Improved Landau Gauge Fixing and Discretisation Errors ∗

Gauge fixing in lattice gauge theory simulations is crucial for many calculations e.g. the study of gauge dependent quantities such as the gluon propagator [1]. However, the standard lattice Landau gauge condition [2] is the same as the continuum condition, ∑ μ ∂μAμ = 0, only to leading order in the lattice spacing, a. The focus of this talk is to use mean-fieldimproved perturbation theory [3] to compare different lattice definitions of the Landau gauge, and quantify the sizes of the discretisation errors. In particular, we derive a new O(a2) improved Landau-gauge-fixing functional, and a method of generalising this to O(an).