https://doi.org/10.1140/epjc/s10052-019-6533-x
Regular Article - Theoretical Physics
Unveiling regions in multi-scale Feynman integrals using singularities and power geometry
1
Centre for High Energy Physics, Indian Institute of Science, Bangalore, Karnataka, 560012, India
2
Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE, 19716, USA
3
Department of Physics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India
* e-mail: ratansarkar@iisc.ac.in
Received:
16
October
2018
Accepted:
2
January
2019
Published online:
22
January
2019
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.
© The Author(s), 2019
