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Hidden zeros in massive field theories

Mariana Carrillo Gonzalez1,2,* and Freddie Ward1,†

  • *Contact author: m.carrillo-gonzalez@imperial.ac.uk; m.carrillo-gonzalez@soton.ac.uk
  • †Contact author: freddie.ward23@imperial.ac.uk
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Phys. Rev. D 113, 125018 – Published 15 June, 2026

DOI: https://doi.org/10.1103/9wbw-9jxb

Abstract

We investigate whether the hidden zeros and associated factorizations found for massless color-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 TrΦ3 with a uniform mass, the zeros and their factorization patterns are inherited after a massive shift of planar variables, and an analogous statement holds for Kaluza-Klein reductions where the relevant nonplanar variables are modified by conserved mode numbers. For the nonlinear sigma model (NLSM), a naive pion mass term generically spoils hidden zeros, while a spurion induced potential restores them. This allows factorization near zeros, including odd point channels described by an appropriately mass deformed NLSM + ϕ3 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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Phys. Rev. D 113, 125018– Published 15 June, 2026
  • Received 6 February 2026
  • Accepted 23 April 2026
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