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PreprintCC BY 4.0arXiv

From Hidden Zeros to Exact Splittings and New Zeros

  • Yang Li
  • Laurentiu Rodina
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Abstract

Hidden zeros impose constraints on scattering amplitudes beyond their familiar factorization properties. We explore their structure in two related directions. We first promote hidden zeros to explicit splitting formulas that organize full amplitudes at generic kinematics. Ordered Tr(ϕ3) amplitudes, nonlinear sigma model (NLSM) amplitudes, and cosmological wavefunctions share the same defining exact splitting structure 𝒜=∑αRα 𝒥α,L𝒥α,R 𝒥α,out, adapted to any hidden zero. Each prefactor Rα is a condition of the hidden zero locus, so this decomposition manifests the hidden vanishing term by term. The remaining factors are lower point amplitudes or currents. Using these representations, we can systematically find new zero loci beyond the usual ones. In particular, we obtain five new all-multiplicity zero families. We also find continuous families of zeros: the coefficients of their defining equations can vary continuously while the amplitude remains zero.

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Cite

BibTeXRIS
BibTeX
@misc{li2026from,
  title = {{From Hidden Zeros to Exact Splittings and New Zeros}},
  author = {Yang Li and Laurentiu Rodina},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01775},
  eprint = {2610.01775},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01775},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - From Hidden Zeros to Exact Splittings and New Zeros
AU  - Yang Li
AU  - Laurentiu Rodina
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01775
UR  - https://arxiv.org/abs/2610.01775
AB  - Hidden zeros impose constraints on scattering amplitudes beyond their familiar factorization properties. We explore their structure in two related directions. We first promote hidden zeros to explicit splitting formulas that organize full amplitudes at generic kinematics. Ordered Tr(ϕ^3) amplitudes, nonlinear sigma model (NLSM) amplitudes, and cosmological wavefunctions share the same defining exact splitting structure 𝒜=∑_αR_α 𝒥_α,L𝒥_α,R 𝒥_α,out, adapted to any hidden zero. Each prefactor R_α is a condition of the hidden zero locus, so this decomposition manifests the hidden vanishing term by term. The remaining factors are lower point amplitudes or currents. Using these representations, we can systematically find new zero loci beyond the usual ones. In particular, we obtain five new all-multiplicity zero families. We also find continuous families of zeros: the coefficients of their defining equations can vary continuously while the amplitude remains zero.
ER  -