Geometric approach to asymptotic expansion of Feynman integrals

Abstract

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.

6 pages, 2 figures

References in corpus (2)

• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Heavy-to-heavy quark decays at NNLO

Cited by in corpus (44)

• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• Expansion by regions: revealing potential and Glauber regions automatically
• Collider Physics at the Precision Frontier
• The method of regions and next-to-soft corrections in Drell-Yan production
• FeynCalc 10: Do multiloop integrals dream of computer codes?
• One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory
• Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
• Landau Discriminants
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Feynman Polytopes and the Tropical Geometry of UV and IR Divergences
• Numerical Scattering Amplitudes with pySecDec
• Higgs boson contribution to the leading two-loop Yukawa corrections to $gg\to HH$
• Towards all-order factorization of QED amplitudes at next-to-leading power
• On the relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks
• The on-shell expansion: from Landau equations to the Newton polytope
• MB Tools reloaded
• Real corrections to Higgs boson pair production at NNLO in the large top quark mass limit
• Intersection theory rules symbology
• Exposing the threshold structure of loop integrals
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• Dissecting polytopes: Landau singularities and asymptotic expansions in $2\to 2$ scattering
• Resummation methods for Master Integrals
• Three-loop banana integrals with four unequal masses
• A factorization approach to next-to-leading-power threshold logarithms
• Massive two-loop four-point Feynman integrals at high energies with AsyInt
• The Higgs-gluon form factor at three loops in QCD with three mass scales
• Expansion by regions meets angular integrals
• Feynman integral reduction using Gröbner bases
• Three-loop non-singlet matching coefficients for heavy quark currents
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Expansion by regions with pySecDec
• Region analysis of $H\to \gamma \gamma$ via a bottom quark loop
• Classical gravitational scattering from a gauge-invariant double copy
• Master integrals for mixed QCD-QED corrections to charged-current Drell-Yan production of a massive charged lepton
• Disperon QED
• Unregulated Divergences of Feynman Integrals
• On Finite Representation of Dimensionally Regularized One-loop Integrals
• A stroll through the loop-tree duality
• Analytic results for two-loop planar master integrals for Bhabha scattering
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point
• Master integrals for two-loop $C$-odd contribution to $e^{+}{e}^{-}\to {\ell }^{+}{\ell }^{-}$ process
• CoLoRFulNNLO for hadron collisions: integrating the iterated single unresolved subtraction terms