A Monte Carlo Approach to the 4D Scattering Equations

TL;DR

This paper introduces a Monte Carlo method for solving 4D scattering equations, providing a new computational tool and a Mathematica package for calculating tree-level amplitudes in various supergravity and super Yang-Mills theories.

Contribution

It presents the first publicly available Mathematica package for solving 4D scattering equations using a Monte Carlo algorithm, enabling efficient amplitude calculations.

Findings

Developed a Monte Carlo algorithm for 4D scattering equations.

Created the first public Mathematica package for amplitude calculations.

Tabulated numerical solutions up to 9 points in MHV sectors.

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.