The properties of non-interacting σ and π0 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.Comment: V1: 26 pages, 15 figures; V2: Discussions improved, references added.
Version accepted for publication in PR