Measuring the broken phase sphaleron rate nonperturbatively

Abstract

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 $\mathrm{exp}(\ensuremath{-}3.6).$ 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 $\ensuremath{\lambda}{/g}^{2}$ is less than 0.037.