Sphaleron rate in the symmetric electroweak phase

Recently Bodeker has presented an effective infrared theory for the dynamics of Yang-Mills theory, suitable for studying the rate of baryon number violation in the early universe. We extend his theory to include Higgs fields, and study how much the Higgs affects the baryon number violation rate in the symmetric phase, at the phase coexistence temperature of a first order electroweak phase transition. The rate is about 20% smaller than in pure Yang-Mills theory. We also analyze the sphaleron rate in the analytic crossover regime. Our treatment relies on the ergodicity conjecture for 3-D scalar $\phi^4$ theory.