Strong-Coupling Lattice QCD on Anisotropic Lattices

TL;DR

This paper develops a nonperturbative method to determine anisotropy renormalization in strong-coupling lattice QCD, improving the accuracy of phase boundary and mass calculations, with implications for high-temperature QCD studies.

Contribution

It introduces a simple criterion for nonperturbative anisotropy renormalization and computes key coefficients for SU(3) lattice QCD, revealing significant corrections to mean field predictions.

Findings

Mean field predictions are significantly corrected by nonperturbative effects.

The phase boundary shows reduced lattice dependence with the new renormalization.

Estimated pion decay constant and chiral condensate in strong coupling limit.

Abstract

Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalisation of the anisotropy coupling in strongly-coupled SU($N$) or U($N$) lattice QCD with massless staggered fermions. We then compute the renormalised anisotropy, and the strong-coupling analogue of Karsch's coefficients (the running anisotropy), for $N=3$. We achieve high precision by combining diagrammatic Monte Carlo and multi-histogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass, and of the location of the phase boundary associated with chiral symmetry restoration. In particular, the phase boundary, evaluated on different finite lattices, has a dramatically smaller dependence on the lattice time extent. We also estimate, as a byproduct, the pion decay constant and the chiral condensate of massless SU(3) QCD in the strong coupling limit at zero temperature.