Non-perturbative renormalisation of Delta F=2 four-fermion operators in two-flavour QCD

TL;DR

This paper presents a non-perturbative lattice QCD study of four-fermion operators relevant for flavor physics, focusing on their renormalisation and running using Schroedinger Functional methods with two dynamical Wilson quarks.

Contribution

It provides the first non-perturbative renormalisation and RG running results for specific four-fermion operators in two-flavour QCD using Schroedinger Functional techniques.

Findings

Computed non-perturbative renormalisation constants.

Determined renormalisation group running of operators.

Results applicable to phenomenological calculations like B_K and B_B.

Abstract

Using Schroedinger Functional methods, we compute the non-perturbative renormalisation and renormalisation group running of several four-fermion operators, in the framework of lattice simulations with two dynamical Wilson quarks. Two classes of operators have been targeted: (i) those with left-left current structure and four propagating quark fields; (ii) all operators containing two static quarks. In both cases, only the parity-odd contributions have been considered, being the ones that renormalise multiplicatively. Our results, once combined with future simulations of the corresponding lattice hadronic matrix elements, may be used for the computation of phenomenological quantities of interest, such as B_K and B_B (the latter also in the static limit).