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Journal of High Energy Physics

, 2019:71 | Cite as

Bootstrapping solutions of scattering equations

  • Zhengwen LiuEmail author
  • Xiaoran Zhao
Open Access
Regular Article - Theoretical Physics

Abstract

The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations based on the numerical algebraic geometry. The cornerstone of our method is the concept of the physical homotopy between different points in the kinematic space, which naturally induces a homotopy of the scattering equations. As a result, the solutions of the scattering equations with different points in the kinematic space can be tracked from each other. Finally, with the help of soft limits, all solutions can be bootstrapped from the known solution for the four-particle scattering.

Keywords

Scattering Amplitudes Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Centre for Cosmology, Particle Physics and Phenomenology (CP3), UCLouvainLouvain-la-NeuveBelgium

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