Abstract

We study the transverse momentum distributions of identified particles produced in Au + Au and d + Au collisions at  GeV. The Tsallis description is applied in the multisource model. The results are compared with the experimental data in detail. We obtain some information of the thermodynamic properties of matter produced in the collisions. The difference of the transverse momentum distributions in Au + Au and d + Au collisions is not significant.

1. Introduction

Nucleus-nucleus collisions at high energy are important experiments to study the matter at an extreme temperature. Relativistic heavy ion collider (RHIC) in Brookhaven National Laboratory (BNL) is a valuable tool to probe quark-gluon plasma (QGP) produced in the collisions. In order to understand QGP more deeply, scientists have built a large hadron collider (LHC) at the European Organization for Nuclear Research (CERN). In the high-energy collisions, thousands of final-state particles are produced per event. The investigation of the identified particles produced in the collisions brings valuable insight into properties of QGP. In Au + Au collisions, final-state particle yields provided the information of the temperature and chemical potential by using a statistical model [1]. The transverse momentum of a particle is defined as , where and are the momentum components in the transverse momentum plane. The transverse momentum distributions of the final-state particles are called first observations in the high-energy experiments. To describe such many-particle system, statistical approaches have been used widely over past few years.

In order to describe transverse momentum spectra of the identified particles, the Tsallis statistics have been utilized to understand the particle production in high-energy physics and have been used to describe the transverse momentum spectra measured at the RHIC [2] and at the LHC [3, 4]. By the analysis of the experimental data, the Tsallis distribution has gained prominence with very good descriptions. Recently, the Tsallis distribution was improved to satisfy the thermodynamic consistence in the case of relativistic high-energy quantum distribution [5]. By fitting the data observed at LHC, the temperature and the parameter have been estimated. One-particle rapidity (or pseudorapidity) distributions measured at RHIC are well described by the Ornstein-Uhlenbeck process [6, 7].

In our previous work [8], inclusive transverse momentum spectra of meson in Au-Au, d-Au, and p-p collisions were studied in the framework of a thermalized cylinder model. In the region of high transverse momentum, the considered distributions of meson have a tail part at the maximum energy of RHIC. To explain the wider transverse momentum spectra, we considered the relative importance of hard and soft processes in the particle production. The experimental data of the PHENIX Collaboration have been described by the improved cylinder model, which contains two fundamental components. The multisource thermal model was developed from the cylinder model [9–11]. In this paper, we consider the different longitudinal rapidity of emission sources produced in Au + Au and d + Au collisions at 200 GeV and extend the one-source Tsallis distribution to the multisource Tsallis distribution in the picture of the multisource thermal model.

2. The Distribution Law of Particles Produced in AuAu and dAu Collisions at 200 GeV

At high energy, the primary nucleon-nucleon collision may be treated as a few sources. The participant nucleons in the primary collisions have probabilities to collide with latter nucleons in cascade collisions. Furthermore, the particles produced in primary or cascade nucleon-nucleon collisions have probabilities to take part in secondary collisions with latter nucleons and other particles. Each cascade or secondary collision is also treated as an emission source or a few emission sources. The identified particles are emitted from the emission sources produced in Au + Au and d + Au collisions at RHIC. According to the improved Tsallis distribution [5], the total number of the particles is where , , , , , and are the momentum, the energy, the temperature, the chemical potential, the volume, and the degeneracy factor, respectively. The parameter characterizes the degree of nonequilibrium. Then, we have momentum distribution At midrapidity , for zero chemical potential, the transverse momentum spectrum is given by The distribution of the particles is contributed by an emission source at midrapidity . Considering the contributions of the sources at the different rapidities [13], the spectrum is

Figure 1 shows the invariant yields of positive pions and negative pions as a function of the transverse momentum for , , , , and centralities in Au + Au collisions and for , , , , and centralities in d + Au collisions at 200 GeV. The scattered symbols denote the experimental data measured by the PHENIX Collaboration [12]. The yields are scaled by arbitrary factors indicated in the figure for the sake of clarity and for keeping the collision species grouped together. The lines are the results calculated by the model. The parameters and used in the calculations and the corresponding /dof are given in Table 1. The maximum /dof is 0.495. Our results of and are in good agreement with the experimental data for all concerned centralities. The values of the temperature increase slowly with increasing the centrality. The does not change significantly. In both Au + Au and d + Au, the trends of and are the same.

