Strange matter and kaon to pion ratio in the SU(3) Polyakov–Nambu–Jona-Lasinio model

Abstract

The behavior of strange matter in the frame of the SU(3) Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model including the ${U}_{A}(1)$ anomaly is considered. We discuss the appearance of a peak in the ratio of the number of strange mesons to nonstrange mesons known as the ``horn.'' The PNJL model gives a schematic description of the chiral phase transition and meson properties at finite temperature and density. By using the model, we can show that the splitting of kaon and antikaon masses appears as a result of the introduction of density. This may explain the difference in the ${K}^{+}/{\ensuremath{\pi}}^{+}$ ratio and the ${K}^{\ensuremath{-}}/{\ensuremath{\pi}}^{\ensuremath{-}}$ ratio at low $\sqrt{{s}_{NN}}$ and their tendency to the same value at high $\sqrt{{s}_{NN}}$. We also show that the rise in the ratio ${K}^{+}/{\ensuremath{\pi}}^{+}$ appears near the critical endpoint when we build the ${K}^{+}/{\ensuremath{\pi}}^{+}$ ratio along the phase-transition diagram and it can be considered as a critical region signal.