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

This study investigates how finite temperature and magnetic fields influence the mass spectra and Mott transitions of neutral mesons using a three-flavor PNJL model, highlighting effects of gluons and inverse magnetic catalysis.

Contribution

It introduces a detailed analysis of meson mass behavior and Mott transitions under magnetic fields and temperature, incorporating gluon effects and IMC in the PNJL framework.

Findings

Meson masses show characteristic behavior around Mott transitions.

Magnetic field influences the Mott transition temperatures of mesons.

Inverse magnetic catalysis shifts Mott transition temperatures lower.

Abstract

Mass spectra and Mott transitions of neutral mesons $K_0,{\bar K}_0,\pi_0,\eta,\eta'$ 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 parameter. Mass spectra show similar structure when introducing the gluon and IMC effect. The mass of $K_0\ ({\bar K}_0)$ meson $m_{K_0}=m_{{\bar K}_0}$ 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. $\pi_0$ meson is not only the pseudo-Goldstone boson of chiral symmetry breaking, but also influenced by the flavor mixing of $\pi_0-\eta-\eta'$. The behavior of $m_{\pi_0}$ is different from $m_{K_0}$ only at high temperature region, which decreases with temperature. $\eta,\eta'$ mesons are affected by both the $U_A(1)$ anomaly and the flavor mixing of $\pi_0-\eta-\eta'$. The mass of $\eta$ meson $m_{\eta}$ decreases with temperature in low temperature region and then shows a jump at its Mott transition. After that $m_{\eta}$ firstly decreases and later increases with temperature. $\eta'$ meson is a resonant state, and its mass $m_{\eta'}$ continuously decreases and then increases with temperature. The mass jumps of $K_0,{\bar K}_0,\pi_0,\eta$ mesons are caused by the dimension reduction of the constituent quarks under external magnetic field. In PNJL model, the Mott transition temperature of $K_0,{\bar K}_0,\pi_0$ mesons ($\eta$ meson) decreases (increases) with magnetic field. The IMC effect leads to no qualitative change to the meson Mott transition temperature but shifts them to the lower values.