Bootstrapping solutions of scattering equations

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.

v2: published version. The code is available at https://github.com/zxrlha/sehomo

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Cited by in corpus (4)

• Aspects of Scattering Amplitudes and Moduli Space Localization
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• Note on solutions of scattering equations
• Scattering and Strebel graphs