The Realization of the Sharpe-Singleton Scenario

TL;DR

This paper investigates how the Sharpe-Singleton first order scenario manifests in lattice QCD by analyzing the eigenvalues of the Wilson Dirac operator, highlighting differences between dynamical and quenched theories.

Contribution

It provides a detailed spectral analysis including leading order corrections, demonstrating the realization of the Sharpe-Singleton scenario and constraints on low energy constants in Wilson chiral perturbation theory.

Findings

Sharpe-Singleton scenario occurs only with dynamical fermions.

Aoki phase can occur in both quenched and unquenched theories.

Constraints on low energy constants from gamma_5-Hermiticity.

Abstract

The microscopic spectral density of the Wilson Dirac operator for two flavor lattice QCD is analyzed. The computation includes the leading order a^2 corrections of the chiral Lagrangian in the microscopic limit. The result is used to demonstrate how the Sharpe-Singleton first order scenario is realized in terms of the eigenvalues of the Wilson Dirac operator. We show that the Sharpe-Singleton scenario only takes place in the theory with dynamical fermions whereas the Aoki phase can be realized in the quenched as well as the unquenched theory. Moreover, we give constraints imposed by gamma_5-Hermiticity on the additional low energy constants of Wilson chiral perturbation theory.