Diffusion and Debye Screening Near Expanding Domain Walls

We study the effect of Debye screening of hypercharge when a net fermion number is reflected from a domain wall during a first order phase transition, which may be relevant for electroweak baryogenesis. We give a simple method for computing the effect of screening within the diffusion approximation, whose results are compatible with those of a more elaborate treatment based on the Boltzmann equation. Our formalism takes into account the differences in mobility of different particle species. We believe it is conceptually simpler than other accounts of screening that have appeared in this context. Somewhat surprisingly, we find that Debye screening can actually enhance electroweak baryogenesis by a modest factor (∼ 2). An important ingredient of the charge transport mechanism of electroweak baryogenesis [1, 2] is the diffusion of net left-handed fermion number into the false vacuum, after quarks and leptons reflect from expanding domain walls during the electroweak phase transition. This left-handed asymmetry is what drives sphalerons to produce a baryon asymmetry. It is desirable to understand how it propagates into the plasma because the more efficiently it does so, the longer it can drive baryon production before getting stopped by collisions and overtaken by the advancing wall. A number of papers have examined the diffusion problem from various angles [3]-[8]. In the early days of the charge transport proposal, there were some worries that the chiral asymmetry, because it carries hypercharge, might be prevented from penetrating deep into the plasma due to Debye screening, since hypercharge is an unbroken gauged charge [9]. Indeed this would be the case if there were only one species of fermion carrying both chirality and hypercharge. It was argued however that when there are many species, the hypercharge can be screened without implying that chirality is also screened [10, 11]. In fact reference [10] concluded that Debye screening has no effect whatever on the rate of baryon production (up to small effects due to the difference between Fermi-Dirac and Bose-Einstein statistics. In the present work we reexamine the effects of screening and show that in fact it can have some effect on the baryon violation rate, actually making it somewhat larger than if one had neglected screening. The reason for the discrepancy in conclusions is that we allow for the various species to have different diffusion coefficients, which leads to some particles being more efficient screeners than others. We show how to explicitly compute the effects of screening by incoporating the gauge forces responsible for it into the diffusion approximation. In this formalism one can derive rather elegantly the final values of particle asymmetries after screening and diffusion, starting from some initial asymmetries produced at the domain wall. Our starting point, similarly to references [9] and [10], is the Boltzmann equation, including force terms for long range interactions. For each species of particle it is