ONE-LOOP TENSOR INTEGRALS IN DIMENSIONAL REGULARIZATION

We show how to evaluate tensor one-loop integrals in momentum space av oiding the usual plague of Gram determinants. We do this by constructi ng combinations of n- and (n - 1)-point scalar integrals that are fini te in the limit of vanishing Gram determinant These non-trivial combin ations of dilogarithms, logarithms and constants are systematically ob tained by either differentiating with respect to the external paramete rs - essentially yielding scalar integrals with Feynman parameters in the numerator - or by developing the scalar integral in D = 6 - 2 epsi lon or higher dimensions. An additional advantage is that other spurio us kinematic singularities are also controlled. As an explicit example , we develop the tensor integrals and associated scalar integral combi nations for processes where the internal particles are massless and wh ere up to five (four massless and one massive) external particles are involved. For more general processes, we present the equations needed for deriving the relevant combinations of scalar integrals. (C) 1997 E lsevier Science B.V.