New Double Soft Emission Theorems

TL;DR

The paper analyzes double soft emissions at tree level across a range of scalar theories, distinguishing non-color (sGal, DBI, EMS) from color (NLSM, YMS) sectors. It proposes universal leading and subleading double-soft factors, with a theory-dependent higher-order term for two soft scalars, and derives a compact leading double-soft photon theorem using a Pfaffian structure, all aided by the CHY representation. Through explicit amplitude checks and CHY-based proofs, it establishes leading-order double-soft theorems for both scalar and color-ordered amplitudes, and discusses how a degenerate CHY solution dominates the double-soft limit. The work explores connections to asymptotic symmetries, the role of the CHY framework in conjectural formulas, and future directions for extending these results with BCFW-like methods and symmetry interpretations.

Abstract

We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, DBI, Einstein-Maxwell-Scalar, NLSM and Yang-Mills-Scalar. We use the recently found CHY representation of these theories in order to give a simple proof of the leading order part of all these theorems