Chiral Symmetry Breaking for Domain Wall Fermions in Quenched Lattice QCD

The domain wall fermion formulation exhibits full chiral symmetry for finite lattice spacing except for the effects of mixing between the domain walls. Close to the continuum limit these symmetry breaking effects should be described by a single residual mass. We determine this mass from the conservation law obeyed by the conserved axial current in quenched simulations with β = 5.7 and 6.0 and domain wall separations varying between 12 and 48 on 8× 32 and 16× 32 lattices. Using the resulting values for the residual mass we perform two complete and independent calculations of the pion decay constant. Good agreement is found between these two methods and with experiment.