Baryon asymmetry at the weak phase transition in presence of arbitrary CP violation

We consider interactions of fermions with the domain wall bubbles produced during a first order phase transition. A new exact solution of the Dirac equations is obtained for a wall profile incorporating a position dependent CP violating phase. The reflection coefficients are computed, a resonance effect is uncovered for rapidly varying phases. This resonance effect happens when the energy and mass of the incident particles are $E\mathrm{/}m=\mathrm{\Delta }\theta \mathrm{/}2$. Where $\mathrm{\Delta }\theta$ is the phase variation across the wall width. We calculate the chiral charge flux through the wall surface and the corresponding baryon asymmetry of the Universe. It agrees in sign and magnitude with the observed baryonic excess ${\rho }_B\mathrm{/}s\approx {10}^{-10}$ for a large range of parameters and CP violation. As a function of $\mathrm{\Delta }\theta$, the ratio ${\rho }_b\mathrm{/}s$ reach a maximum for $\mathrm{\Delta }\theta \approx 2-4\pi$ and $m\approx m_{top}$. PACS: 11.27.+d, 03.65.-w, 02.30.Hq, 02.30.Gp, 11.30.Fs, 98.80.Cq