O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory

TL;DR

This paper analytically computes the one-loop order O(a) improvement coefficients for static axial and vector currents in lattice QCD using hypercubic actions, enhancing precision in static observable calculations.

Contribution

It provides the first analytical derivation of improvement coefficients for static currents with hypercubic actions at one-loop order in perturbation theory.

Findings

Improvement coefficients are explicitly calculated from on-shell correlators.

The static self-energy minimum is localized and closely matches non-perturbative results.

The hypercubic action improves the signal-to-noise ratio in static observable measurements.

Abstract

We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schroedinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.