Ding Huiqiang, Cheng Luan, Dai Tingting, Wang Enke, Zhang Wei-Ning
School of Physics, Dalian University of Technology, Dalian 116024, China.
Institute of Quantum Matter, South China Normal University, Guangzhou 510631, China.
Entropy (Basel). 2023 Dec 13;25(12):1655. doi: 10.3390/e25121655.
We establish a statistical two-body fractal (STF) model to study the spectrum of J/ψ. J/ψ serves as a reliable probe in heavy-ion collisions. The distribution of J/ψ in hadron gas is influenced by flow, quantum and strong interaction effects. Previous models have predominantly focused on one or two of these effects while neglecting the others, resulting in the inclusion of unconsidered effects in the fitted parameters. Here, we study the issue from a new point of view by analyzing the fact that all three effects induce a self-similarity structure, involving a J/ψ-π two-meson state and a J/ψ, π two-quark state, respectively. We introduce modification factor qTBS and q2 into the probability and entropy of charmonium. qTBS denotes the modification of self-similarity on J/ψ, q2 denotes that of self-similarity and strong interaction between and c¯ on quarks. By solving the probability and entropy equations, we derive the values of qTBS and q2 at various collision energies and centralities. Substituting the value of qTBS into distribution function, we successfully obtain the transverse momentum spectrum of low-pT J/ψ, which demonstrates good agreement with experimental data. The STF model can be employed to investigate other mesons and resonance states.
我们建立了一个统计两体分形（STF）模型来研究J/ψ的能谱。J/ψ在重离子碰撞中是一个可靠的探针。强子气体中J/ψ的分布受流、量子和强相互作用效应的影响。先前的模型主要关注这些效应中的一两种，而忽略了其他效应，导致拟合参数中包含了未考虑的效应。在此，我们从一个新的角度研究这个问题，通过分析这样一个事实：所有这三种效应都会诱导出自相似结构，分别涉及一个J/ψ - π两介子态和一个J/ψ、π两夸克态。我们将修正因子qTBS和q2引入到粲夸克偶素的概率和熵中。qTBS表示对J/ψ自相似性的修正，q2表示对自相似性以及夸克上的和c¯之间强相互作用的修正。通过求解概率和熵方程，我们推导出了不同碰撞能量和中心度下qTBS和q2的值。将qTBS的值代入分布函数，我们成功得到了低pT J/ψ的横向动量谱，它与实验数据显示出良好的一致性。STF模型可用于研究其他介子和共振态。
