Measuring the broken phase sphaleron rate nonperturbatively

We present details for a method to compute the broken phase sphaleron rate (rate of hot baryon number violation below the electroweak phase transition) nonperturbatively, using a combination of multicanonical and real time lattice techniques. The calculation includes the “dynamical prefactor,” which accounts for prompt recrossings of the sphaleron barrier. The prefactor depends on the hard thermal loops, getting smaller with increasing Debye mass; but for realistic Debye masses the effect is not large. The baryon number erasure rate in the broken phase is slower than a perturbative estimate by about $\exp (-3.6).$ Assuming the electroweak phase transition has enough latent heat to reheat the universe to the equilibrium temperature, baryon number is preserved after the phase transition if the ratio of (“dimensionally reduced” thermal) scalar to gauge couplings $\lambda {/g}^2$ is less than 0.037.