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Likelihood Equations and Scattering Amplitudes

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arxiv 2012.05041 v1 pith:JTX4YCB7 submitted 2020-12-09 math.AG hep-thmath.STstat.TH

Bernd Sturmfels , Simon Telen This is my paper · ORCID
classification math.AGhep-thmath.STstat.TH
keywords amplitudesmodelsscatteringalgebraiccomputecriticalequationsfunction
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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.

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  1. The CEGM NLSM

    hep-th 2025-02 conditional novelty 6.0 of 10

    A systematic deformation theory for CEGM amplitudes yields generalized nonlinear sigma model amplitudes, with dimension gcd(k,n)-1 for pure deformations and an embedding of ordinary NLSM amplitudes as residues.

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