Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD

TL;DR

This paper develops non-perturbative renormalization schemes for four-quark operators in quenched lattice QCD, enabling precise calculation of their scale dependence and renormalization constants.

Contribution

It introduces Schroedinger Functional schemes for four-quark operators and computes their non-perturbative renormalization group running in quenched lattice QCD.

Findings

Controlled continuum limit extrapolations using Wilson and Clover actions

Non-perturbative determination of renormalization constants at various scales

Calculation of the ratio of renormalization group invariant to scale-dependent operators

Abstract

We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\Delta F = 1$ and $\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.