Chiral perturbation theory at O(a2) for lattice QCD

We construct chiral effective Lagrangian for two lattice theories: one with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson valence fermions. For each of these theories we construct the Symanzik action through O(a2). The chiral Lagrangian is then derived, including terms of O(a2), which have not been calculated before. We find that there are only few new terms at this order. Corrections to existing coefficients in the continuum chiral Lagrangian are proportional to a2 and appear in the Lagrangian at O(a2p2) or higher. Similarly, O(4) symmetry-breaking terms enter the Symanzik action at O(a2), but contribute to the chiral Lagrangian at O(a2p4) or higher. We calculate the light meson masses in chiral perturbation theory for both lattice theories. At next-to-leading order, we find that there are no O(a2) corrections to the valence-valence meson mass in the mixed theory due to the enhanced chiral symmetry of the valence sector