and which occur out of thermal equilibrium. It appears that the standard model (SM) satisfies all three conditions [@sak; @EB]; the baryon number is not conserved at quantum level due to the $B+L$ anomaly [@B+L], a CP violation source does exist in the quark sector ($CKM$ matrix), and a departure from thermal equilibrium could in principle be achieved through a strong first-order phase transition [@EB]. However, detail calculations show that the SM fails to generate the observed baryon asymmetry due to the smallness of the $CP$ violation effect and the weakness of the electroweak phase transition (EWPT) [@RT].

In gauge theories, a first-order phase transition takes place if the vacuum of the theory does not correspond to the global minimum of the potential. Since it is energetically unfavored, the field changes its value to the true vacuum ( i.e., the absolute minimum of the potential). Because of the existence of a barrier between the two minima, this mechanism can happen by tunneling or thermal fluctuations via bubble nucleation. The electroweak baryogenesis scenario is realized when the $B$ and $CP$ violating interactions pass through the bubble wall. These interactions are very fast outside the bubbles but suppressed inside. Then a net 