Predicting the Aoki phase using the chiral Lagrangian

This work is concerned with the phase diagram of Wilson fermions in the mas s and coupling constant plane for two-flavor (unquenched) QCD. We show that as the continuum limit is approached, one can study the lattice theory usi ng the continuum chiral Lagrangian, supplemented by additional terms propor tional to powers of the lattice spacing. We find two possible phase structu res at non-zero lattice spacing: (1) There is an Aoki phase of spontaneousl y broken flavor and parity, with two massless Goldstone-pions, and a width Delta m(0) similar to a(3). (2) There is no spontaneous symmetry breaking, and all three pions have equal mass of order a. Present numerical simulatio ns suggest that the former option is realized.