Properties of neutral mesons in a hot and magnetized quark matter

TL;DR

This paper investigates how neutral mesons' properties, such as masses and refraction indices, are affected by temperature, chemical potential, and magnetic fields in a hot, magnetized quark matter using an extended NJL model.

Contribution

It derives dispersion relations and explores anisotropic effects on neutral mesons in a hot, magnetized medium, including nontrivial form factors and directional refraction indices.

Findings

Neutral meson masses depend on temperature and magnetic field.

Magnetic field induces anisotropy in meson refraction indices.

Transverse refraction indices are larger than unity.

Abstract

The properties of non-interacting $\sigma$ and $\pi^{0}$ mesons are studied at finite temperature, chemical potential and in the presence of a constant magnetic field. To do this, the energy dispersion relations of these particles, including nontrivial form factors, are derived using a derivative expansion of the effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio (NJL) model up to second order. The temperature dependence of the pole and screening masses as well as the directional refraction indices of magnetized neutral mesons are explored for fixed magnetic fields and chemical potentials. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the refraction index and the screening mass of neutral mesons exhibit a certain anisotropy in the transverse and longitudinal directions with respect to the direction of the external magnetic field. In contrast to their longitudinal refraction indices, the transverse indices of the neutral mesons are larger than unity.