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Hidden zeros are equivalent to enhanced ultraviolet scaling and lead to unique amplitudes in Tr($\phi^3$) theory

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arxiv 2406.04234 v5 pith:KUJVESBA submitted 2024-06-06 hep-th

Laurentiu Rodina This is my paper
classification hep-th
keywords amplitudeszerosenhancedhiddenscalingamplitudeconjectureequivalent
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We investigate the hidden amplitude zeros discovered by Arkani-Hamed et al., which describe a non-trivial vanishing of scattering amplitudes on special external kinematics. We first prove that every type of hidden zero is equivalent to what we call a "subset" enhanced scaling under Britto-Cachazo-Feng-Witten shifts, for any rational function built from planar Lorentz invariants $X_{ij}{=}(p_i{+}p_{i+1}{+}\ldots{+}p_{j-1})^2$. This directly applies to Tr($\phi^3$), non-linear sigma model, or Yang-Mills-scalar amplitudes, revealing a novel type of enhanced UV scaling in these theories. We also use this observation to prove the conjecture that Tr($\phi^3$) amplitudes are uniquely fixed by the zeros, up to an overall normalization, when assuming an ordered and local propagator structure and trivial numerators. In the case of Yang-Mills theory, we conjecture the zeros, combined with the Bern-Carrasco-Johansson color-kinematic duality in the form of amplitude relations, uniquely fix the $\lfloor n/2\rfloor$ distinct polarization structures of $n$-point gluon amplitudes. Our approach opens a new avenue for understanding previous similar uniqueness results, and also extending them beyond tree level for the first time.

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Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Analytic Boundaries of Infinite-Spin-Tower Amplitudes from Hidden Zero

    hep-th 2026-07 conditional novelty 7.0 of 10

    The exact analytic boundary of unitary infinite-spin-tower amplitudes is derived and shown to be maximal unless energy poles accumulate.

  2. Universal Interpretation of Hidden Zero and $2$-Split of Tree-Level Amplitudes Using Feynman Diagrams, Part $\mathbf{I}$: ${\rm Tr}(\phi^3)$, NLSM and YM

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    A universal diagrammatic interpretation unifies hidden zeros (from massless on-shell conditions) and 2-splits (from double-line separation) in Tr(φ³), NLSM, and YM tree amplitudes using extended shuffle factorization ...

  3. Towards New Hidden Zero and $2$-Split of Loop-Level Feynman Integrands in ${\rm Tr}(\phi^3)$ Model

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Loop-level hidden zeros and 2-split structures are found in Tr(φ³) Feynman integrands with simple kinematic conditions, generalizing the tree-level case to an L-loop integrand expressed as a sum over L+1 terms each wi...

  4. On differential operators for scalar-scaffolded gluons

    hep-th 2025-12 conditional novelty 6.0 of 10

    Differential operators on scalar-scaffolded variables extract individual phi^3 diagrams from gluon amplitudes, and the independent mixed amplitudes are counted by Catalan numbers.

  5. Hidden zeros for higher-derivative YM and GR amplitudes at tree-level

    hep-th 2025-10 unverdicted novelty 6.0 of 10

    Hidden zeros extend to higher-derivative tree-level gluon and graviton amplitudes, with systematic cancellation of propagator singularities shown via bi-adjoint scalar expansions.

  6. A new recursion relation for tree-level NLSM amplitudes based on hidden zeros

    hep-th 2025-08 unverdicted novelty 6.0 of 10

    A recursion for NLSM tree amplitudes based on hidden zeros reproduces the Adler zero, generates amplitudes from Tr(φ³) via δ-shift, expands them into bi-adjoint scalars, and claims these plus factorization uniquely de...

  7. Can Locality, Unitarity, and Hidden Zeros Completely Determine Tree-Level Amplitudes?

    hep-th 2026-04 unverdicted novelty 5.0 of 10

    Locality, unitarity, and hidden zeros determine tree-level YM and NLSM amplitudes by reconstructing their soft theorems.

  8. $2$-split from Feynman diagrams and Expansions

    hep-th 2025-08 unverdicted novelty 5.0 of 10

    Proof via Feynman diagrams that tree-level BAS⊕X amplitudes with X=YM,NLSM,GR obey 2-split under kinematic conditions, extended to pure X amplitudes with byproduct universal expansions of X currents into BAS currents.

  9. Soft theorems of tree-level ${\rm Tr}(\phi^3)$, YM and NLSM amplitudes from $2$-splits

    hep-th 2025-05 unverdicted novelty 5.0 of 10

    Extends a 2-split factorization approach to reproduce known leading and sub-leading soft theorems for Tr(φ³) and YM single-soft and NLSM double-soft amplitudes while deriving higher-order universal forms and a kinemat...

  10. Hidden Zeros and $2$-split via BCFW Recursion Relation

    hep-th 2025-04 unverdicted novelty 4.0 of 10

    Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.

  11. Note on hidden zeros and expansions of tree-level amplitudes

    hep-th 2025-02 unverdicted novelty 4.0 of 10

    Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.

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