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arXiv · 1809.03399

The number of master integrals as Euler characteristic

Thomas Bitoun·Christian Bogner·René Pascal Klausen·Erik Panzer
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Abstract

We give a brief introduction to a parametric approach for the derivation of shift relations between Feynman integrals and a result on the number of master integrals. The shift relations are obtained from parametric annihilators of the Lee-Pomeransky polynomial $\mathcal{G}$. By identification of Feynman integrals as multi-dimensional Mellin transforms, we show that this approach generates every shift relation. Feynman integrals of a given family form a vector space, whose finite dimension is naturally interpreted as the number of master integrals. This number is an Euler characteristic of the polynomial $\mathcal{G}$.

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Thomas Bitoun, Christian Bogner, René Pascal Klausen, Erik Panzer. 2018-09-10. The number of master integrals as Euler characteristic. https://arxiv.org/abs/1809.03399

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