Domain wall fermions and fermion loop observables

Abstract

Physical observables which involve fermion loops, such as the chiral condensate,〈ψ¯ψ〉, or matrix elements of the four-fermi operators which_ enter weak decays, require accurate off shell fermion behaviour. We investigate such off-shell contributions to〈ψ¯ψ〉 for domain wall fermions (DWF). After removing the unphysical, short-distance contributions to〈ψ¯ψ〉 by Pauli-Villars subtraction, we compare the mass dependence of the resulting physical quantity, evaluated with both the Wilson and DBW2 gauge actions, since these two actions are known to give quite different 5-dimensional DWF behaviour. We also examine the dependence of the amplitudes entering〈ψ¯ψ〉 on the fifth dimension s, to gain insight into potentially different s-dependence for low- and high-energy modes. Finally, we summarise the present RBC results for conventionally normalised〈ψ¯ψ〉 for the various actions studied.