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

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.

11 pages, 16 figures, references are updated

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• Kaon mixing matrix elements from beyond-the-Standard-Model operators in staggered chiral perturbation theory
• Non-perturbative Renormalization for Improved Staggered Bilinears
• Perturbative renormalization functions of local operators for staggered fermions with stout improvement
• Beyond the Standard Model corrections to $K^0-{\bar{K}}^0$ mixing
• Beyond the Standard Model B-parameters with improved staggered fermions in $N_f=2+1$ QCD
• Toolkit for staggered $\Delta S=2$ matrix elements
• Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators
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