Chirally improving Wilson fermions I. O(a) improvement

We show that it is possible to improve the chiral behaviour and the approachto the continuum limit of correlation functions in lattice QCD with Wilsonfermions by taking arithmetic averages of correlators computed in theoriesregularized with Wilson terms of opposite sign. Improved hadronic masses andmatrix elements can be obtained by similarly averaging the correspondingphysical quantities separately computed within the two regularizations. To dealwith the problems related to the spectrum of the Wilson--Dirac operator, whichare particularly worrisome when Wilson and mass terms are such as to givecontributions of opposite sign to the real part of the eigenvalues, we proposeto use twisted-mass lattice QCD for the actual computation of the quantitiestaking part to the averages. The choice $\pm \pi/2$ for the twisting angle isparticularly interesting, as O($a$) improved estimates of physical quantitiescan be obtained even without averaging data from lattice formulations withopposite Wilson terms. In all cases little or no extra computing power isnecessary, compared to simulations with standard Wilson fermions ortwisted-mass lattice QCD.Comment: 71 pages, Latex, Keywords: Lattice, Improvement, Chirality. Version v2: mistake corrected in transformation properties under \omega -> -\omega, sect. 5.3.1 (see also sect. 6.1). Minor corrections in App. D and argument clarified in App. F. Version v3: minor modifications in sect. 2 (pag. 8-10: on the odd r-parity of M_crit(r)), in sect. 3.1.3 and 5.4.1 (few sentences about cutoff effects at small quark mass) and in sect. 3.2 (details of discussion below eq. 3.17); updated/added some reference