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arXiv · 1810.06270

Unveiling Regions in multi-scale Feynman Integrals using Singularities and Power Geometry

B. Ananthanarayan·Abhishek Pal·S. Ramanan·Ratan Sarkar
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Abstract

We introduce a novel approach for solving the problem of identifying regions in the framework of Method of Regions by considering singularities and the associated Landau equations given a multi-scale Feynman diagram. These equations are then analyzed by an expansion in a small threshold parameter via the Power Geometry technique. This effectively leads to the analysis of Newton Polytopes which are evaluated using a Mathematica based convex hull program. Furthermore, the elements of the Gröbner Basis of the Landau Equations give a family of transformations, which when applied, reveal regions like potential and Glauber. Several one-loop and two-loop examples are studied and benchmarked using our algorithm which we call ASPIRE.

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B. Ananthanarayan, Abhishek Pal, S. Ramanan, Ratan Sarkar. 2019-01-14. Unveiling Regions in multi-scale Feynman Integrals using Singularities and Power Geometry. https://doi.org/10.1140/epjc%2Fs10052-019-6533-x

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