Collinear limits beyond the leading order from the scattering equations

TL;DR

This paper investigates the sub-leading collinear limits of tree-level scattering amplitudes for massless bosons using the CHY formulation, revealing universal structures and extending to various effective field theories.

Contribution

It provides a detailed analysis of sub-leading collinear limits beyond the leading order using scattering equations, including universal convolution structures and relations among amplitudes.

Findings

Collinear limits at sub-leading order are expressed as convolutions with universal kernels.

The representation obeys amplitude relations replacing collinear gluons with a graviton.

Extension of analysis to effective field theories like non-linear sigma model and Einstein-Maxwell-Scalar.

Abstract

The structure of tree-level scattering amplitudes for collinear massless bosons is studied beyond their leading splitting function behavior. These near-collinear limits at sub-leading order are best studied using the Cachazo-He-Yuan (CHY) formulation of the S-matrix based on the scattering equations. We compute the collinear limits for gluons, gravitons and scalars. It is shown that the CHY integrand for an n-particle gluon scattering amplitude in the collinear limit at sub-leading order is expressed as a convolution of an (n-1)-particle gluon integrand and a collinear kernel integrand, which is universal. Our representation is shown to obey recently proposed amplitude relations in which the collinear gluons of same helicity are replaced by a single graviton. Finally, we extend our analysis to effective field theories and study the collinear limit of the non-linear sigma model, Einstein-Maxwell-Scalar and Yang-Mills-Scalar theory.