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.
Highlights
The classical vacuum of QCD is not unique; there are an infinite number of topologically distinct classical vacua defined by different integer values of the Chern-Simons number
We show how the sphaleron rate 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
This is visible on the right-hand side of Fig. 3, where we show the correlator as a function of 1=N2τ for some selected separations at flow times chosen from a flow range which we will define [see Eq (8)]
Summary
The classical vacuum of QCD is not unique; there are an infinite number of topologically distinct classical vacua defined by different integer values of the Chern-Simons number. The sphaleron rate is defined as the mean-squared change in ChernSimons number per spacetime volume It was first considered within QCD because of the role it may play in electroweak baryogenesis [1,2]. The sphaleron rate Γsphal is defined as the rate of the mean squared change in the topological charge per Minkowski 4-volume, or equivalently the integration of the Wightman correlator of the topological charge density. For electroweak interacting matter the sphaleron rate has been well understood and determined using Bödeker’s effective theory [10,11,12,13] in the weak-coupling regime These innovations allowed for a nonperturbative semiclassical realtime evaluation on a Minkowski lattice [14,15].
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