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arXiv · 1603.05204

A Probabilistic Angle on One Loop Scalar Integrals

Kamel Benhaddou
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Abstract

Recasting the $N$-point one loop scalar integral as a probabilistic problem, allows the derivation of integral recurrence relations as well as exact analytical expressions in the most common cases. $ε$ expansions are derived by writing a formula that relates an $N$-point function in decimal dimension to an $N$-point function in integer dimension. As an example, we give relations for the massive 5-point function in dimension $n=4-2ε$, $n=6-2ε$. The reduction of tensor integrals of rank 2 with $N=5$ is achieved showing the method's potential. Hypergeometric functions are not needed but only integration of arcsine function whose analytical continuation is well known.

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Kamel Benhaddou. 2017-03-08. A Probabilistic Angle on One Loop Scalar Integrals. https://doi.org/10.1088/1751-8121%2Faa6779

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