Abstract
The ASPIRE program, which is based on the Landau singularities and the method of Power geometry to unveil the regions required for the evaluation of a given Feynman diagram asymptotically in a given limit, also allows for the evaluation of scaling coming from the top facets. In this work, we relate the scaling having equal components of the top facets of the Newton polytope to the maximal cut of given Feynman integrals. We have therefore connected two independent approaches to the analysis of Feynman diagrams.
Highlights
The present work is a sequel to Ref. [1] which presents a novel approach to the Method of Regions [2,3,4,5,6,7] (MoR) based on the analysis of Landau equations associated with given Feynman diagrams
We have considered given multi-scale Feynman diagrams in a given limit and obtained the scalings required for the asymptotic expansion of the diagram
The exploration here, which is based on Landau equations, allows us going beyond the bottom facet results
Summary
The present work is a sequel to Ref. [1] which presents a novel approach to the Method of Regions [2,3,4,5,6,7] (MoR) based on the analysis of Landau equations associated with given Feynman diagrams. The set of Landau equations [18,19] for a given Feynman integral while combined with Bruno’s theorem [15,16,17] in Power Geometry implies that the top facet scalings with equal components correspond to the case of maximal cut of the given integral. We explore the correspondence between the parametric integrals constructed based on the scalings having equal components of the top facets and the maximal cut for given Feynman diagrams. In a recent work [29], maximal cuts of Feynman diagrams have been analyzed based on multi-dimensional residues in a geometric way. 3, we derive the one loop generalization of correlation of the maximal cut to the top facet integral with equal components using the large mass expansion limit. In Appendix B we give the Feynman parametric form of the cut integrals in the one loop case
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