Chirally improving Wilson fermions II. Four-quark operators

TL;DR

This paper explores how twisted lattice QCD at maximal twist can be used to accurately compute four-quark operator matrix elements, overcoming chiral symmetry breaking issues and ensuring positive determinants and O(a) improvement.

Contribution

It introduces a computational scheme leveraging twisted lattice QCD to handle four-quark operators with improved accuracy despite chiral symmetry breaking.

Findings

Bypass of wrong chirality and parity mixings in matrix element calculations

Achieves positive determinant for non-degenerate quarks

Provides full O(a) improvement without additional action or operator modifications

Abstract

In this paper we discuss how the peculiar properties of twisted lattice QCD at maximal twist can be employed to set up a consistent computational scheme in which, despite the explicit breaking of chiral symmetry induced by the presence of the Wilson and mass terms in the action, it is possible to completely bypass the problem of wrong chirality and parity mixings in the computation of the CP-conserving matrix elements of the $\Delta S=1,2$ effective weak Hamiltonian and at the same time have a positive determinant for non-degenerate quarks as well as full O($a$) improvement in on-shell quantities with no need of improving the lattice action and the operators.