On J/psi and transverse momentum distributions in high energy collisions

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 integrated. The results are in good agreement with the experimental data of proton-proton ( ) and proton-lead ( -Pb) collisions at LHC energies. The temperature of the emission source and the nonequilibrium degree of the collision system are extracted.


Introduction
The creation and study of nuclear matter at high energy densities are the purpose of Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) [1][2][3][4][5][6][7]. As a new matter state, quark gluon plasma (QGP) is a thermalized system which consists of strong coupled quarks and gluons in a limited region. The suppression of J/ψ meson with respect to proton-proton (p p ) collisions is regarded as a distinctive signature of the QGP formation and brings valuable insight into properties of the nuclear matter. In proton-nucleus (p-A) collisions, the prompt J/ψ meson suppression has also been observed at large rapidity [8]. But, QGP is not expected to be created in the small system. 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 T p spectra of identified particles produced in the collisions are a vital research for physicists. Now, different models have been developed to describe the T p distributions of the final-state particles in high energy collisions [9][10][11][12], such as Boltzmann distribution, Rayleigh distribution, Erlang distribution, the multisource thermal model, Tsallis statistics and soon on. Different phenomenological models of initial coherent multiple interactions and particle transport have been proposed to discuss the particle production in high-energy collisions. In condensed matter research, Tsallis statistics can deal with non-equilibrated complex systems [13]. Then, Tsallis statistics are developed to describe the particle production [14][15][16][17][18].
In our previous work [11], 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

Tsallis statistics in an emission source
According to the multisource thermal model [11], at the initial stage of nucleon-nucleon (or nucleon-nucleus) collisions, a projectile cylinder and a target cylinder are formed at the rapidity y space when the projectile nucleon and target nucleon pass each other. The projectile and target cylinder can be regarded as one emission source with a rapidity width. The source emits the observed particles, which follow a certain distribution.
In order to describe the transverse momentum spectra in high-energy collisions, several versions of Tsallis distribution are proposed. But, they originate from the Ref. [13], the meson number is given by It is worth noting that the T where  

Transverse momentum spectra and discussions
, and   3S  mesons respectively, the B is the dimuon branching fraction. The experimental data are taken from Ref. [20]. The symbols and lines represent the same meanings as those in Fig. 1. The results are also in agreement with the experiment data. The parameters T and q taken in the calculation are listed in Table 1   13TeV. The experimental data are taken from Ref. [21].
The symbols and lines represent the same meanings as those in Fig. 1. The results are also in agreement with the experiment data. The T and q values used in the calculation are listed in Table 2. The temperature T decreases with increasing the rapidity bins. As the emission source draws closer to the center, the excitation degree increases. The T values are larger than that at  NN s 8 TeV in the same y range. The q behavior is similar to that of Fig. 1 and 2.
For comparison, Fig. 5 presents the double-differential cross-section 2 / T d dp dy Ref. [22]. The symbols and lines represent the same meanings as those in Fig. 1. The results are also in agreement with the experiment data. The parameters T and q taken in the calculation are listed in Table 2. The emission source temperature T decreases with increasing the rapidity bins. The values of q are between 1.031 and 1.065.

Conclusions
In the framework of the emission source, where Tsallis statistics are consistently integrated, we investigate the transverse momentum spectra of  / J and  mesons produced in pp and p -Pb collisions over an energy range from 5 to 13 TeV. The results agree with the experimental data of the LHCb Collaboration in LHC. By comparing with the experimental data, the emission source temperature T is extracted and decreases with increasing the rapidity bins.
It is consistent with the corresponding rapidity that the closer the emission source is to the y center, the larger the excitation degree is. The temperature T increases with increasing the collision energy. So, the excitation degree of the emission source also increases with increasing the collision energy. The parameter q does not show an obvious change, which means the collision system is not very unstable.
Final-state particle production in high-energy collisions have attracted much attention, since attempt has been made to understand the properties of strongly coupled QGP by studying the production mechanisms. Thermal-statistical models have been successful in describing particle