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.