Chiral pions in a magnetic background

We investigate the modification of the pion self-energy at finite temperature due to its interaction with a low-density, isospin-symmetric nuclear medium embedded in a constant magnetic background. To one loop, for fixed temperature and density, we find that the pion effective mass increases with the magnetic field. For the $\pi^{-}$, interestingly, this happens solely due to the trivial Landau quantization shift $\sim |eB|$, since the real part of the self-energy is negative in this case. In a scenario in which other charged particle species are present and undergo an analogous trivial shift, the relevant behavior of the effective mass might be determined essentially by the real part of the self-energy. In this case, we find that the pion mass decreases by $\sim 10$ for a magnetic field $|eB|\sim m_\pi^2$, which favors pion condensation at high density and low temperatures.