Advances in High Energy Physics

Volume 2017 (2017), Article ID 9383540, 7 pages

https://doi.org/10.1155/2017/9383540

## On and Transverse Momentum Distributions in High Energy Collisions

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

Correspondence should be addressed to Bao-Chun Li

Received 27 December 2016; Revised 14 March 2017; Accepted 26 March 2017; Published 18 May 2017

Academic Editor: Chao-Qiang Geng

Copyright © 2017 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

The transverse momentum distributions of final-state particles are very important for high energy collision physics. In this work, we investigate and meson distributions in the framework of a particle-production source, where Tsallis statistics are consistently incorporated. The results are in good agreement with the experimental data in and -Pb collisions at LHC energies. The temperature of the emission source and the nonequilibrium degree of the collision system are extracted.

#### 1. Introduction

The investigation of nuclear matter at high energy densities is the main purpose of Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) [1–7]. As a new matter state, quark-gluon plasma (QGP) is a thermalized system, which consists of strongly coupled quarks and gluons in a limited region. The suppression of meson with respect to proton-proton () collisions is regarded as a distinctive signature of the QGP formation and brings valuable insight into properties of the nuclear matter. In proton-nucleus collisions, the prompt meson suppression has also been observed at large rapidity [8]. The low-viscosity QGP may be created in the small system, ^{3}He + Au collisions [9]. The heavy quarkonium production can be suppressed by the suppression cold-nuclear-matter (CNM) effects, such as nuclear absorption, nuclear shadowing (antishadowing), and parton energy loss.

The transverse momentum spectra of identified particles produced in the collisions are a vital research for physicists. Now, different models have been suggested to describe the distributions of the final-state particles in high energy collisions [10–13], such as Boltzmann distribution, Rayleigh distribution, Erlang distribution, the multisource thermal model, and Tsallis statistics. Different phenomenological models of initial coherent multiple interactions and particle transport have been proposed to discuss the particle production in high energy collisions. Tsallis statistics can deal with nonequilibrated complex systems in condensed-matter research [14]. It is developed to describe the particle production in recent years [15–24].

In our previous work [12], the temperature information was understood indirectly by an excitation degree. We have obtained the emission source location dependence of the exciting degree specifically. In this paper, the temperature of the emission source is given directly by combining a picture of the particle-production source with Tsallis statistics. We discuss the transverse momentum distributions of in collisions at TeV, TeV, and TeV and -Pb collisions at TeV. And the distributions in collisions at TeV are also taken into account for comparison.

#### 2. Tsallis Statistics in an Emission Source

According to the multisource thermal model [12] and the nuclear geometry picture, at the initial stage of the collision, two cylinder-shaped groups are formed along the beam direction. In the laboratory reference frame, it is assumed that the projectile cylinder is at the positive space and the target cylinder is at the negative space. The cylinders are not a real shape and are understood to be a rapidity range of the emission source. The projectile and target cylinders can be regarded as an emission source with a rapidity width. The observed particles are emitted from the emission source.

With Tsallis statistics’ success in dealing with nonequilibrated complex systems in condensed-matter research [14], it has been used to understand the particle production in high energy physics. In order to describe the transverse momentum spectra in high energy collisions, several versions of Tsallis distribution are proposed [15–24]. Recently, an improved form of the Tsallis distribution was proposed [18–20] and can meet the thermodynamic consistency. The meson number [16, 17] is given bywhere , , , , and are the degeneracy factor, the volume, the momentum, the energy, and the chemical potential, respectively. The parameter is the temperature of the emission source and the parameter is the nonequilibrium degree. Generally, is greater than 1 and is close to 1. The corresponding momentum distribution is given byThen, the transverse momentum distribution isWhen the chemical potential is neglected, at midrapidity , the distribution isIt is worth noting that the distribution function of is only the distribution of mesons emitted from an emission point at in the emission source, not the final-state distribution due to the nonzero rapidity width of the emission source. By summing the contributions of all emission points, the transverse momentum distribution is rewritten as where is a normalize constant and and are the maximum and minimum values of the observed rapidity.

#### 3. Transverse Momentum Spectra and Discussions

Figure 1 shows the double-differential cross section of mesons in collisions at TeV. Figures 1(a), 1(b), 1(c), and 1(d) present prompt with no polarisation, from with no polarisation, prompt with full transverse polarisation, and prompt with full longitudinal polarisation, respectively. The experimental data in bins are from the LHCb Collaboration [25]. The solid lines indicate our model results, which are in good agreement with the experimental data in all rapidity ranges. The parameters and taken for the calculation are listed in Table 1. In different rapidity ranges, the values of the temperature are different and decrease with increasing the rapidity bins in all four figures of Figure 1. The closer the emission source is to the center , the larger the excitation degree is. The values of do not change regularly with the rapidity bins.