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.

40 pages, 6 figures