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

TL;DR

This work introduces a strategy to achieve $O(a)$ improvement in lattice QCD with Wilson fermions by averaging correlators computed with Wilson terms of opposite sign (Wilson averaging) or opposite quark masses (mass averaging). It then extends these ideas to twisted-mass LQCD (tm-LQCD), showing that many observables, especially at twisting angles $\omega=\pm\pi/2$, become automatically $O(a)$-improved and sometimes require no averaging at all. The authors develop a detailed symmetry and Symanzik-expansion framework, discuss critical-mass behavior, reflection positivity, renormalization, and practical computational considerations, and illustrate a concrete application to computing $F_\pi$ with automatic $O(a)$ improvement. The results offer a cost-effective route to smoother chiral behavior and more reliable continuum extrapolations, with clear guidance for unquenched simulations and for matrix elements relevant to weak interactions. These insights pave the way for robust, systematically improved lattice determinations of hadronic observables and weak matrix elements.

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 $\pm π/2$ 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.