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Algebraic evaluation of rational polynomials in one-loop amplitudes

One-loop amplitudes are to a large extent determined by their unitarity cuts in four dimensions. We show that the remaining rational terms can be obtained from the ultraviolet behaviour of the amplitude, and determine universal form factors for these rational parts by applying reduction techniques to the Feynman diagrammatic representation of the amplitude. The method is valid for massless and massive internal particles. We illustrate this method by evaluating the rational terms of the one-loop amplitudes for gg --> H, the 4-photon and 4-gluon amplitude, the amplitude for 2 photons plus 3 gluons and the 6-photon amplitude.