Hidden Zeros in Massive Theories

TL;DR

This paper explores the persistence of hidden zeros in massless amplitude factorisations when extended to massive theories, revealing conditions under which these zeros and their structures are preserved or broken.

Contribution

It demonstrates that hidden zeros survive only under symmetry-controlled mass generation and introduces a massive on-shell recursion for NLSM amplitudes.

Findings

Hidden zeros persist in certain massive theories with symmetry-controlled mass generation.

Naive pion mass terms generally spoil hidden zeros, but spurion-induced potentials can restore them.

Spontaneously broken gauge theories preserve hidden zeros, unlike simple massive Yang-Mills theories.

Abstract

We investigate whether the hidden zeros and associated factorisations found for massless colour-ordered amplitudes persist under massive deformations. Using the kinematic mesh construction, we show that hidden zeros survive only for symmetry controlled mass generation. For massive $\text{Tr} \Phi^3$ with a uniform mass, the zeros and their factorisation patterns are inherited after a massive shift of planar variables, and an analogous statement holds for Kaluza-Klein reductions where the relevant non-planar variables are modified by conserved mode numbers. For the non-linear sigma model (NLSM), a naive pion mass term generically spoils hidden zeros, while a spurion induced potential restores them. This allows factorisation near zeros, including odd point channels described by an appropriately mass deformed NLSM + $\phi^3$ theory, and leads to a hidden zero based on-shell recursion for massive NLSM amplitudes. For spin-one, a simple massive Yang-Mills theory fails to exhibit hidden zeros, while spontaneously broken gauge theories preserve them.