Chirally improving Wilson fermions - I. O(a) improvement

TL;DR

This paper proposes a method to improve chiral symmetry and continuum limit approach in lattice QCD with Wilson fermions by averaging correlators from theories with opposite Wilson terms, utilizing twisted-mass QCD for practical computation.

Contribution

It introduces a novel averaging technique of correlators from opposite Wilson term regularizations and suggests using twisted-mass QCD to address spectral issues, achieving O(a) improvement with minimal extra computation.

Findings

Averaging correlators improves chiral behavior and continuum limit.

Twisted-mass QCD at specific angles enables O(a) improvement without averaging.

Minimal additional computational cost compared to standard Wilson fermions.

Abstract

We show that it is possible to improve the chiral behaviour and the approach to the continuum limit of correlation functions in lattice QCD with Wilson fermions by taking arithmetic averages of correlators computed in theories regularized with Wilson terms of opposite sign. Improved hadronic masses and matrix elements can be obtained by similarly averaging the corresponding physical quantities separately computed within the two regularizations. To deal with the problems related to the spectrum of the Wilson--Dirac operator, which are particularly worrisome when Wilson and mass terms are such as to give contributions of opposite sign to the real part of the eigenvalues, we propose to use twisted-mass lattice QCD for the actual computation of the quantities taking part to the averages. The choice $\pm \pi/2$ for the twisting angle is particularly interesting, as O($a$) improved estimates of physical quantities can be obtained even without averaging data from lattice formulations with opposite Wilson terms. In all cases little or no extra computing power is necessary, compared to simulations with standard Wilson fermions or twisted-mass lattice QCD.