O(a**2) cutoff effects in Wilson fermion simulations

We show that the size of the O(a^2) flavour violating cutoff artifacts that have been found to affect the value of the neutral pion mass in simulations with maximally twisted Wilson fermions is controlled by a continuum QCD quantity that is fairly large and is determined by the dynamical mechanism of spontaneous chiral symmetry breaking. One can argue that the neutral pion mass is the only physical quantity blurred by such cutoff effects. O(a^2) corrections of this kind are also present in standard Wilson fermion simulations, but they can either affect the determination of the pion mass or be shifted from the latter to other observables, depending on the way the critical mass is evaluated.