Helicity Constraints To Soft Factor Of All Spin
Andriniaina Narindra Rasoanaivo
TL;DR
The paper develops a helicity-based, non-perturbative framework to constrain soft operators in massless scattering. By enforcing $[H_I,S_r]=h_r\delta_{Ir} S_r$ and employing spinor-helicity variables, it reformulates the problem as PDEs for the leading soft factor $S^{(0)}$ and imposes high-/low-energy boundaries to fix the allowed spin $s$ and helicity $h_r$. The authors derive a general expression $S^{(0)}_{s,h_r}$, which for spins $s=0,1,2$ reproduces the known scalar, photon, and graviton soft factors up to a coupling, and they interpret $s$ as the spin of the soft particle. The approach yields a master, analytic formula for the single-soft factor applicable to arbitrary spin/helicity, connecting soft theorems to Lorentz symmetry and little-group representations with potential non-perturbative extensions.
Abstract
In this note, we derive for the first time a set of non-perturbative constraints for soft operators that preserve the helicities of scattering amplitudes in a soft limit. We also show that the resolution of such constraints generates a master formula for the analytic expression of the single soft factor of any given spin and helicity.