Axial charge segregation and CP violation during the electroweak phase transition with hypermagnetic fields

We study the scattering of fermions off the true vacuum bubbles nucleated during a first order electroweak phase transition in the presence of a background hypermagnetic field. By considering the limit of an infinitely thin bubble wall, we derive and analytically solve the Dirac equation in three spatial dimensions for left and right chirality modes and compute reflection and transmission coefficients for the case when the fermions move from the symmetric toward the broken symmetry phase. Given the chiral nature of the fermion coupling with the background field in the symmetric phase, an axial asymmetry is generated during the scattering processes. This mechanism is thus shown to provide an additional source of CP violation within the standard model. We discuss possible implications for baryon number generation.