Four quark operators in maximally twisted Wilson LQCD

TL;DR

This paper presents a lattice QCD computational scheme using maximally twisted Wilson fermions that enables accurate calculation of CP-conserving matrix elements without operator mixing, ensuring automatic O(a) improvement and positive determinants.

Contribution

It introduces a novel lattice framework leveraging maximally twisted Wilson fermions to improve the calculation of weak Hamiltonian matrix elements in QCD.

Findings

Framework guarantees automatic O(a) improvement.

Ensures positive determinants for non-degenerate quark pairs.

Allows evaluation of matrix elements without mixing with wrong-chirality operators.

Abstract

We discuss how the peculiar properties of maximally twisted Wilson fermions can be exploited to set up a consistent LQCD computational scheme in which the CP-conserving matrix elements of the $\Delta S =1,2$ effective weak Hamiltonian can be evaluated without mixing with wrong-chirality and/or -parity operators. The proposed lattice framework guarantees automatic O($a$) improvement and positive determinant also for pairs of non-degenerate quarks.