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arXiv · 2601.16860

Hidden Zeros in Massive Theories

Mariana Carrillo González·Freddie Ward
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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.

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Mariana Carrillo González, Freddie Ward. 2026-01-23. Hidden Zeros in Massive Theories. https://arxiv.org/abs/2601.16860

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