Identifying regions in wide-angle scattering via graph-theoretical approaches

Abstract

The method of regions, which provides a systematic approach for computing Feynman integrals involving multiple kinematic scales, proposes that a Feynman integral can be approximated and even reproduced by summing over integrals expanded in certain regions. A modern perspective of the method of regions considers any given Feynman integral as a specific Newton polytope, defined as the convex hull of the points associated with Symanzik polynomials. The regions then correspond one-to-one with the lower facets of this polytope. As Symanzik polynomials correspond to the spanning trees and spanning 2-trees of the Feynman graph, a graph-theoretical study of these polynomials may allow us to identify the complete set of regions for a given expansion. In this work, our primary focus is on three specific expansions: the on-shell expansion of generic wide-angle scattering, the soft expansion of generic wide-angle scattering, and the mass expansion of heavy-to-light decay. For each of these expansions, we employ graph-theoretical approaches to derive the generic forms of the regions involved in the method of regions. The results, applicable to all orders, offer insights that can be leveraged to investigate various aspects of scattering amplitudes.

167 pages, 61 figures

References in corpus (21)

• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Expansion by regions: revealing potential and Glauber regions automatically
• Geometric approach to asymptotic expansion of Feynman integrals
• The method of regions and next-to-soft corrections in Drell-Yan production
• Hard-Soft-Collinear Factorization to All Orders
• Massive vector form factors to three loops
• Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
• Massive three-loop form factor in the planar limit
• Higgs boson contribution to the leading two-loop Yukawa corrections to $gg\to HH$
• Disentangling the Regge cut and Regge pole in perturbative QCD
• Principal Landau Determinants
• Collinear expansion for color singlet cross sections
• Analytic three-loop QCD corrections to top-quark and semileptonic $b\to u$ decays
• Bound muon decay spectrum in the leading logarithmic accuracy
• Soft-collinear gravity beyond the leading power
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• Dissecting polytopes: Landau singularities and asymptotic expansions in $2\to 2$ scattering
• Local infrared safety in time-ordered perturbation theory
• Semi-numerical power expansion of Feynman integrals

Cited by in corpus (2)

• Three-loop banana integrals with four unequal masses
• Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices