Evolution of midrapidity average transverse momentum of pions, kaons, protons and antiprotons in Au plus Au collisions in (s_nn)^1/2 =7-39-GeV energy range from the beam energy scan program

The < N-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 Au + 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(pion) < alpha(kaon) < alpha((anti)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 Au+Au collision energy from (s(nn))(1/2 )= 7.7GeV to (s(nn))(1/2 )= 39GeV. Drastic change observed in the energy (snn) dependence of the parameter alpha for the charged kaons at ((s(nn))(1/2 )approximate to 39GeV could possibly indicate a significant change in the mechanism(s) of the charged kaon production in Au + Au collisions at around (s(nn))(1/2 )approximate to 39GeV. Significant change in the (s(nn))(1/2) dependence of the parameter alpha for the charged pions observed at around (s(nn))(1/2 )approximate to 20GeV is consistent with a possible change in the mechanism(s) of the particle production in Au + Au collisions at around(s(nn))(1/2 )approximate to 20GeV, 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 )= 7-20GeV. These gaps diminish and practically disappear with (pi(+)) approximate to alpha(pi(-)) and alpha (protons) approximate to alpha (antiprotons) in the region (s(nn))(1/2 )> 20GeV. 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 Au + Au collisions at around (s(nn))(1/2 )approximate to 20GeV. 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.