Semianalytical approaches to local electroweak baryogenesis

Abstract

We examine two semianalytical methods for estimating the baryon asymmetry of the Universe (BAU) generated in scenarios of ``local'' electroweak baryogenesis (in which the requisite baryon number violation and $\mathrm{CP}$ violation occur together in space and time). We work with the standard electroweak theory augmented by the addition of a $\mathrm{CP}$-violating dimension-six operator. We work in the context of a first order phase transition, but the processes we describe can also occur during the evolution of a network of topological defects. Both the approaches we explore deal with circumstances where the bubble walls which convert the high temperature phase to the low temperature phase are thin and rapidly moving. We first consider the dynamics of localized configurations with winding number one which remain in the broken phase immediately after the bubble wall has passed. Their subsequent decay can anomalously produce fermions. In a prelude to our analysis of this effect, we demonstrate how to define the $C$ and $\mathrm{CP}$ symmetries in the bosonic sector of the electroweak theory when configurations with nonzero winding are taken into account. Second, we consider the effect of the passage of the wall itself on configurations which happen to be near the crest of the ridge between vacua as the wall arrives. We find that neither of the simple approaches followed here can be pushed far enough to obtain a convincing estimate of the BAU which is produced. A large scale numerical treatment seems necessary.