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

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.