On-shell constructibility of Born amplitudes in spontaneously broken gauge theories

TL;DR

This paper investigates the minimal on-shell recursion shifts needed to construct Born amplitudes in spontaneously broken gauge theories, revealing that most amplitudes can be built with two or three-line shifts, with some requiring up to five.

Contribution

It identifies the minimal shifts necessary for constructing amplitudes in broken gauge theories and revisits selection rules using on-shell recursion and little-group transformations.

Findings

Two-line or three-line shifts suffice for most amplitudes with five or more particles.

Amplitudes involving longitudinal vector bosons or scalars may require up to five-line shifts.

Revised selection rules for multi-boson amplitudes using on-shell recursion.

Abstract

We perform a comprehensive study of on-shell recursion relations for Born amplitudes in spontaneously broken gauge theories and identify the minimal shifts required to construct amplitudes with a given particle content and spin quantum numbers. We show that two-line or three-line shifts are sufficient to construct all amplitudes with five or more particles, apart from amplitudes involving longitudinal vector bosons or scalars, which may require at most five-line shifts. As an application, we revisit selection rules for multi-boson amplitudes using on-shell recursion and little-group transformations.