Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes

TL;DR

This paper investigates the double soft theorem in generalized biadjoint scalar theories, revealing how degenerate and non-degenerate solutions influence the leading contributions, with results applicable to any k and specific cases for adjacent soft states.

Contribution

It provides a detailed analysis of double soft theorems in generalized biadjoint scalar theories, highlighting the role of degenerate solutions and generalizing results to arbitrary k.

Findings

Degenerate solutions dominate when double soft limit does not factorize.

Non-degenerate solutions dominate when the limit factorizes.

Explicit analytic results for adjacent soft states for any k.

Abstract

We study double soft theorem for the generalised biadjoint scalar field theory whose amplitudes are computed in terms of punctures on $\mathbb{CP}^{k-1}$. We find that whenever the double soft limit does not decouple into a product of single soft factors, the leading contributions to the double soft theorems come from the degenerate solutions, otherwise the non degenerate solutions dominate. Our analysis uses the regular solutions to the scattering equations. Most of the results are presented for $k=3$ but we show how they generalise to arbitrary $k$. We have explicit analytic results, for any $k$, in the case when soft external states are adjacent.