Subleading Terms in the Collinear Limit of Yang-Mills Amplitudes

TL;DR

This paper investigates the subleading terms in the collinear limit of Yang-Mills amplitudes, revealing their relation to Einstein-Yang-Mills amplitudes with a graviton replaced by collinear gauge bosons.

Contribution

It provides a precise definition of the collinear limit and links subleading Yang-Mills terms to graviton-inserted amplitudes at tree level.

Findings

Subleading non-singular terms relate to graviton-inserted amplitudes.

In Einstein-Yang-Mills, a graviton can be replaced by collinear gauge bosons.

Defines the collinear limit precisely at tree level.

Abstract

For two massless particles i and j, the collinear limit is a special kinematic configuration in which the particles propagate with parallel four-momentum vectors, with the total momentum P distributed as p_i=xP and p_j=(1-x)P, so that s_{ij}=(p_i+p_j)^2=P^2=0. In Yang-Mills theory, if i and j are among N gauge bosons participating in a scattering process, it is well known that the partial amplitudes associated to the (single trace) group factors with adjacent i and j are singular in the collinear limit and factorize at the leading order into N-1-particle amplitudes times the universal, x-dependent Altarelli-Parisi factors. We give a precise definition of the collinear limit and show that at the tree level, the subleading, non-singular terms are related to the amplitudes with a single graviton inserted instead of two collinear gauge bosons. To that end, we argue that in one-graviton Einstein-Yang-Mills amplitudes, the graviton with momentum P can be replaced by a pair of collinear gauge bosons carrying arbitrary momentum fractions xP and (1-x)P.