Nonperturbative renormalization of domain wall fermions: Quark bilinears

We find the renormalization coefficients of the quark field and the flavor nonsinglet fermion bilinear operators for the domain wall fermion action, in the regularization independent (RI) renormalization scheme. Our results are from a quenched simulation, on a ${16}^3\times 32$ lattice, with $\beta =6.0\mathrm{}$ and an extent in the fifth dimension of $16.$ We also discuss the expected effects of the residual chiral symmetry breaking inherent in a domain wall fermion simulation with a finite fifth dimension, and study the evidence for both explicit and spontaneous chiral symmetry breaking effects in our numerical results. We find that the relations between different renormalization factors predicted by chiral symmetry are, to a good approximation, satisfied by our results and that systematic effects due to the (low energy) spontaneous chiral symmetry breaking and zero modes can be controlled. Our results are compared against the perturbative predictions for both their absolute value and renormalization scale dependence.