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, 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 Tc, 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 Tc) are also discussed.

Maximal temperature of strongly-coupled dark sectors

“…Apart from phenomenological issues, there are also theoretical ingredients that could be built into our framework. Hoping that exploratory low-temperature investigations of the friction coefficient [21,22] turn ultimately into a semi-quantitative tool, the error bands in figure 5 could be reduced. Were the same to happen with the shear viscosity η, the gravitational wave estimate in section 4.2 could be sharpened.…”

“…Unfortunately, extracting real-time information from the latter is exponentially hard (cf., e.g., refs. [19,20]), even if exploratory studies for determining Υ IR have been launched [21,22]. For this reason, our estimates contain a systematic error, reflected by the x-dependence introduced in eq.…”

Asymmetric Dark Matter in Baryon Asymmetrical Universe

“…[17], some first estimations of prefactors (summing zero modes for vacuum-vacuum transitions) for known temperature dependences of the rates in the symmetric and broken phases are given. Then, lattice studies of the sphaleron rates for different temperature ranges in pure-gauge SU(2), pureglue strong theory, symmetric phase, and broken phase have evolved and been improved significantly using different approaches [43][44][45][46]. So, to date, there are known calculated values both for the temperature dependence of Higgs field vacuum condensate and for prefactors that sum the nonperturbative small fluctuations against the background of the sphaleron solution.…”

“…Lattice methods were applied to QCD sphalerons, and, in the pure-gauge case where T ≈ 1.24T c , where T − C ≈ 300 MeV, it was found that Γ sph = 0.079 (25) • T 4 in the symmetric phase [45].…”

The topological susceptibility slope χ′ of the pure-gauge SU(3) Yang-Mills theory

“…Topological properties are among the most interesting non-perturbative features of 4d SU(N ) gauge theories, both for their theoretical implications and for their relation with phenomenological aspects of strong interactions. In this respect, an interesting topological quantity to investigate is the Euclidean topological charge density 2-point correlator [1][2][3][4][5][6][7][8][9]:…”