Full $\mathcal{O}(a)$ improvement of EQCD

TL;DR

This paper achieves a precise $ ext{O}(a)$ improvement of EQCD by numerically determining the scalar mass renormalization, enhancing lattice studies of hot QCD's infrared sector.

Contribution

It provides the first numerical determination of the unknown $ ext{O}(a)$ matching coefficient in EQCD, enabling more accurate lattice simulations.

Findings

Successful numerical determination of the scalar mass renormalization coefficient.

Enhanced precision in lattice EQCD matching to continuum theory.

Foundation laid for high-precision studies of transverse momentum diffusion.

Abstract

EQCD is a 3D bosonic theory containing SU(3) and an adjoint scalar, which efficiently describes the infrared, nonperturbative sector of hot QCD and which is highly amenable to lattice study. We improve the matching between lattice and continuum EQCD by determining the final unknown coefficient in the $\mathcal{O}(a)$ matching, an additive scalar mass renormalization. We do this numerically by using the symmetry-breaking phase transition line of EQCD as a line of constant physics. This prepares the ground for a precision study of the transverse momentum diffusion coefficient $C(q_\perp)$ within this theory.