Excitation Function of Initial Temperature of Heavy Flavor Quarkonium Emission Source in High Energy Collisions

The transverse momentum spectra of J/ψ, ψð2SÞ, and YðnS, n = 1, 2, 3Þ produced in proton-proton ðp + pÞ, proton-antiproton
ðp + �pÞ, proton-lead ðp + PbÞ, gold-gold ðAu + AuÞ, and lead-lead (Pb + Pb) collisions over a wide energy range are analyzed
by the (two-component) Erlang distribution, the Hagedorn function (the inverse power-law), and the Tsallis-Levy function.
The initial temperature is obtained from the color string percolation model from the fit by the (two-component) Erlang
distribution in the framework of a multisource thermal model. The excitation functions of several parameters such as the
mean transverse momentum and initial temperature increase from 39 GeV to 13 TeV, which is considered in this work.
The mean transverse momentum and initial temperature decrease (increase slightly or do not change significantly) with
the increase of rapidity (centrality). Meanwhile, the mean transverse momentum of YðnS, n = 1, 2, 3Þ is larger than that of
J/ψ and ψð2SÞ, and the initial temperature for YðnS, n = 1, 2, 3Þ emission is higher than that for J/ψ and ψð2SÞ emission,
which shows a mass-dependent behavior.