Gauged Soft Recursion: On-Shell Construction of Goldstone-Gauge Amplitudes

TL;DR

This paper introduces a new on-shell recursion method for constructing scattering amplitudes involving Goldstone bosons and gauge bosons, overcoming gauge interaction challenges by leveraging gauge boson soft theorems and a novel amplitude decomposition.

Contribution

It develops a gauged soft recursion technique that systematically constructs tree-level amplitudes with Goldstone and gauge bosons, extending on-shell methods to gauge-involved spontaneous symmetry breaking.

Findings

Enables systematic construction of mixed Goldstone-gauge amplitudes

Works for both Abelian and non-Abelian gauge theories

Demonstrates explicit examples of the formalism in action

Abstract

We present a new on-shell recursion relation for scattering amplitudes involving Nambu-Goldstone bosons with a gauged unbroken symmetry. A central challenge is that gauge interactions break Adler's zero condition for charged scalars, invalidating the standard soft recursion. To overcome this, we introduce a ``gauged soft recursion'' that leverages the soft theorems of the gauge bosons themselves, combined with a novel decomposition of amplitudes into gauge-invariant components where Adler's zero is partially restored. The formalism, which also incorporates internal gauge bosons via angular momentum constraints, enables the systematic construction of tree-level amplitudes with arbitrary numbers of Goldstone bosons and gauge bosons in both Abelian and non-Abelian theories, as we demonstrate with explicit examples.