Likelihood Equations and Scattering Amplitudes

Abstract

We relate scattering amplitudes in particle physics to maximum likelihood estimation for discrete models in algebraic statistics. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. We study the ML degree of low-rank tensor models in statistics, and we revisit physical theories proposed by Arkani-Hamed, Cachazo and their collaborators. Recent advances in numerical algebraic geometry are employed to compute and certify critical points. We also discuss positive models and how to compute their string amplitudes.

arXiv comment18 pages

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Cited by in corpus (12)

• Planar Matrices and Arrays of Feynman Diagrams
• Planar Matrices and Arrays of Feynman Diagrams: Poles for Higher $k$
• Notes on Worldsheet-Like Variables for Cluster Configuration Spaces
• 3D genome reconstruction from partially phased Hi-C data
• Bayesian Integrals on Toric Varieties
• Adjoints and Canonical Forms of Polypols
• Logarithmic Voronoi polytopes for discrete linear models
• Scattering and Strebel graphs
• Planarity in Generalized Scattering Amplitudes: PK Polytope, Generalized Root Systems and Worldsheet Associahedra
• Nonlinear Algebra and Applications
• Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective
• Co-homology of Differential Forms and Feynman diagrams