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.

arXiv comment167 pages, 61 figures

References in corpus (102)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Asymptotic expansion of Feynman integrals near threshold
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• Connection between Feynman integrals having different values of the space-time dimension
• Infrared singularities of scattering amplitudes in perturbative QCD
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• Multipole-expanded soft-collinear effective theory with non-abelian gauge symmetry
• FIESTA 4: optimized Feynman integral calculations with GPU support
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• Revisiting $B\to D\ell \nu$
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Top-Quark Decay at Next-to-Next-to-Leading Order in QCD
• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Summing up Subleading Sudakov Logarithms
• Expansion by regions: revealing potential and Glauber regions automatically
• Asymptotic Expansions in Momenta and Masses and Calculation of Feynman Diagrams
• Problems of the Strategy of Regions
• An Effective Field Theory for Forward Scattering and Factorization Violation
• FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions
• Geometric approach to asymptotic expansion of Feynman integrals
• FIESTA 2: parallelizeable multiloop numerical calculations
• Critical points and number of master integrals
• Foundation and generalization of the expansion by regions
• The method of regions and next-to-soft corrections in Drell-Yan production
• Hard-Soft-Collinear Factorization to All Orders
• The two-loop soft current in dimensional regularization
• Single soft gluon emission at two loops
• Non-abelian factorisation for next-to-leading-power threshold logarithms
• $O({\alpha }_s^2)$ corrections to fully-differential top quark decays
• FIESTA5: numerical high-performance Feynman integral evaluation
• Transverse momentum dependent PDFs at N${}^3$LO
• Double Higgs boson production at NLO in the high-energy limit: complete analytic results
• Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable
• Real-Virtual contributions to the inclusive Higgs cross-section at N3LO
• Cuts from residues: the one-loop case
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• The strategy of regions for asymptotic expansion of two-loop vertex Feynman diagrams
• Threshold factorization of the Drell-Yan process at next-to-leading power
• Challenges in Semileptonic B Decays
• Infrared Singularities of Scattering Amplitudes and N${}^3$LL Resummation for $n$-Jet Processes
• Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion
• A geometric method of sector decomposition
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• Tropical Monte Carlo quadrature for Feynman integrals
• Massive vector form factors to three loops
• Power Counting in the Soft-Collinear Effective Theory
• Removing infrared divergences from two-loop integrals
• Drell-Yan process with jet vetoes: breaking of generalized factorization
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• Tropical Feynman integration in the Minkowski regime
• The Heavy Fermion Contributions to the Massive Three Loop Form Factors
• Nonfactorizable QCD Effects in Higgs Boson Production via Vector Boson Fusion
• On the status of expansion by regions
• Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
• Small-mass effects in heavy-to-light form factors
• TMD Fragmentation Functions at N${}^3$LO
• FeynGKZ: a Mathematica package for solving Feynman integrals using GKZ hypergeometric systems
• Heavy Quark Form Factors at Three Loops in the Planar Limit
• Massive three-loop form factor in the planar limit
• Higgs boson contribution to the leading two-loop Yukawa corrections to $gg\to HH$
• Soft gluon emission at two loops in full color
• Disentangling the Regge cut and Regge pole in perturbative QCD
• On next-to-leading power threshold corrections in Drell-Yan production at N${}^3$LO
• N-jettiness beam functions at N3LO
• Unveiling Regions in multi-scale Feynman Integrals using Singularities and Power Geometry
• Principal Landau Determinants
• The on-shell expansion: from Landau equations to the Newton polytope
• Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
• Hepp's bound for Feynman graphs and matroids
• High-Energy Expansion of Two-Loop Massive Four-Point Diagrams
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Analytic approximations of $2\to 2$ processes with massive internal particles
• A Forest Formula to Subtract Infrared Singularities in Amplitudes for Wide-angle Scattering
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Analytic three-loop QCD corrections to top-quark and semileptonic $b\to u$ decays
• Collinear expansion for color singlet cross sections
• Tree-level soft emission of a quark pair in association with a gluon
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• Bound muon decay spectrum in the leading logarithmic accuracy
• Soft-collinear gravity beyond the leading power
• Gravitational soft theorem from emergent soft gauge symmetries
• Soft gluon-quark-antiquark emission in QCD hard scattering
• Generalized Cuts of Feynman Integrals in Parameter Space
• Revisiting the double-soft asymptotics of one-loop amplitudes in massless QCD
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• 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
• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• Local infrared safety in time-ordered perturbation theory
• Graph complexes and Feynman rules
• Two-Loop master integrals for heavy-to-light form factors of two different massive fermions
• Semi-numerical power expansion of Feynman integrals
• Soft-collinear gravity with fermionic matter
• Three-loop planar master integrals for heavy-to-light form factors

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