Chiral phase transition and kaon-to-pion ratios in the entanglement SU(3) PNJL model

Within the three-flavor PNJL and EPNJL chiral quark models we have obtained pseudoscalar meson properties in quark matter at finite temperature $T$ and baryochemical potential $mu_B$. We compare the meson pole (Breit-Wigner) approximation with the Beth-Uhlenbeck (BU) approach that takes into account the continuum of quark-antiquark scattering states when determining the partial densities of pions and kaons. We evaluate the kaon-to-pion ratios along the (pseudo-)critical line in the $T-mu_B$ plane as a proxy for the chemical freezeout line, whereby the variable $x=T/mu_B$ is introduced that corresponds to the conserved entropy per baryon as initial condition for the heavy-ion collision experiments. We present a comparison with the experimental pattern of kaon-to-pion ratios within the BU approach and using $x$-dependent pion and strange quark potentials. A sharp horn effect in the energy dependence $K^+/pi^+$ ratio is explained by the enhanced pion production at energies above $sqrt{s_{NN}}=8$ GeV, when the system enters the regime of meson dominance. This effect is in line with the enhancement of low-momentum pion spectra that is discussed as a precursor of the pion Bose condensation and entails the 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.