New multiple soft theorem from split-helicity amplitude decomposition

TL;DR

This work addresses how multiple soft gluon emissions factorize in tree-level amplitudes with split-helicity configurations. It develops a soft-decomposition framework that links inverse soft limit recursions to BCFW shifts, enabling the construction of $A_{n,m}^{\text{split}}$ from lower-point amplitudes. By expressing non-perturbative double and triple soft operators as explicit combinations of single soft operators, the authors reproduce leading and subleading soft factors when expanded, and verify consistency with perturbative BCFW results reported in the literature. The approach provides a constructive, non-perturbative mechanism to generate multi-soft factors for gluon amplitudes, with potential extension to higher-point processes via generalized soft operators.

Abstract

We investigate the soft decomposition of tree-level gluon amplitudes with split-helicity configurations. First, we show how any split-helicity amplitude can be fully fixed from inverse soft limit using BCFW calculation. We show how the double and triple soft theorems can manifest beyond perturbative calculations through split-helicity decomposition. Next, we obtain a compact formula for the corresponding soft operator which is a simple combination of individual single soft operators. Then we generate the leading and sub-leading soft factors using soft momentum expansion, to compare with results derived from standard calculation.

Figures (2)

• Figure 1: Soft reconstruction of a six point split-helicity amplitude.
• Figure 2: Soft reconstruction of a seven point split-helicity amplitude.