Sphalerons, small fluctuations, and baryon-number violation in electroweak theory.

Abstract

We study the formalism of the sphaleron approximation to baryon-number violation in the standard model at temperatures near 1 TeV. We investigate small fluctuations of the sphaleron, the competition of large-scale sphalerons with thermal fluctuations, and the damping of the transition rate in the plasma. We find a suppression of the rate due to Landau damping and due to factors arising from zero modes. Our approximations are valid in the regime 2${M}_{W}$(T)\ensuremath{\ll}T\ensuremath{\ll}2${M}_{W}$(T)/${\ensuremath{\alpha}}_{W}$ for models where \ensuremath{\lambda}\ensuremath{\sim}${g}^{2}$. We find that the rate of baryon-number violation is still significantly larger than the expansion rate of the Universe.