The Sphaleron Rate from 4D Euclidean Lattices

Abstract

We develop a new method to determine thermal activation rates, such as for bubble nucleation, topology change, \textsl{etc.}, using 4-dimensional Euclidean methods. This allows nonperturbative study on the lattice. We then investigate the strong sphaleron rate in pure-glue QCD at temperatures between 1.3 $\Tc$ and 1000 $T_\mathrm{c}$, making contact with previous results but extending them down close to the critical temperature. The extension to full QCD will be straightforward. Limitations of the proposal (the inability to compute a certain dynamical prefactor, puzzling large-volume behavior, and the inability to treat temperatures $T < 1.3 \, T_\mathrm{c}$) are also discussed.