Sh. Fayazbakhsh, S. Sadeghian, N. Sadooghi
The dynamics of noninteracting \sigma and \pi^0 mesons is 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 velocities of magnetized neutral mesons are explored for fixed magnetic fields and chemical potentials. It is shown that the velocity 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, and that, because of explicit Lorentz violation by the background magnetic field, neutral mesons travel, in the transverse direction, at more than the speed of light.
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http://arxiv.org/abs/1206.6051
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