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The structure of tree-level scattering amplitudes for collinear masslessbosons is studied beyond their leading splitting function behavior. Thesenear-collinear limits at sub-leading order are best studied using theCachazo-He-Yuan (CHY) formulation of the S-matrix based on the scatteringequations. We compute the collinear limits for gluons, gravitons and scalars.It is shown that the CHY integrand for an n-particle gluon scattering amplitudein 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 isuniversal. Our representation is shown to obey recently proposed amplituderelations in which the collinear gluons of same helicity are replaced by asingle graviton. Finally, we extend our analysis to effective field theoriesand study the collinear limit of the non-linear sigma model,Einstein-Maxwell-Scalar and Yang-Mills-Scalar theory.

Collinear limits beyond the leading order from the scattering equations