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

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

2011-12-02

arxiv.org/abs/1112.0537v1

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

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 ($\mu_0=1.145 \GeV$) using four different non-exceptional RI-SMOM schemes on a large, coarse lattice ($a\sim 0.14\fm$) 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 $3\GeV$. We give the numerical results for the different steps of the computation in two different non-exceptional lattice schemes, and the connection to $\msbar$ at $3\GeV$ is made using one-loop perturbation theory.

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