The sphaleron rate from Euclidean lattice correlators: an exploration

TL;DR

This paper develops a lattice-based method to determine the sphaleron rate, related to topological charge diffusion, through analytical continuation of Euclidean correlators, involving continuum and zero-flow extrapolations.

Contribution

It introduces a novel approach to extract the sphaleron rate from Euclidean lattice correlators using spectral reconstruction and flow time extrapolations.

Findings

High-precision measurements of topological correlators at $1.5 T_c$

Successful continuum and zero-flow extrapolations of correlators

First lattice-based estimate of sphaleron rate using this method

Abstract

We show how the sphaleron rate (the Minkowski rate for topological charge diffusion) can be determined by analytical continuation of the Euclidean topological-charge-density two-point function, which we investigate on the lattice, using gradient flow to reduce noise and provide improved operators which more accurately measure topology. We measure the correlators on large, fine lattices in the quenched approximation at $1.5\,T_c$ with high precision. Based on these data we first perform a continuum extrapolation at fixed physical flow time and then extrapolate the continuum estimates to zero flow time. The extrapolated correlators are then used to study the sphaleron rate by spectral reconstruction based on perturbatively motivated models.