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

TL;DR

This paper explores the complex vacuum structure of two-flavor Wilson fermion QCD, proposing two scenarios with implications for Hermiticity and phase structure, supported by numerical simulations favoring a new phase beyond the Aoki phase.

Contribution

It introduces two possible vacuum scenarios in two-flavor Wilson fermion QCD, highlighting the role of spectral density asymmetry and proposing new phases with distinct symmetry properties.

Findings

Spectral density asymmetry can violate Hermiticity affecting meson mass calculations

Numerical simulations favor the existence of new phases beyond the Aoki phase

New vacua characterized by nonzero pseudoscalar condensates are proposed

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.