Explicit CP Breaking and Electroweak Baryogenesis

We investigate spatial behaviors of the CP-violating angle $\theta$ by solving the equation of motion of the two-Higgs-doublet model in the presence of a small explicit CP breaking $\delta$. The moduli of the two Higgs scalars are fixed to be the kink shape with a common width. In addition to solutions $\theta \sim O(\delta)$ in all the region, we find several sets of two solutions of opposite signs, whose magnitudes become as large as $O(1)$ around the surface of the bubble wall while the CP violation in the broken phase limit is of $O(\delta)$. Such set of solutions not only yield sufficient amount of the chiral charge flux, but also avoid the cancellation in the net baryon number because of a large discrepancy in their energy densities driven nonperturbatively by the small $\delta$.