Advances in High Energy Physics

Volume 2015 (2015), Article ID 741816, 10 pages

http://dx.doi.org/10.1155/2015/741816

## Tsallis Statistical Interpretation of Transverse Momentum Spectra in High-Energy *p*A Collisions

Department of Physics, Shanxi University, Taiyuan, Shanxi 030006, China

Received 17 July 2014; Revised 25 August 2014; Accepted 2 September 2014

Academic Editor: Chen Wu

Copyright © 2015 Bao-Chun Li 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

In Tsallis statistics, we investigate charged pion and proton production for *p*Cu and *p*Pb interactions at 3, 8, and 15 GeV/c. Two versions of Tsallis distribution are implemented in a multisource thermal model. A comparison with experimental data of the HARP-CDP group shows that they both can reproduce the transverse momentum spectra, but the improved form gives a better description. It is also found that the difference between *q* and *q′* is small when the temperature *T* = *T′* for the same incident momentum and angular interval, and the value of *q* is greater than *q′* in most cases.

#### 1. Introduction

Heavy ion collisions at Large Hadron Collider (LHC) are essential for the investigation of strongly interacting matter at high-energy density [1]. Proton-nucleus () program is used as a baseline measurement for nucleus-nucleus () collisions and is also crucial to discuss the various domains of quantum chromodynamics (QCD). So, the collision has been considered as an important component of the heavy ion collisions [2]. Measurements of the transverse momentum spectra of identified particles, to some extent, can provide an insight into the dynamics of the colliding systems.

In recent years, many models have been proposed in the interpretation of the spectra in high-energy collisions, such as multisource thermal model [3–5], diffusion model [6], and Tsallis statistics [7–11]. In particular, Tsallis distribution has successfully reproduced the spectra and has aroused interest of scientists recently. The statistics can extract two parameters, Tsallis temperature and , which is used to characterize a degree of nonequilibrium in the system. For example, a Tsallis-like distribution has given excellent descriptions to the experimental data, which have been measured by the STAR [7] and PHENIX [8] collaborations at the RHIC and by the ALICE [9], ATLAS [10], and CMS [11] collaborations at the LHC. Generally, the Tsallis parameter goes to 1. A thermodynamically consistent form of Tsallis statistics has also been proposed to fit the transverse momentum spectra [12, 13]. In our previous work [14], we have consistently embedded the improved form of the Tsallis distribution into a multisource thermal model to describe systematically pseudorapidity distributions in (), AuAu, CuCu, and PbPb collisions at RHIC and LHC energies. The result shows that a rapidity shift of longitudinal sources needs to be considered. In this paper, we will use the Tsallis distributions with the rapidity shift to analyze proton and charged pion distributions in and interactions at 3, 8, and 15 GeV/c in the hadron production (HARP) experiment at CERN [15]. The results obtained from the two forms of Tsallis distribution are compared in detail.

The paper is organized as follows: in Section 2, the improved Tsallis distribution is introduced and the results are compared with the experimental data; at the end, we give discussions and conclusions in Section 3.

#### 2. Tsallis Statistics Description of the Transverse Momentum Spectra

According to Tsallis statistics, the particle number iswhere , , , , and are the degeneracy factor, the volume, the momentum, the energy, and the chemical potential, respectively. The parameters and are temperature and nonequilibrium factor, respectively. The distribution of the corresponding momentum is given byIn terms of the transverse momentum and the rapidity , the distribution function is

For , at midrapidity , the transverse momentum distribution isThe Tsallis distribution is a quantum form, which can meet the thermodynamic consistency [10, 11]. Approximately, the can equal 1 and the distribution is given by The two distribution functions both represent a single spectrum of one source at . Therefore, we need to consider the distribution width of the rapidity of final-state particles [14]. Equations (4) and (5) will be used in the following analysis.

Figures 1, 2, and 3 show , , and double-differential cross-sections as a function of the transverse momentum in collisions, respectively. From left to right, the incident proton momenta are 3, 8, and 15 GeV/c, respectively. And from top to bottom, the angular intervals are 30°–40°, 60°–75°, and 105°–125°, respectively. The symbols denote the experimental data measured in the hadron production (HARP) experiment at CERN [15]. The solid lines are results fitted by (4) and the dashed lines are results fitted by (5). The Tsallis parameters , , , and are given in Tables 1 and 2. From the figures, one can see that the results of (4) and (5) are in agreement with the experimental data in the whole observed region, but (4) can give a better fit. The values of and show slight difference when for the fixed incident momentum and angular interval. And, in most cases, . The minimum difference is 0.002 and the maximum difference is 0.02. For proton production, the scaling properties behave well at . The case is similar for production at 60°–75° and 105°–125°.