Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes

TL;DR

This paper extends deformation techniques to two complex variables to analyze higher codimension singularities in Yang-Mills amplitudes, enabling recursive construction of these amplitudes beyond traditional methods.

Contribution

It introduces a two-complex-variable deformation approach to explore higher codimension singularities in Yang-Mills amplitudes, advancing recursive construction methods.

Findings

Successfully constructed Yang-Mills tree amplitudes using two-variable deformation.

Extended Risager's deformation to a $\

Demonstrated the role of the global residue theorem in analyzing higher singularities.

Abstract

Yang-Mills tree-level amplitudes contain singularities of codimension one like collinear and multi-particle factorizations, codimension two such as soft limits, as well as higher codimension singularities. Traditionally, BCFW-like deformations with one complex variable were used to explore collinear and multi-particle channels. Higher codimension singularities need more complex variables to be reached. In this paper, along with a discussion on higher singularities and the role of the global residue theorem in this analysis, we specifically consider soft singularities. This is done by extending Risager's deformation to a $\mathbb C^2$-plane, i.e., two complex variables. The two-complex-dimensional deformation is then used to recursively construct Yang-Mills tree amplitudes.