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arXiv · hep-ph/9306240

Dimensionally Regulated Pentagon Integrals

Z. Bern·L. Dixon·D. A. Kosower
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Abstract

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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Z. Bern, L. Dixon, D. A. Kosower. 1998-05-18. Dimensionally Regulated Pentagon Integrals. https://doi.org/10.1016/0550-3213(94)90398-0

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