# Full O(a) improvement in EQCD

## TL;DR

This paper achieves full O(a) improvement in EQCD by numerically determining the scalar mass renormalization, enhancing the precision of lattice-continuum matching for studying nonperturbative hot QCD effects.

## Contribution

It provides the first complete O(a) matching coefficient for EQCD, enabling more accurate lattice simulations of hot QCD phenomena.

## Key findings

- Determined the unknown scalar mass renormalization coefficient.
- Updated the EQCD phase diagram.
- Facilitates 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 O(a) matching, an additive scalar mass renormalization. We do this numerically by using the symmetry-breaking phase transition point of the theory as a line of constant physics. This prepares the ground for a precision study of the transverse momentum diffusion coefficient C(qperp) within this theory. As a byproduct, we provide an updated version of the EQCD phase diagram.