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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 gaugefield is not symmetric in $\lambda$, Hermiticity is violated and Hermiticityviolation effects could influence numerical determinations of the $\eta$ mesonmass if we are not near enough to the continuum limit, where Hermiticity shouldbe recovered; (ii) otherwise we argue that, under certain assumptions, newphases appear beside the Aoki phase, which can be characterized by anonvanishing vacuum expectation value of$i\bar\psi_u\gamma_5\psi_u+i\bar\psi_d\gamma_5\psi_d$, and with vacuum statesthat cannot be connected with the Aoki vacua by parity-flavor symmetrytransformations. Quenched numerical simulations suggest that the secondscenario is more likely realized.

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