Fermion Scattering off Electroweak Bubble Wall and Baryogenesis

Abstract

By treating CP-violating interaction as a perturbative term, we solve the Dirac equation in the background of electroweak bubble wall (the distorted wave Born approximation). We obtain the transmission and reflection coefficients for a chiral fermion incident from the symmetric-phase region and for the one from the broken-phase region respectively. There hold the respective sets of unitarity relations and also reciprocity relations among them. These relations enable us to rigorously derive quantum-number flux through the bubble wall, which is the first order quantity of the CP violation. The flux is found to be negligible for a thick wall such that $m_0/a\gsim 2$, where $1/a$ is the wall thickness and $m_0$ is the fermion mass.