Non-perturbative running and renormalization of kaon four-quark operators with nf=2+1 domain-wall fermions

Abstract

We compute the renormalization factors of four-quark operators needed for the study of $K\to \pi \pi$ decay in the $\Delta I=3/2$ channel. We evaluate the Z-factors at a low energy scale (${\mu }_0=1.145\text{GeV}$) using four different non-exceptional RI-SMOM schemes on a large, coarse lattice ($a\sim 0.14\text{fm}$) on which the bare matrix elements are also computed. Then we compute the universal, non-perturbative, scale evolution matrix of these renormalization factors between ${\mu }_0$ and $3\text{GeV}$. We give the numerical results for the different steps of the computation in two different non-exceptional lattice schemes, and the connection to $\text{msbar}$ at $3\text{GeV}$ is made using one-loop perturbation theory.

Comments: 11 pages, XXIX International Symposium on Lattice Field Theory, July 10 -16 2011, Squaw Valley, Lake Tahoe, California