Two-loop RI/SMOM-$\overline{\text{MS}}$ matching factors for the renormalization of bi-local operators contributing to ${\epsilon }_K$

Abstract

The measure of indirect CP violation in the neutral kaon system, ${\epsilon }_K$, is an important precision test of the Standard Model. A first-principles Standard Model prediction of ${\epsilon }_K$ requires evaluating the long-distance contribution in which the $\Delta S=2$ process proceeds via two $\Delta S=1$ operators. The non-perturbative nature of QCD in the relevant energy regimes requires a lattice QCD simulation. In this paper we present the two-loop, $O({\alpha }_s)$ RI/SMOM - $\overline{\text{MS}}$ matching factors required to renormalize a lattice QCD calculation of the long-distance contribution to ${\epsilon }_K$.

arXiv comment41 pages, 6 figures, 13 tables