Table 1 
The parameters and in Figure 1.

Figure 1 
Invariant yield of and as a function of in Au + Au and d + Au collisions at = 200 GeV. The scattered symbols denote the experimental data measured by the PHENIX Collaboration [12] and statistical uncertainties are too small to be seen. The solid lines denote the results of the model.

In Figure 2, we show the transverse momentum spectra of positive kaons and negative kaons in Au + Au and d + Au collisions at 200 GeV. The scattered symbols denote the experimental data measured by the PHENIX Collaboration [12] and the solid lines are the results calculated by the formula of the multisource thermal model. The parameters and are given in Table 2 with the corresponding /dof. The mass of the kaon is heavier than that of the poin. But, for and with all concerned centralities, our results are also in good agreement with the experimental data. The maximum /dof is 0.425. Similarly, the values of the temperature increase slowly with the centrality and the parameter hardly changes in both Au + Au and d + Au collisions.

Table 2 
The parameters and in Figure 2.

Figure 2 
Invariant yield of and as a function of in Au + Au and d + Au collisions at = 200 GeV. The scattered symbols denote the experimental data measured by the PHENIX Collaboration [12] and statistical uncertainties are too small to be seen. The solid lines denote the results of the model.

Figure 3 presents the invariant yields of protons and negative protons for , , , , and centralities in Au + Au collisions and for , , , , and centralities in d + Au collisions at 200 GeV. The scattered symbols denote the experimental data [12] in different centrality cuts indicated in the figure. The solid lines are our results calculated by the model. The parameters and are given in Table 3 with /dof. The range of /dof is 0.151–1.440. Therefore, the model can approximately describe the experimental data of and for all concerned centralities in Au + Au and d + Au systems. It is also found that the temperature increases slowly with increasing the centrality and the does not change significantly in both Au + Au and d + Au collisions.

Table 3 
The parameters and in Figure 3.

Figure 3 
Invariant yield of and as a function of in Au + Au and d + Au collisions at 200 GeV. The scattered symbols denote the data measured by the PHENIX Collaboration [12] and statistical uncertainties are too small to be seen. The solid lines denote the results of the model.

3. Conclusions

We have studied the invariant yields of , , , , , and produced in Au + Au and d + Au collisions at = 200 GeV in the framework of the multisource model, which is combined with Tsallis statistics. A formula was introduced to describe the transverse momentum distributions and to obtain and the temperature . For the two collision systems Au + Au and d + Au at high energy, the mechanism of the particle production has the commonality of their inherent and fundamental laws. So the identified particles can be described in the same model. In recent years, the particle production in high-energy ion collisions has attracted much attention to understand the strongly coupled QGP (sQGP) by analyzing the production mechanisms [14, 15]. Thermal-statistical models have succeeded in the description of particle yields in various collision systems at different energies [10, 11, 16]. In the rapidity space, different sources of final-state particles stay at different positions due to stronger longitudinal flow [17].

In our previous work, the transverse momentum distributions of meson in Au + Au, d + Au, and p + p collisions were investigated in the framework of a thermalized cylinder model. There is a tail part in the transverse momentum distributions of mesons at RHIC energies. To explain the wider transverse momentum spectra, the hard and soft processes have been taken into account in the particle production. The improved cylinder model with two-component distribution is successful in the description of the meson production. But we can only obtain an indirect association with the temperature of the emission sources. The multisource thermal model was improved from the cylinder model. In this paper, we consider the different longitudinal rapidity of the emission sources created in Au + Au and d + Au collisions at 200 GeV and extend the improved Tsallis distribution with one source to the Tsallis distribution with multisource in the picture of the multisource thermal model. The relativistic treatment for the transverse direction would be needed as long as the stochastic approach is adopted. Our results are in agreement with the experimental data of PHENIX Collaboration. Even more important, the model can quantitatively provide the temperature information of the emission sources.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The author would like to thank Dr. J. H. Kang for her guidance throughout the work. The author thanks also Dr. B. C. Li for his improvements to the paper.