ar X iv : h ep - l at / 9 70 90 96 v 1 2 3 Se p 19 97 1 Further one - loop results in O ( a ) improved lattice QCD ∗

Recent work by the ALPHA collaboration has focused on non-perturbative renormalization and on-shell O(a) improvement of lattice QCD with Wilson quarks [1–7]. Various improvement coefficients could be determined as functions of the bare coupling g0, including the coefficient of the Sheikholeslami-Wohlert term in the lattice action [8]. While a non-perturbative determination of the improvement coefficients is clearly preferable perturbative estimates are nevertheless useful. First of all, any non-perturbative determination should establish contact with perturbation theory at sufficiently small values of the bare coupling constant. This provides a non-trivial check for the chosen strategy and criteria to assess the quality of a given improvement condition. Secondly, for those coefficients which account for lattice effects due to non-zero quark masses, perturbative estimates may indeed be satisfactory provided the quark masses are small when measured in lattice units. In this contribution we present our one-loop results for the on-shell O(a) improved isovector composite operators which are bilinear in the quark fields. The computational strategy and most of the results have already been published in refs. [9,10]. In addition we here also include the results for the improved isovector tensor and scalar densities.