Sphaleron Rate in the Minimal Standard Model

We use large-scale lattice simulations to compute the rate of baryon number violating processes (the sphaleron rate), the Higgs field expectation value, and the critical temperature in the standard model across the electroweak phase transition temperature. While there is no true phase transition between the high-emperature symmetric phase and the low-temperature broken phase, the crossover is sharp and located at temperature T-c = (159.5 +/- 1.5) GeV. The sphaleron rate in the symmetric phase (T > T-c) is Gamma/T-4 = (18 +/- 3)alpha(5)(W), and in the broken phase in the physically interesting temperature range 130 GeV < T < T-c it can be parametrized as log (Gamma/T-4) = (0.83 +/- 0.01)T.GeV - (147.7 +/- 1.9). The freeze-out temperature in the early Universe, where the Hubble rate wins over the baryon number violation rate, is T-* = (131.7 +/- 2.3) GeV. These values, beyond being intrinsic properties of the standard model, are relevant for, e.g., low-scale leptogenesis scenarios.