Order α improved renormalization constants -: art. no. 074505

We present nonperturbative results for the constants needed for an-shell O(a) improvement of bilinear operators composed of Wilson fermions. We work at beta =6.0 and 6.2 in the quenched approximation. The calculation is done by imposing axial and vector Ward identities on correlators similar to those used in standard hadron mass calculations. A crucial feature of the calculation is the use of nondegenerate quarks. We also obtain results for the constants needed for off-shell O(a) improvement of bilinears, and for the scale- and scheme-independent renormalization constants, Z(A), Z(v), and Z(S)/Z(P). Several of the constants are determined using a variety of different Ward identities, and we compare their relative efficacies. In this way, we find a method for calculating c(V) that gives smaller errors than that used previously. Wherever possible, we compare our results with those of the ALPHA Collaboration (who use the Schrodinger functional and with one-loop tadpole-improved perturbation theory.