Non-perturbative scale evolution of four-fermion operators

TL;DR

This paper uses the Schroedinger Functional formalism with Wilson fermions to non-perturbatively study the scale evolution of four-fermion operators relevant to the Standard Model's weak interactions.

Contribution

It introduces a non-perturbative method to determine the renormalisation group running of four-fermion operators using the SF formalism with Wilson fermions.

Findings

Preliminary results for the operator $O_{VA}$ are presented.

The approach provides a framework for precise non-perturbative renormalisation.

Results contribute to understanding weak interaction processes in the Standard Model.

Abstract

We apply the Schroedinger Functional (SF) formalism to determine the renormalisation group running of four-fermion operators which appear in the effective weak Hamiltonian of the Standard Model. Our calculations are done using Wilson fermions and the parity-odd components of the operators. Preliminary results are presented for the operator $O_{VA}=(\bar s \gamma_\mu d)(\bar s \gamma_\mu \gamma_5 d)$.