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

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)≪T≪2$M_W$(T)/${\alpha }_W$ for models where λ∼$g^2$. We find that the rate of baryon-number violation is still significantly larger than the expansion rate of the Universe.