Fermion scattering off aCP-violating electroweak bubble wall

A general prescription to solve the Dirac equation in the presence of a CP-violating electroweak bubble wall is presented. The profile of the bubble wall is not specified except that the wall height is ${\mathit{m}}_0$ and zero deep in the broken- and the symmetric-phase regions, respectively, where ${\mathit{m}}_0$ is a fermion mass given by the Higgs vacuum, expectation value and the Yukawa coupling. The CP-violating effects are evaluated by regarding the CP-violating part of the bubble wall as a perturbation to CP-conserving solutions. The basic quantity ${\mathit{R}}_{\mathit{R}\to \mathit{L}}$-R${\mathrm{¯}}_{\mathit{R}\to \mathit{L}}$, which would contribute to the cosmological baryon asymmetry, is estimated for some profiles of the wall, where ${\mathit{R}}_{\mathit{R}\to \mathit{L}}$ (R${\mathrm{¯}}_{\mathit{R}\to \mathit{L}}$) is the reflection coefficient of the right-handed chiral fermion (antifermion).