On the chiral limit in lattice gauge theories with Wilson fermions

The chiral limit κ ≃ κc (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 $$\tilde m_\pi$$ for the calculation of the pseudoscalar mass mπ is proposed which does not suffer from ’divergent’ contributions at κ ≃ κc (β)We conclude that the main contribution to the pion mass comes from larger modes, and ’exceptional’ eigenvalues play no physical role. The behaviour of the subtracted chiral condensate $$\left\langle {\bar \psi \psi } \right\rangle _{subt}$$ near κc(β) is determined. We observe a comparatively large value of $$\left\langle {\bar \psi \psi } \right\rangle _{subt} \cdot Z_P^{ - 1}$$, which could be interpreted as a possible effect of the quenched approximation.