Weak Matrix Elements without Quark Masses on the Lattice

TL;DR

This paper presents a new parameterization for four-fermion matrix elements on the lattice that eliminates quark mass dependence, reducing systematic uncertainties and simplifying scheme matching, with applications to specific operators.

Contribution

Introduces a quark-mass-independent parameterization of four-fermion matrix elements, improving accuracy and scheme matching in lattice QCD calculations.

Findings

Quadratic dependence of e'/e on m_s is removed.

Results expressed in Renormalization Group Invariant B-parameters.

Matrix elements for specific four-fermion operators computed.

Abstract

We introduce a new parameterization of four-fermion matrix elements which does not involve quark masses and thus allows a reduction of systematic uncertainties in physical amplitudes. As a result the apparent quadratic dependence of e'/e on m_s is removed. To simplify the matching between lattice and continuum renormalization schemes, we express our results in terms of Renormalization Group Invariant B-parameters which are renormalization-scheme and scale independent. As an application of our proposal, matrix elements of DeltaI=3/2 and SUSY DeltaF=2 (F=S,C,B) four-fermion operators have been computed.