Collinear limits beyond the leading order from the scattering equations

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.

arXiv comment38 pages

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• Expansion of Einstein-Yang-Mills Amplitude
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• Cosmological Scattering Equations
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• One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds
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• Multi-Regge kinematics and the scattering equations
• CHY Theory for Several Fields
• Gravitational Scattering in the High-Energy Limit