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 + /π + ratio and the K − /π − ratio at low √ s NN and their tendency to the same value at high √ s NN. We also show that the rise in the ratio K + /π + appears near the critical endpoint when we build the K + /π + ratio along the phase-transition diagram and it can be considered as a critical region signal.

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

“…For the HRG model, see Figures 1 and 4 of reference [65], where the similarity of the K + /π + ratio with the Wroblewski factor λ s = 2 ss /( uū + dd ) was noticed. For the PNJL model, this behaviour has been shown in Figure 7 of [34] in the BW approximation and in Figure 3 of [66] for the BU approach. The lines of constant K − /π − ratio have the opposite slope and cross the freezeout line only once, thus forming a monotonously rising function of the increasing freezeout temperature (or √ s N N ).…”

“…In this approach it is clearly seen from the behaviour of the corresponding phase shifts for pseudoscalar mesons as functions of energy that there are scattering state contributions from the quarkantiquark continuum and for finite temperatures and baryon chemical potentials an unusual plasmon mode appears in the K + channel which develops a bound state pole under conditions that would correspond to the chemical freeze-out in the region of the "horn" [31]. As we have shown in reference [34], a decisive role in the description of the different patterns of the K + /π + and K − /π − ratios as a function of √ s N N is played by the chemical potentials that are conjugate to (quasi) conserved charges in the system.…”

“…For the numerical calculations in this work we used the following set of parameters: the current quark masses m 0u = m 0d = 5.5 MeV, m 0s = 0.131 GeV, the cut-off Λ = 0.652 GeV and the couplings g D Λ 5 = 10.592, g S Λ 2 = 1.828. We also introduced the strange quark chemical potential as µ s = 0.55µ u and µ u = µ d [34]. It can be seen from the right panel of Figure 1 that the pseudocritical temperature of the chiral crossover transition at µ B = 0 GeV in the PNJL model case is T c = 0.218 GeV (black dashed line), and thus higher than the T c = 156.5 ± 1.5 GeV obtained by the ab-initio simulations of Lattice QCD [1].…”

“…Both Figures 2 and 3 clearly demonstrate the splitting of the charged multiplet mass with increasing density. The splitting can be explained by the modification of the Fermi sea by the presence of the medium [34,61,62]. In dense baryon matter the concentration of light quarks is very high so that the Pauli blocking factor…”

“…In the BU approach one obtains not only the mass splitting of the charge multiplets in hot and dense matter that is also seen in the BW approximation to solutions of the in-medium Bethe-Salpeter equation [32][33][34]. In this approach it is clearly seen from the behaviour of the corresponding phase shifts for pseudoscalar mesons as functions of energy that there are scattering state contributions from the quarkantiquark continuum and for finite temperatures and baryon chemical potentials an unusual plasmon mode appears in the K + channel which develops a bound state pole under conditions that would correspond to the chemical freeze-out in the region of the "horn" [31].…”