On the chiral limit in lattice gauge theories with Wilson fermions

TL;DR

This paper investigates the chiral limit in lattice gauge theories with Wilson fermions, introducing a new estimator for the pion mass that avoids divergence issues and analyzing the behavior of the chiral condensate near the critical point.

Contribution

A novel estimator for the pseudoscalar mass is proposed, which remains stable near the critical hopping parameter, and the role of exceptional eigenvalues is shown to be negligible.

Findings

The new estimator $\mpr_{\pi}$ effectively avoids divergence at $\kappa_c$.

Exceptional eigenvalues do not significantly affect the pion mass.

The subtracted chiral condensate remains large near $\kappa_c$, possibly due to quenched approximation effects.

Abstract

The chiral limit $~\kappa \simeq \kappa_c(\beta)~$ in lattice gauge theories with Wilson fermions and problems related to near--to--zero ('exceptional') eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $~\mpr_{\pi}~$ for the calculation of the pseudoscalar mass $~m_{\pi}~$ is proposed which does not suffer from 'divergent' contributions at $\kappa \simeq \kappa_c(\beta)$. We conclude that the main contribution to the pion mass comes from larger modes, and 'exceptional' eigenvalues play {\it no} physical role. The behaviour of the subtracted chiral condensate $~\langle \psb \psi \rangle_{subt}~$ near $~\kappa_c(\beta)~$ is determined. We observe a comparatively large value of $~\langle \psb \psi \rangle_{subt} \cdot Z_P^{-1}~$, which could be interpreted as a possible effect of the quenched approximation.