A recursive reduction of tensor Feynman integrals

We perform a new, recursive reduction of one-loop n-point rank R   tensor Feynman integrals [in short: (n,R)(n,R)-integrals] for n⩽6n⩽6 with R⩽nR⩽n by representing (n,R)(n,R)-integrals in terms of (n,R−1)(n,R−1)- and (n−1,R−1)(n−1,R−1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, a recursive reduction for the tensors is found. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories.