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Application of the negative-dimension approach to massless scalar box integrals

C. Anastasiou·E. W. N. Glover·C. Oleari
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Abstract

We study massless one-loop box integrals by treating the number of space-time dimensions D as a negative integer. We consider integrals with up to three kinematic scales (s, t and either zero or one off-shell legs) and with arbitrary powers of propagators. For box integrals with q kinematic scales (where q=2 or 3) we immediately obtain a representation of the graph in terms of a finite sum of generalised hypergeometric functions with q-1 variables, valid for general D. Because the power each propagator is raised to is treated as a parameter, these general expressions are useful in evaluating certain types of two-loop box integrals which are one-loop insertions to one-loop box graphs. We present general expressions for this particular class of two-loop graphs with one off-shell leg, and give explicit representations in terms of polylogarithms in the on-shell case.

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C. Anastasiou, E. W. N. Glover, C. Oleari. 1999-07-28. Application of the negative-dimension approach to massless scalar box integrals. https://doi.org/10.1016/s0550-3213(99)00636-7

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