Evolution of midrapidity average transverse momentum of pions, kaons, protons and antiprotons in Au+Au collisions in (snn)1∕2= 7–39-GeV energy range from the beam energy scan program

The $〈N_{\mathrm{\text{part}}}〉$ dependencies of the experimental average transverse momentum, $〈p_t〉$, of the charged pions, charged kaons, protons and antiprotons produced at midrapidity ($|y|<0.1$) in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions from the Beam Energy Scan (BES) program at the RHIC (Relativistic Heavy Ion Collider), measured by STAR Collaboration in the ${(s_{nn})}^{1∕2}=7$–39-GeV energy range, have been described quite well with the power-law model function. We have obtained $0<\alpha (\mathrm{\text{pion}})<\alpha (\mathrm{\text{kaon}})<\alpha ((\mathrm{\text{anti}})\mathrm{\text{proton}})<0.2$ inequality at all BES energies, indicating the clear mass ordering (dependence) of the power parameter $\alpha$. On the whole, the exponent parameter $\alpha$ for the charged kaons as well as (anti)protons decreases noticeably with increasing $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collision energy from ${(s_{nn})}^{1∕2}=7.7$$$GeV to ${(s_{nn})}^{1∕2}=39$$$GeV. Drastic change observed in the energy ($s_{nn}$) dependence of the parameter $\alpha$ for the charged kaons at ${(s_{nn})}^{1∕2}\approx 39$$$GeV could possibly indicate a significant change in the mechanism(s) of the charged kaon production in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions at around ${(s_{nn})}^{1∕2}\approx 39$$$GeV. Significant change in the ${(s_{nn})}^{1∕2}$ dependence of the parameter $\alpha$ for the charged pions observed at around ${(s_{nn})}^{1∕2}\approx 20$$$GeV is consistent with a possible change in the mechanism(s) of the particle production in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions at around ${(s_{nn})}^{1∕2}\approx 20$$$GeV, reported earlier by STAR Collaboration. Significant gaps between $\alpha$ (protons) and $\alpha$ (antiprotons) as well as between (${\pi }^{+}$) and $\alpha ({\pi }^{-})$ have been seen in the region ${(s_{nn})}^{1∕2}=7$–20$$GeV. These gaps diminish and practically disappear with $({\pi }^{+})\approx \alpha ({\pi }^{-})$ and $\alpha$ (protons) $\approx \alpha$ (antiprotons) in the region ${(s_{nn})}^{1∕2}>20$$$GeV. Altogether, the findings, regarding collision energy dependencies of the parameter $\alpha$ for the studied particle species, could indicate the probable phase transition of a nuclear matter to the mixed phase of QGP and hadrons taking place in $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collisions at around ${(s_{nn})}^{1∕2}\approx 20$$$GeV. The differences found between parameter $\alpha$ versus ${(s_{nn})}^{1∕2}$ dependencies of the particles and antiparticles have been connected with the ratios of antiparticle and particle yields and differences in the mechanisms of production of particles and antiparticles. It is deduced that the exponent parameter $\alpha$ should be sensitive to the degree of particle (system) thermalization and particle production mechanisms, and its drastic change could be related to the change in the mechanisms of particle production or/and phase transitions in the nuclear/hadronic matter.