Penguin diagrams for improved staggered fermions

TL;DR

This paper computes one-loop penguin diagrams for improved staggered fermion operators with various fat links, showing that certain mixing coefficients are unchanged and off-diagonal mixing vanishes for specific fat links, aiding in precise lattice QCD calculations.

Contribution

It provides the first detailed one-loop calculation of penguin diagrams for improved staggered fermions with various fat links, clarifying mixing properties and aiding in accurate operator matching.

Findings

Diagonal mixing coefficients are identical between unimproved and improved operators.

Off-diagonal mixing vanishes for Fat7, $ar{ m Fat7}$, and HYP (II) fat links.

Complete one-loop matching includes all ${ m O}(g^2)$ corrections.

Abstract

We calculate, at the one loop level, penguin diagrams for improved staggered fermion operators constructed using various fat links. The main result is that diagonal mixing coefficients with penguin operators are identical between the unimproved operators and the improved operators using such fat links as Fat7, Fat7+Lepage, $\bar{\rm Fat7}$, HYP (I) and HYP (II). In addition, it turns out that the off-diagonal mixing vanishes for those constructed using fat links of Fat7, $\bar{\rm Fat7}$ and HYP (II). This is a consequence of the the fact that the improvement by various fat links changes only the mixing with higher dimension operators and off-diagonal operators. The results of this paper, combined with those for current-current diagrams, provide the complete matching at the one loop level with all corrections of ${\cal O}(g^2)$ included.