Non-perturbative renormalization and running of Delta F=2 four-fermion operators in the SF scheme

TL;DR

This paper reports a non-perturbative study of the scale-dependent renormalization of four-fermion operators relevant for B-parameter calculations, using Schrödinger Functional schemes with improved Wilson fermions.

Contribution

It provides the first non-perturbative determination of the renormalization group running and matching matrices for Delta F=2 operators in the SF scheme with Wilson fermions.

Findings

Computed the non-perturbative renormalization group running matrix.

Established the relation between RGI operators and SF-renormalized operators.

Determined the non-perturbative matching between lattice and SF schemes.

Abstract

We present preliminary results of a non-perturbative study of the scale-dependent renormalization constants of a complete basis of Delta F=2 parity-odd four-fermion operators that enter the computation of hadronic B-parameters within the Standard Model (SM) and beyond. We consider non-perturbatively O(a) improved Wilson fermions and our gauge configurations contain two flavors of massless sea quarks. The mixing pattern of these operators is the same as for a regularization that preserves chiral symmetry, in particular there is a "physical" mixing between some of the operators. The renormalization group running matrix is computed in the continuum limit for a family of Schrodinger Functional (SF) schemes through finite volume recursive techniques. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale, together with the non-perturbative matching matrix between the lattice regularized theory and the various SF schemes.