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The behaviour of pseudoscalar mesons within the SU(3)PNJL-like models isconsidered for finite T and $\mu_B$. We compare the pole approximation(Breit-Wigner) with the Beth-Uhlenbeck approach. We evaluate the $K/\pi$ ratiosalong the phase transition line in the T-$\mu_B$ plane with constant and$T/\mu_B$-dependent pion and strange quark chemical potentials. Using themodel, we can show that the splitting of kaon and anti-kaon masses appears as aresult of introduction of density and this explains the difference in the$K^+/\pi^+$ ratio and $K^-/\pi^-$ ratio at low $\sqrt{s_{NN}}$ and theirtendency to the same value at high $\sqrt{s_{NN}}$. A sharp "horn" effect inthe $K^+/\pi^+$ ratio is explained by the enhanced pion production which can bedescribed by occurrence of a nonequilibrium pion chemical potential of theorder of the pion mass. We elucidate that the horn effect is not related to theexistence of a critical endpoint in the QCD phase diagram.

Mott dissociation and kaon to pion ratio in the EPNJL model