  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.
