Quark Diffusion and Baryogenesis at the Electroweak Phase Transition

Baryogenesis at the electroweak phase transition may take place through CP-violating reflections of quarks from expanding bubbles of the broken symmetry phase. We formulate and approximately solve the transport equations for the reflected quark asymmetries. The results are comparable to a previous Monte Carlo calculation and allow for analytic estimates of the baryon asymmetry ∆B when the bubble walls have a small velocity. Our method predicts no velocity-dependence for ∆B in the small v limit, unlike results obtained from a simplified treatment based on the diffusion equation. There is currently much interest in the possibility that the baryon asymmetry of the universe was created during the electroweak phase transition, using its first-order nature as the means for departure from thermal equilibrium, as is required in any theory of baryogenesis [1-4]. There are two paradigms, depending on whether the bubbles of true vacuum which nucleate in the symmetric phase during the transition have relatively thin or thick walls. In the thin-wall regime which is investigated here, CP-violation in the Higgs sector causes an asymmetry between fermions and antifermions reflected from the bubble walls. To leading order in αweak it consists of equal and opposite excesses of right-handed and lefthanded fermions, due to CPT conservation, so that the net baryon or lepton number in the disturbance is zero, but its chirality is nonzero. This asymmetry is subsequently converted to a baryon asymmetry by sphaleron interactions. The expanding wall overtakes the baryon asymmetry and incorporates it into the true vacuum phase where it is preserved because of the freezeout of sphalerons. To compute the resulting baryon asymmetry in this scenario, it is necessary to know the distribution functions of the fermions and antifermions in front of the wall in some detail. So far several treatments have been given, including a Monte Carlo simulation of the diffusion of reflected quarks [3] (hereafter called CKN), and the diffusion equation [4]. Our aim is to complement these approaches by starting with the exact Boltzmann equation and solving for the distributions with the help of a few reasonable approximations. We will find the profile for the reflected quark asymmetry, estimate the effect of nonvanishing domain wall thickness on the baryon asymmetry, and show that the present method disagrees with the diffusion equation approach concerning the velocity dependence of the final result. Our starting point to compute the transport of reflected quarks with distribution functions fi is the Boltzmann equation,