QCD CHIRAL LAGRANGIAN ON THE LATTICE, STRONG-COUPLING EXPANSION, AND WARD IDENTITIES WITH WILSON FERMIONS

We discuss a general strategy to compute the coefficients of the QCD c hiral Lagrangian using lattice QCD with Wilson fermions. This procedur e requires the introduction of a lattice chiral Lagrangian as an inter mediate step in the calculation. The QCD chiral Lagrangian is then obt ained by expanding the lattice effective theory in increasing powers o f the lattice spacing and the external momenta. In order to investigat e the general structure of the lattice effective Lagrangian, we perfor m an analytical calculation at the leading order of the strong-couplin g and large-N expansion. We find that the explicit chiral symmetry bre aking, introduced on the lattice by the Wilson term, is reproduced in the effective theory by a set of additional terms, which do not have d irect correspondence in the continuum chiral Lagrangian. We argue that these terms can be conveniently reabsorbed by a suitable renormalizat ion procedure. This is shown explicitly at the leading order of the st rong-coupling and large-N expansion. In fact, we find that at this ord er, as is known to be the case in the opposite weak-coupling limit, th e vector and axial Ward identities of the continuum theory are reprodu ced on the lattice provided that the bare quark mass and the lattice o perators are properly renormalized.