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 ${\rho }_U(\lambda ,\kappa )$ 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.

Comments: 9 pages, 6 figures, to be published in Physical Review D1