Perturbative calculations for the HISQ action: the gluon action at $O(N_f\alpha_sa^2)$

TL;DR

This paper introduces a new algorithm for deriving lattice Feynman rules, enabling perturbative calculations involving complex actions like HISQ, and compares fermionic contributions to the gluonic action with previous methods.

Contribution

A novel algorithm for deriving Feynman rules for complex lattice actions, allowing perturbative analysis of HISQ fermions' effects on gluonic actions.

Findings

Fermionic contributions to the gluonic action are larger for HISQ than for asqtad.

The algorithm successfully handles complex actions like HISQ.

Perturbative corrections are computed for the Lüscher-Weisz gauge action.

Abstract

We present a new (and general) algorithm for deriving lattice Feynman rules which is capable of handling actions as complex as the Highly Improved Staggered Quark (HISQ) action. This enables us to perform a perturbative calculation of the influence of dynamical HISQ fermions on the perturbative improvement of the gluonic action in the same way as we have previously done for asqtad fermions. We find the fermionic contributions to the radiative corrections in the L\"uscher-Weisz gauge action to be somewhat larger for HISQ fermions than for asqtad.