A complete algebraic reduction of one-loop tensor Feynman integrals

Guided by the need to eliminate inverse Gram determinants ()5 from tensorial 5-point functions and sub-Gram determinants ()4 from tensorial 4-point functions, we set up a new and very efficient approach for the tensor reduction of Feynman integrals. We eliminate all Gram determinants for one-loop 5-point integrals up to tensors of rank R=5 by reducing their tensor coefficients to higherdimensional 4-point tensor coefficients. These in turn are reduced to expressions which are free of inverse powers of ()4, but depend on higher-dimensional integrals I4(d) with d≤2R. Their expression in terms of scalar integrals defined in the generic dimension, I4; I3; I2; I1, however, introduces coefficients [1=()4]R for tensors of rank R. For small or vanishing ()4, an efficient expansion is found so that a stable numerical evaluation of massive and massless Feynman integrals at arbitrary values of the Gram determinants is made possible. Finally, some relations are mentioned which may be useful for analytic simplifications of the original Feynman diagrams. (orig.)