One-loop matching of improved four-fermion staggered operators with an improved gluon action

TL;DR

This paper computes one-loop matching factors for four-fermion operators with HYP-smeared staggered fermions using an improved gluon action, aiding precise lattice QCD calculations of B-meson parameters.

Contribution

It extends previous calculations by incorporating the tree-level improved Symanzik gauge action into the one-loop matching of four-fermion operators with HYP smearing.

Findings

Impact of improved gluon action on matching factors is minimal.

One-loop coefficients are of order alpha_s, indicating good perturbative convergence.

Results support accurate lattice QCD calculations of B_K and related matrix elements.

Abstract

We present results for one-loop matching factors of four-fermion operators composed of HYP-smeared staggered fermions. We generalize previous calculations by using the tree-level improved Symanzik gauge action. These results are needed for our companion numerical calculation of $B_K$ and related matrix elements. We find that the impact on one-loop matching factors of using the improved gluon action is much smaller than that from the use of either HYP smearing or mean-field improvement. The one-loop coefficients for mean-field improved, HYP-smeared operators with the Symanzik gauge action have a maximum magnitude of $O(1)\times \alpha_s$, indicating that perturbation theory is reasonably convergent.