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arxiv: hep-ph/9306240 · v2 · submitted 1993-06-07 · ✦ hep-ph

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Dimensionally Regulated Pentagon Integrals

Z. Bern , L. Dixon , D. A. Kosower
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classification ✦ hep-ph
keywords integralspentagonepsilondimensionally-regulatedresultalongappearassociated
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We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2 epsilon dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O(epsilon) corrections, a result which is the dimensionally-regulated version of a D=4 result of Melrose, and of van Neerven and Vermaseren. We obtain and solve differential equations for various dimensionally-regulated box integrals with massless internal lines, which appear in one-loop n-point calculations in QCD. We give a procedure for constructing the tensor pentagon integrals needed in gauge theory, again through O(epsilon^0).

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