Double Soft Limit of Graviton Amplitude from the Cachazo-He-Yuan Formalism

TL;DR

This paper analyzes the double soft limit of graviton amplitudes within the Cachazo-He-Yuan (CHY) formalism, distinguishing nondegenerate and degenerate scattering-equation solutions. It derives leading and subleading soft factors, showing that the leading term is the product of two single-soft factors arising from nondegenerate solutions, while subleading contributions comprise noncontact terms and a degenerate contact term from the pinch of soft punctures; the full result matches existing BCFW-based analyses and holds in arbitrary spacetime dimensions. The work clarifies the local (contact) versus nonlocal (noncontact) structure of double-soft graviton emissions and demonstrates how CHY can reproduce known soft-theorem results, suggesting further links to asymptotic symmetries and potential loop-corrections study. Overall, it extends the CHY soft-limit program to gravity, providing a comprehensive, dimension-independent account of double-soft behavior and reconciling CHY with BCFW outcomes.

Abstract

We present a complete analysis for double soft limit of graviton scattering amplitude using the formalism proposed by Cachazo, He and Yuan. Our results agree with that obtained via BCFW recursion relations in arXiv:1504.05558. In addition we find precise relations between degenerate and nondegenerate solutions of scattering equations with local and nonlocal terms in the soft factor.