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 c 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.
Keywords: J/ψ distribution; statistical two-body fractal model; transverse momentum spectrum.