Learning the Simplicity of Scattering Amplitudes

Abstract

The simplification and reorganization of complex expressions lies at the core of scientific progress, particularly in theoretical high-energy physics. This work explores the application of machine learning to a particular facet of this challenge: the task of simplifying scattering amplitudes expressed in terms of spinor-helicity variables. We demonstrate that an encoder-decoder transformer architecture achieves impressive simplification capabilities for expressions composed of handfuls of terms. Lengthier expressions are implemented in an additional embedding network, trained using contrastive learning, which isolates subexpressions that are more likely to simplify. The resulting framework is capable of reducing expressions with hundreds of terms - a regular occurrence in quantum field theory calculations - to vastly simpler equivalent expressions. Starting from lengthy input expressions, our networks can generate the Parke-Taylor formula for five-point gluon scattering, as well as new compact expressions for five-point amplitudes involving scalars and gravitons. An interactive demonstration can be found at https://spinorhelicity.streamlit.app .

25+15 pages, 9+6 figures, v2: typos correction and extended the introduction, conclusion, sections 2.2, 2.4 and appendix F

References in corpus (35)

• Array Programming with NumPy
• LLaMA: Open and Efficient Foundation Language Models
• Longformer: The Long-Document Transformer
• Perturbative Gauge Theory As A String Theory In Twistor Space
• The Curious Case of Neural Text Degeneration
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• The Amplituhedron
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Scattering Equations and KLT Orthogonality
• A Duality For The S Matrix
• Unifying Relations for Scattering Amplitudes
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Scattering Amplitudes
• Modern Machine Learning and Particle Physics
• A factorisation-aware Matrix element emulator
• Targeting Multi-Loop Integrals with Neural Networks
• Point Cloud Transformers applied to Collider Physics
• The Amplituhedron from Momentum Twistor Diagrams
• Symmetries, Safety, and Self-Supervision
• Using neural networks for efficient evaluation of high multiplicity scattering amplitudes
• Self-supervised Anomaly Detection for New Physics
• Investigating the Limitations of Transformers with Simple Arithmetic Tasks
• Learning the language of QCD jets with transformers
• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• The one-loop amplitudes for Higgs + 4 partons with full mass effects
• Extracting analytical one-loop amplitudes from numerical evaluations
• Deep Symbolic Regression for Recurrent Sequences
• Jet Diffusion versus JetGPT -- Modern Networks for the LHC
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory
• End-to-end symbolic regression with transformers
• Vector boson pair production at one loop: analytic results for the process $q\bar{q}\ell \bar{\ell }{\ell }^{\prime }{\bar{\ell }}^{\prime }g$
• SpinorHelicity4D: a Mathematica toolbox for the four-dimensional spinor-helicity formalism
• PASCL: Supervised Contrastive Learning with Perturbative Augmentation for Particle Decay Reconstruction

Cited by in corpus (2)

• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC