder (PC) in rapidity interval . It is expected that the LT and TC are mainly contributed by the target nucleus, and the LP and PC are mainly contributed by the projectile nucleus. Because the TC and PC are linked at midrapidity, they can be regarded as a whole central cylinder. For symmetric collisions such as Au-Au collisions which are studied in the present work, the equations , , and can be used. The free rapidity shifts are then , , and .

In the rest frame of each source, the source is assumed to emit final-state particles isotropically, and the rapidity of a considered particle is . Then, the rapidity of the considered particle in the center-of-mass reference frame isAccording to different origins of different final-state particles, can be in , , , or corresponding to the LT, LP, TC, and PC, respectively. Generally, can be obtained by the definition of rapidity, and can be obtained due to different contribution ratios of the four sources.

In the Tsallis statistics [8–10, 15, 16], let denote the temperature parameter of the considered source, denote the nonextensive parameter (entropy index), denote the number of particles, and , , and denote the momentum, rest mass, and chemical potential of the considered particle, respectively. We have the final-state particle momentum distribution in the rest frame of the considered source to bewhere is the normalization constant which gives (2) to be a probability distribution. Generally, the chemical potential can be neglected due to its small value at high energy. Then, (2) can be simplified as

In the Monte Carlo method, we can obtain the momentum , the energy , the polar angle , the azimuth , the transverse momentum , the -component of momentum , the -component of momentum , the longitudinal momentum , the rapidity , the rapidity shift , the energy , the longitudinal momentum , the transverse velocity , the -component of the velocity , the -component of the velocity , the longitudinal velocity , and so forth, where the quantities with no mark denote those in the center-of-mass reference frame.

By using the above method, we can get many distributions and scatter plots for a given collision process. Generally, and are sensitive to the transverse momentum distribution and insensitive to the rapidity distribution. We can use the transverse momentum distribution to determine values of and . The rapidity shifts and contribution ratios of different sources are usually determined by the rapidity distribution. The contributions of the TC and PC are mainly in the central rapidity region, and the contributions of the LT and LP are mainly in the backward and forward rapidity regions, respectively, where the latter two regions are also called the fragmentation regions. In the present work, to describe the rapidity distribution as accurate as possible, we may use and obtained from distribution at for the TC and PC and and obtained from distribution at (or 2.9) for the LT and LP.

Particularly, for the considered Au-Au collisions at 62.4 and 200 GeV in the present work, we can describe distribution obtained by the above Monte Carlo method by the analytic expression [10]where and denote the minimum and maximum rapidities, respectively, and is the normalization constant which gives (4) to be a (normalized) probability distribution. At the same time, () distribution obtained by the above Monte Carlo method can be approximately parameterized towhere is the normalization constant which gives (5) to be a probability distribution. In the present calculation, we can fit a given distribution by using the Monte Carlo method or analytic expression to obtain values of free parameters and . It should be noted that the given central in (4) and (5) should be shifted to 0 when we extract and because the effect of vectored longitudinal motion has to be subtracted.

#### 3. Comparisons and Extractions

Figure 1 shows the transverse momentum distributions of net-baryons produced in central Au-Au collisions at (a)–(d) 62.4 and (e)–(h) 200 GeV. From Figures 1(a)–1(d), the corresponding rapidities are = 0, 0.65, 2.3, and 3.0, respectively. From Figures 1(e)–1(h), the corresponding rapidities are = 0, 0.9, 1.9, and 2.9, respectively. The symbols represent the experimental data of the BRAHMS Collaboration [17–19] measured at the RHIC and collected together in [20] in which the longitudinal axis should not be , but . The solid curves are the Tsallis fitting results by us. The values of free parameters and obtained by using the analytic expression, normalization constant obtained by fitting the experimental data, and (number of degree of freedom) obtained in the fit are given in Table 1, where the last three points in Figure 1(h) have not been included in the calculation of due to the low statistics.