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

Abstract

We discuss the vacuum structure of QCD with two flavors of Wilson fermions. We derive two possible scenarios: (i) If the spectral density $ρ_U(λ,κ)$ of the overlap hamiltonian in a fixed background gauge field is not symmetric in $λ$, Hermiticity is violated and Hermiticity violation effects could influence numerical determinations of the $η$ 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 $i\barψ_uγ_5ψ_u+i\barψ_dγ_5ψ_d$, 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.