Improved determination of the classical sphaleron transition rate

We determine the sphaleron transition rate using real time lattice simulations of the classical system. An improved definition of the lattice topological charge allows us to obtain a more reliable estimate of the transition rate. For an SU(2) Yang-Mills-Higgs system in the broken phase we find the transition rate to be strongly suppressed, and we have observed no sphaleron transitions in the range of coupling constants used. For a pure SU(2) Yang-Mills system in large volumes the rate behaves as $\kappa (\alpha_w T)^4$, with $\kappa$ slightly decreasing as the lattice spacing is reduced. If the lattice size is reduced to about twice the magnetic screening length, the rate is suppressed by finite-size effects, and $\kappa$ is approximately proportional to the lattice spacing. Our rate measurements are supplemented by analysis of gauge field correlation functions in the Coulomb gauge.