Constructing canonical Feynman integrals with intersection theory

DOI10.1016/j.physletb.2021.136085OpenAlexW3047948546WikidataQ114141543 ScholiaQ114141543MaRDI QIDQ2232552

Li Lin Yang, Xiaofeng Xu, Jiaqi Chen, Xuhang Jiang

Publication date: 6 October 2021

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.03045

Mathematics Subject Classification ID

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Perturbation theories for operators and differential equations in quantum theory (81Q15) (2)-body potential quantum scattering theory (81U05) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) PDEs on time scales (35R07)

Related Items (18)

Beam functions for \(N\)-jettiness at \(\mathrm{N^3LO}\) in perturbative QCD ⋮ \(\varepsilon\)-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves ⋮ Reduction to master integrals via intersection numbers and polynomial expansions ⋮ AdS super gluon scattering up to two loops: a position space approach ⋮ Macaulay matrix for Feynman integrals: linear relations and intersection numbers ⋮ A study of Feynman integrals with uniform transcendental weights and their symbology ⋮ Real time lattice correlation functions from differential equations ⋮ Intersection numbers from higher-order partial differential equations ⋮ Evaluating master integrals in non-factorizable corrections to \(t\)-channel single-top production at NNLO QCD ⋮ Collider physics at the precision frontier ⋮ Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight ⋮ Decomposition of Feynman integrals by multivariate intersection numbers ⋮ Duals of Feynman integrals. I: Differential equations ⋮ A first look at the function space for planar two-loop six-particle Feynman integrals ⋮ On epsilon factorized differential equations for elliptic Feynman integrals ⋮ On the computation of intersection numbers for twisted cocycles ⋮ Baikov representations, intersection theory, and canonical Feynman integrals ⋮ Top-Down Decomposition: A Cut-Based Approach to Integral Reductions

Uses Software

• Azurite
• Fuchsia
• epsilon
• DiffExp
• CANONICA

Cites Work

• Magnus and Dyson series for master integrals
• Iterative structure of finite loop integrals
• On the maximal cut of Feynman integrals and the solution of their differential equations
• Numerical evaluation of multiple polylogarithms
• Leading singularities and off-shell conformal integrals
• Critical points and number of master integrals
• Multiple polylogarithms, cyclotomy and modular complexes
• Cuts of Feynman integrals in Baikov representation
• Feynman integrals and intersection theory
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• \texttt{epsilon}: a tool to find a canonical basis of master integrals
• Solving differential equations for Feynman integrals by expansions near singular points
• Local integrals for planar scattering amplitudes
• The amplituhedron
• \textsc{Azurite}: an algebraic geometry based package for finding bases of loop integrals
• Logarithmic forms and differential equations for Feynman integrals
• From infinity to four dimensions: higher residue pairings and Feynman integrals
• Decomposition of Feynman integrals on the maximal cut by intersection numbers
• The three-loop form factor in \(\mathcal{N} = {4}\) super Yang-Mills
• Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
• Reducing differential equations for multiloop master integrals
• Logarithmic singularities and maximally supersymmetric amplitudes
• Grassmannian Geometry of Scattering Amplitudes
• Theory of Hypergeometric Functions
• Iterated path integrals
• Algorithmic transformation of multi-loop master integrals to a canonical basis with \textit{CANONICA}

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