Mott Dissociation and Kaon to Pion Ratio in the EPNJL Model

Abstract

The behaviour of pseudoscalar mesons within the SU(3) PNJL-like models is considered for finite T and $${{\mu }_{B}}$$ . We compare the pole approximation (Breit–Wigner) with the Beth–Uhlenbeck approach. We evaluate the $$K{\text{/}}\pi $$ ratios along the phase transition line in the T– $${{\mu }_{B}}$$ plane with constant and $$T{\text{/}}{{\mu }_{B}}$$ -dependent pion and strange quark chemical potentials. Using the model, we can show that the splitting of kaon and anti-kaon masses appears as a result of introduction of density and this explains the difference in the $${{K}^{ + }}{\text{/}}{{\pi }^{ + }}$$ ratio and $${{K}^{ - }}{\text{/}}{{\pi }^{ - }}$$ ratio at low $$\sqrt {{{s}_{{NN}}}} $$ and their tendency to the same value at high $$\sqrt {{{s}_{{NN}}}} $$ . A sharp “horn” effect in the $${{K}^{ + }}{\text{/}}{{\pi }^{ + }}$$ ratio is explained by the enhanced pion production which can be described by occurrence of a nonequilibrium pion chemical potential of the order of the pion mass. We elucidate that the horn effect is not related to the existence of a critical endpoint in the QCD phase diagram.