A Monte Carlo Approach to the 4D Scattering Equations

Abstract

The scattering equation formalism is a general framework for calculation of amplitudes in theories of massless particles. We provide a detailed introduction to the 4D scattering equation framework accessible to non-experts, outline current difficulties solving the equations numerically, and explain how to overcome them with a Monte Carlo algorithm. With this submission we include {\tt treeamps4dJAF}, the first publicly available {\sc Mathematica} package for calculating amplitudes by solving the scattering equations, supporting MHV analytical and N${}^{k-2}$MHV numerical computations. The package provides a powerful and flexible computational tool for calculating tree-level amplitudes in super Yang Mills theories, Einstein supergravity and conformal supergravity. We tabulate sets of numerical solutions up to 9 points in all MHV sectors and 12 points in the NHMV sector which can be used for fast evaluation of amplitudes.

arXiv comment40 pages, 6 figures

References in corpus (33)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Conformal Supergravity in Twistor-String Theory
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Ambitwistor strings in 4-dimensions
• Subleading soft theorem in arbitrary dimension from scattering equations
• Unification of Residues and Grassmannian Dualities
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• All tree-level amplitudes in massless QCD
• Perturbative gravity at null infinity
• Ambitwistor strings at null infinity and subleading soft limits
• The Polynomial Form of the Scattering Equations
• New Representations of the Perturbative S-Matrix
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Integration Rules for Loop Scattering Equations
• Gluons and gravitons at one loop from ambitwistor strings
• On-shell superamplitudes in N<4 SYM
• Integration Rules for Scattering Equations
• On the solutions of the scattering equations
• Connected formulas for amplitudes in standard model
• Collinear limits beyond the leading order from the scattering equations
• A Grassmannian Etude in NMHV Minors
• The connected prescription for form factors in twistor space
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• Twistor/ambitwistor strings and null-superstrings in spacetime of D=4,10 and 11 dimensions
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• New Worldsheet Formulae for Conformal Supergravity Amplitudes

Cited by in corpus (9)

• Unraveling conformal gravity amplitudes
• Cosmological Scattering Equations at Tree-level and One-loop
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Bootstrapping solutions of scattering equations
• Analytical amplitudes from numerical solutions of the scattering equations
• Multi-Regge kinematics and the scattering equations
• Scattering and Strebel graphs