Sphaleron rate of $N_f=2+1$ QCD

TL;DR

This study calculates the sphaleron rate in 2+1 flavor QCD at physical parameters across a temperature range, using a novel lattice method to extract the rate with controlled continuum and smoothing limits.

Contribution

It introduces a lattice-based method to compute the sphaleron rate in physical QCD with dynamical fermions, extending previous quenched analyses.

Findings

Sphaleron rate increases with temperature in the studied range.

Lattice artifacts are mild for the sphaleron rate despite large topological susceptibility artifacts.

Method successfully extrapolates to continuum and zero-smoothing limits.

Abstract

We compute the sphaleron rate of $N_f=2+1$ QCD at the physical point for a range of temperatures $200$ MeV $\lesssim T \lesssim 600$ MeV. We adopt a strategy recently applied in the quenched case, based on the extraction of the rate via a modified version of the Backus-Gilbert method from finite-lattice-spacing and finite-smoothing-radius Euclidean topological charge density correlators. The physical sphaleron rate is finally computed by performing a continuum limit at fixed physical smoothing radius, followed by a zero-smoothing extrapolation. Dynamical fermions were discretized using the staggered formulation, which is known to yield large lattice artifacts for the topological susceptibility. However, we find them to be rather mild for the sphaleron rate.