Perturbative renormalization factors for genericΔS=2four-quark operators in domain-wall QCD with improved gauge action

Abstract

We calculate one-loop renormalization factors of generic $\ensuremath{\Delta}S=2$ four-quark operators for domain-wall QCD with the plaquette gauge action and the Iwasaki gauge action. The renormalization factors are presented in the modified minimal subtraction $(\overline{\mathrm{MS}})$ scheme with the naive dimensional regularization. As an important application we show how to construct the renormalization factors for the operators contributing to ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ mixing in the supersymmetric models with the use of our results.