Chiral fermion mass and dispersion relations at finite temperature in the presence of hypermagnetic fields

We study the modifications to the real part of the thermal self-energy for chiral fermions in the presence of a constant external hypermagnetic field. We compute the dispersion relation for fermions occupying a given Landau level to first order in [Formula Presented] [Formula Presented] and [Formula Presented] and to all orders in [Formula Presented] where [Formula Presented] and g are the [Formula Presented] and [Formula Presented] couplings of the standard model, respectively, [Formula Presented] is the fermion Yukawa coupling, and B is the hypermagnetic field strength. We show that in the limit where the temperature is large compared to [Formula Presented] left- and right-handed modes acquire finite and different B-dependent masses due to the chiral nature of their coupling with the external field. Given the current bounds on the strength of primordial magnetic fields, we argue that the above is the relevant scenario to study the effects of magnetic fields on the propagation of fermions prior to and during the electroweak phase transition. © 2004 The American Physical Society.