On the chiral limit in lattice gauge theories with Wilson fermions

Abstract

The chiral limit $~κ\simeq κ_c(β)~$ 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 $~\mpr_π~$ for the calculation of the pseudoscalar mass $~m_π~$ is proposed which does not suffer from 'divergent' contributions at $κ\simeq κ_c(β)$. 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 $~\langle \psb ψ\rangle_{subt}~$ near $~κ_c(β)~$ is determined. We observe a comparatively large value of $~\langle \psb ψ\rangle_{subt} \cdot Z_P^{-1}~$, which could be interpreted as a possible effect of the quenched approximation.