New Factorizations of Yang-Mills Amplitudes

Abstract

We propose a new factorization pattern for tree-level Yang-Mills (YM) amplitudes, where they decompose into a sum of gluings of two lower-point amplitudes by setting specific two-point non-planar Mandelstam variables within a rectangular configuration to zero. This approach manifests the hidden zeros of YM amplitudes recently identified. Furthermore, by setting specific Lorentz products involving polarization vectors to zero, the amplitudes further reduce to a sum of products of three currents. These novel factorizations provide a fresh perspective on the structure of YM amplitudes, potentially enhancing our understanding and calculation of these fundamental quantities.

Figures (1)

• Figure 1: New factorization of YM amplitudes: An $n$-point Yang-Mills amplitude factorizes into a sum over contributions, each involving a 3-point amplitude and an $(n-1)$-point amplitude. The sum runs over all permutations $\rho$ of the $(m-1)$ external gluons. The internal gluon $\hat{j}$ is exchanged in two diagrams. For simplicity, some rational functions of Mandelstam variables are omitted in this schematic representation. The first graph in this figure also provides an intuitive explanation for the constraints on the Mandelstam variables in $h_m$, as defined in \ref{['eq:constrhm']}. Selecting any two non-adjacent external gluon legs (e.g., $m{+}1$ and $n$) in a color-ordered amplitude naturally partitions the remaining legs into two sets. Setting all two-particle Mandelstam variables that involve legs from both sets to zero gives $h_m = 0$.