On the chiral limit in lattice gauge theories with Wilson fermions

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 ${\text{mpr}}_{\pi }$ 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 $⟨\text{psb}\psi {⟩}_{subt}$ near ${\kappa }_c(\beta )$ is determined. We observe a comparatively large value of $⟨\text{psb}\psi {⟩}_{subt}\cdot Z_P^{-1}$, which could be interpreted as a possible effect of the quenched approximation.

Comments: EXTENDED version. To be published in Z.f.Physik C