The spectrum of low-$p_{T}$ $J/\psi$ in heavy ion collisions in a fractal description

Abstract

Transverse momentum spectrum of particles in hadron gas are affected by flow, quantum and strong interaction effects. Previously, most models focus on only one of the three effects but ignore others. The unconsidered effects are taken into the fitted parameters. In this paper, we study the three effects together from a new fractal angle by physical calculation instead of data fitting. Near the critical temperature, the three effects induce $J/\psi$ and neighboring meson to form a two-meson structure. We set up a two-particle fractal (TPF) model to describe this structure. We propose that under the three effects, $J/\psi$-$\pi$ two-meson state, $J/\psi$ and $\pi$ two-quark states form a self-similarity structure. With evolution, the two-meson structure disintegrate. We introduce an influencing factor $q_{fqs}$ to describe the flow, quantum and strong interaction effects and an escort factor $q_2$ to describe the binding force and the three effects. By solving the probability and entropy equations, we obtain the values of $q_{fqs}$ and $q_2$ at different collision energies and centrality classes. By substituting the value of $q_{fqs}$ into distribution function, we obtain the transverse momentum spectrum of low-$p_T$ $J/\psi$ and find it in good agreement with experimental data. We also analyze the evolution of $q_{fqs}$ with the temperature. It is found that $q_{fqs}$ is larger than 1. This is because the three effects decrease the number of microstates. We also find $q_{fqs}$ decreases with decreasing the temperature. This is consistent with the fact that with the system expansion, the influence of the three effects decrease.Comment: 9 pages, 3 figure