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Mott dissociation and kaon to pion ratio in the EPNJL model

The behaviour of pseudoscalar mesons within the SU(3)PNJL-like models is considered for finite T and $μ_B$. We compare the pole approximation (Breit-Wigner) with the Beth-Uhlenbeck approach. We evaluate the $K/π$ ratios along the phase transition line in the T-$μ_B$ plane with constant and $T/μ_B$-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 $K^+/π^+$ ratio and $K^-/π^-$ ratio at low $\sqrt{s_{NN}}$ and their tendency to the same value at high $\sqrt{s_{NN}}$. A sharp "horn" effect in the $K^+/π^+$ 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.