Order alpha 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 a t 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 thos e used in standard hadron mass calculations. A crucial feature of the calcu lation is the use of nondegenerate quarks. We also obtain results for the c onstants needed for off-shell O(a) improvement of bilinears, and for the sc ale- 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 use d previously. Wherever possible, we compare our results with those of the A LPHA Collaboration (who use the Schrodinger functional and with one-loop ta dpole-improved perturbation theory.