Chirally improving Wilson fermions 1. O(a) improvement

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 +/-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.