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

Abstract

Mass spectra and Mott transitions of neutral mesons $K_0,{\bar K}_0,π_0,η,η'$ 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 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. $π_0$ 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. $η,η'$ mesons 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. $η'$ meson is a resonant state, and its mass $m_{η'}$ continuously decreases and then increases with temperature. The mass jumps of $K_0,{\bar K}_0,π_0,η$ mesons are caused by the dimension reduction of the constituent quarks under external magnetic field. In PNJL model, the Mott transition temperature of $K_0,{\bar K}_0,π_0$ mesons ($η$ 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.