Excitation functions of parameters in Erlang distribution, Schwinger mechanism, and Tsallis statistics in RHIC BES program

Experimental results of the transverse momentum distributions of phi mesons and $\mathrm{\Omega }$ hyperons produced in gold-gold (Au-Au) collisions with different centrality intervals, measured by the STAR Collaboration at different energies (7.7, 11.5, 19.6, 27, and 39 GeV) in the beam energy scan (BES) program at the relativistic heavy ion collider (RHIC), are approximately described by the single Erlang distribution and the two-component Schwinger mechanism. Meanwhile, the STAR experimental transverse momentum distributions of negatively charged particles, produced in Au-Au collisions at RHIC BES energies, are approximately described by the two-component Erlang distribution and the single Tsallis statistics. The excitation functions of free parameters are obtained from the fit to the experimental data. A weak softest point in the string tension in $\mathrm{\Omega }$ hyperon spectra is observed at 7.7 GeV.