Non-perturbative scale evolution of four-fermion operators in two-flavour QCD

TL;DR

This paper uses finite-size recursion and Schrödinger functional methods to study how four-fermion operators evolve with scale in two-flavor QCD, focusing on the B_K parameter relevant for weak interactions.

Contribution

It introduces a non-perturbative approach to determine the scale evolution of four-fermion operators in two-flavor QCD using improved Wilson fermions.

Findings

Preliminary results for the B_K parameter in tmQCD.

Demonstrates the effectiveness of Schrödinger functional techniques.

Provides data on the renormalization group running of four-fermion operators.

Abstract

We apply finite-size recursion techniques based on the Schrodinger functional formalism to determine the renormalization group running of four-fermion operators which appear in the Delta S=2 effective weak Hamiltonian of the Standard Model. Our calculations are done using O(a) improved Wilson fermions with N_f=2 dynamical flavours. Preliminary results are presented for the four-fermion operator which determines the B_K parameter in tmQCD.