Mass spectra and Mott transitions of neutral mesons at finite temperature and magnetic field in frame of three-flavor Polyakov-extended Nambu-Jona-Lasino model

TL;DR

The paper investigates mass spectra and Mott transitions of neutral mesons $K_0$, $\pi_0$, $\eta$, and $\eta'$ at finite temperature and magnetic field within a three-flavor PNJL model. It systematically incorporates gluon dynamics via the Polyakov potential and the inverse magnetic catalysis (IMC) effect through magnetic-field–dependent couplings, and computes meson properties using random phase approximation with flavor-m mixing under a magnetic field. The results reveal that gluon and IMC effects produce qualitatively similar mass structures, with distinct Mott-transition temperatures that shift under magnetic field; IMC generally lowers these transition temperatures, and the $\pi_0-\eta-\eta'$ mixing plays a crucial role in the high-temperature behavior. The findings advance understanding of how magnetic fields and gluon dynamics shape neutral-meson spectra in hot QCD matter, with implications for heavy-ion physics and lattice-model comparisons.

Abstract

Mass spectra and Mott transitions of neutral mesons $K_0, π_0, η, η'$ at finite temperature and magnetic field are investigated in a three-flavor PNJL model. We focus on the effect of gluons, which is simulated by the Polyakov potential and the inverse magnetic catalysis (IMC) effect, which is mimicked by using a magnetic field dependent coupling constant. Mass spectra show similar structure when introducing the contribution of Polyakov potential and IMC effect. The mass of $K_0$ meson $m_{K_0}$ is controlled by chiral symmetry breaking and restoration. It increases with temperature in the low temperature region, and shows a mass jump at the Mott transition. Further increasing temperature, $m_{K_0}$ firstly decreases and then increases with temperature. $π_0$ meson is not only the pseudo-Goldstone boson of chiral symmetry breaking, but also influenced by the flavor mixing of $π_0-η-η'$. The behavior of $m_{π_0}$ is different from $m_{K_0}$ only at high temperature region, which decreases with temperature. For $η$ and $η'$ mesons, they are affected by both the $U_A(1)$ anomaly and the flavor mixing of $π_0-η-η'$. The mass of $η$ meson $m_η$ decreases with temperature in low temperature region and then shows a jump at its Mott transition. After that $m_η$ firstly decreases and later increases with temperature. $η'$ mesons is a resonant state in vacuum and in medium, and its mass $m_{η'}$ continuously decreases and then increases with temperature. The mass jumps of $K_0, π_0, η$ mesons are caused by the dimension reduction of the constituent quarks under external magnetic field. In the PNJL model, the Mott transition temperature of $K_0,\ π_0$ mesons ($ η$ meson) decrease (increases) with magnetic field. The IMC effect leads to the lower value for meson Mott transition temperature.

Figures (3)

• Figure 1: Mass spectra of $K_0$ meson $m_{K_0}$ (red solid lines), $\pi_0$ meson $m_{\pi_0}$ (black solid lines), $\eta$ meson $m_{\eta}$ (blue solid lines), $\eta'$ meson $m_{\eta'}$ (green solid lines) and quark mass sum $m_d+m_s$, $2m_d$, $2m_s$ (gray dotted lines) at finite temperature with fixed magnetic field $eB=20m_{\pi}^2$ and vanishing quark chemical potential $\mu_f=0$ in the PNJL model (upper panel) and in the NJL model (lower panel).
• Figure 2: Mott transition temperature of $K_0$ meson (upper panel), $\pi_0$ meson (middle panel) and $\eta$ meson (lower panel) as a function of magnetic field in PNJL model (solid lines) and in NJL model (dashed lines).
• Figure 3: (upper panel) Magnetic field dependent parameters $G(eB)$ (red line) and $T_0(eB)$ (blue line) fitted from LQCD reported decreasing pseudocritical temperature of chiral restoration phase transition $T_{pc}^c(eB)/T_{pc}^c(eB=0)$ under external magnetic field lattice1. (middle and lower panel) Mass spectra of $K_0$ meson $m_{K_0}$ (red solid lines), $\pi_0$ meson $m_{\pi_0}$ (black solid lines), $\eta$ meson $m_{\eta}$ (blue solid lines), $\eta'$ meson $m_{\eta'}$ (green solid lines) and quark mass sum $m_d+m_s$, $2m_d$, $2m_s$ (gray dotted lines) at finite temperature with fixed magnetic field $eB=20m_{\pi}^2$ and vanishing quark chemical potential $\mu_f=0$ in the PNJL model with IMC effect in $G(eB)$ scheme (middle panel) and with IMC effect in $T_0(eB)$ scheme (lower panel).