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

The behavior of strange matter in the frame of the SU(3) Polyakov-loop extended Nambu–Jona-Lasinio (PNJL) model including the $U_A\left(1\right)$ 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 $K^{+}/{\pi }^{+}$ ratio and the $K^{-}/{\pi }^{-}$ 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 $K^{+}/{\pi }^{+}$ appears near the critical endpoint when we build the $K^{+}/{\pi }^{+}$ ratio along the phase-transition diagram and it can be considered as a critical region signal.

Figure 1

The $K^{+}/{\pi }^{+}$ and $K^{-}/{\pi }^{-}$ ratio as the $\sqrt{s_{NN}}$ function for $\text{Pb}+\text{Pb}$ and $\text{Au}+\text{Au}$ central collisions [1, 3, 4, 5]. Blue circles are the $K^{+}/{\pi }^{+}$ ratio for $pp$ collisions.

Figure 2

(top panel) The mass spectra at ${\mu }_u={\mu }_d={\mu }_s=0$. The solid lines denote the meson masses: meson (black) and pion (blue), dashed lines denote $q\overline{q}$ the thresholds for the mesons, dotted lines denote the meson width (bottom panel) The quark normalized condensates of light and strange quarks and the Polyakov loop field $\mathrm{\Phi }$.

Figure 3

(top panel) The phase diagram in the $T\text{−}{\mu }_B$ plane. (bottom panel) the normalized chiral condensate as a function of ${\mu }_B$ at different values of $T=0$, 0.12, 0.2 GeV before, near, and after the CEP.

Figure 4

The spectra of meson masses as a function of the normalized baryon density at $T=0$ GeV for Case I.

Figure 5

(top panel) $K^{+}/{\pi }^{+},K^{-}/{\pi }^{-}$ ratio as function of $T/{\mu }_B$ for cases I and II. (bottom panel) Experimental data for $K^{+}/{\pi }^{+}$ ratio as a function of the rescaled variable $T/{\mu }_B$.

Figure 6

The $K^{+}/{\pi }^{+}$ ratio as a function of $T/{\mu }_B$ for the different cases I and II.

Figure 7

The contour plot of the $K^{+}/{\pi }^{+}$ ratio on the phase diagram (black line) plane $T\text{−}{\mu }_B$.