QCD with two flavors of Wilson fermions: The QCD vacuum, the Aoki vacuum and other vacua

We discuss the vacuum structure of QCD with two flavors of Wilson fermions. We derive two possible scenarios: (i) If the spectral density $\rho_U(\lambda,\kappa)$ of the overlap hamiltonian in a fixed background gauge field is not symmetric in $\lambda$, Hermiticity is violated and Hermiticity violation effects could influence numerical determinations of the $\eta$ meson mass if we are not near enough to the continuum limit, where Hermiticity should be recovered; (ii) otherwise we argue that, under certain assumptions, new phases appear beside the Aoki phase, which can be characterized by a nonvanishing vacuum expectation value of $i\bar\psi_u\gamma_5\psi_u+i\bar\psi_d\gamma_5\psi_d$, and with vacuum states that cannot be connected with the Aoki vacua by parity-flavor symmetry transformations. Quenched numerical simulations suggest that the second scenario is more likely realized.