Curing O(a) Errors in 3-D Lattice SU(2) x U(1) Higgs Theory
Guy D. Moore
TL;DR
The paper addresses systematic $O(a)$ lattice-spacing errors in a three-dimensional lattice SU(2) x U(1) Higgs theory used to study the electroweak phase transition. It develops a perturbative one-loop matching framework that absorbs hard ultraviolet lattice effects into shifts of bare parameters, leveraging the super-renormalizable structure and focusing on dimension-2 operator renormalizations. The main result is that infrared behavior can be matched to the continuum up to $O(beta_L^{-2})$ corrections by treating hard loops as operator insertions and ensuring $Z_m = Z_op$ while controlling additive counterterms, thereby significantly improving lattice convergence. The approach offers a practical path to reinterpret existing lattice data with reduced lattice artifacts and to study phase-transition strength with coarser, more affordable lattices.
Abstract
We show how to make O(a) corrections in the bare parameters of 3-D lattice SU(2) times U(1) Higgs theory which remove O(a) errors in the match between the infrared behavior and the infrared behavior of the continuum theory. The corrections substantially improve the convergence of lattice data to a small a limit.