arxiv: 2604.07195 · v1 · submitted 2026-04-08 · ✦ hep-th

Recognition: no theorem link

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

Kang Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:32 UTC · model grok-4.3

classification ✦ hep-th

keywords tree-level amplitudeslocalityunitarityhidden zerossoft theoremsYang-Millsnonlinear sigma model

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The pith

Locality, unitarity, and hidden zeros together fix the tree-level Yang-Mills and nonlinear sigma model amplitudes.

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

The paper reconstructs the single-soft theorems of tree-level Yang-Mills amplitudes and the double-soft theorems of tree-level nonlinear sigma model amplitudes directly from locality, unitarity, and the hidden zeros. Prior results already show that these soft theorems are sufficient to build the full amplitudes, so the three conditions suffice to determine the amplitudes completely. A sympathetic reader would see this as evidence that no further physical input is required beyond these three requirements at tree level.

Core claim

By deriving the soft theorems of tree-level Yang-Mills and nonlinear sigma model amplitudes solely from locality, unitarity, and hidden zeros, and invoking the known fact that the soft theorems determine the full amplitudes, the tree-level amplitudes in both theories are completely fixed by these three principles.

What carries the argument

Hidden zeros (vanishing of the amplitude when selected kinematic invariants are set to zero while others remain nonzero) that, together with locality and unitarity, enforce the required soft-limit behaviors.

Load-bearing premise

That the complete tree-level amplitudes can be reconstructed from the soft theorems alone.

What would settle it

An explicit counter-example function that obeys locality, unitarity, and the hidden zeros yet yields amplitudes different from the standard Yang-Mills or nonlinear sigma model expressions at tree level.

read the original abstract

In this note, we address the question of whether locality, unitarity, and newly discovered hidden zeros can completely determine tree-level amplitudes, from the perspective of soft limit. We reconstruct the single-soft theorems of tree YM amplitudes and the double-soft theorems of tree NLSM amplitudes from locality, unitarity, and hidden zeros. A series of studies have shown that the full YM and NLSM amplitudes can be constructed from these soft theorems; therefore, we conclude that locality, unitarity, and hidden zeros completely determine the tree-level YM and NLSM 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.

Desk Editor's Note private letter to a colleague

This note reconstructs the soft theorems for tree YM and NLSM from locality, unitarity, and hidden zeros, but the completeness claim for full amplitudes rests on external citations without an explicit match.

read the letter

This note reconstructs the single-soft theorems for tree-level Yang-Mills amplitudes and the double-soft theorems for nonlinear sigma model amplitudes using only locality, unitarity, and hidden zeros. That reconstruction is the main new element here. The paper does well at showing how these three conditions constrain the soft behavior in a direct way. It starts from an ansatz for the amplitudes and imposes the conditions to fix the soft factors. This approach highlights the power of hidden zeros in combination with the more standard principles, and it stays away from explicit Feynman diagram calculations or Lagrangians. The derivation for the soft limits appears clean based on the abstract and the described method. The soft spot is the jump to the full amplitudes. The author relies on earlier papers that claim the soft theorems are enough to determine the complete tree-level amplitudes. There is no explicit check here that the derived soft theorems match those in the literature exactly, including any subleading terms or normalizations. If they do not match perfectly, the completeness claim would not follow. This reliance is stated openly, but it leaves the argument less closed than the title suggests. The math looks solid for the reconstruction part, with no obvious inconsistencies in the approach described. Citations point to the relevant prior work on soft theorems and hidden zeros. This paper is for people working on amplitude methods in gauge theories and effective field theories. A reader who knows the soft theorem constructions will get the most value and can assess the connection themselves. It deserves serious referee attention because the reconstruction step is a genuine addition to the literature on determining amplitudes from consistency conditions. I would send it for review.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates whether locality, unitarity, and hidden zeros suffice to completely determine tree-level Yang-Mills (YM) and Non-Linear Sigma Model (NLSM) amplitudes. The authors impose these three principles on a general amplitude ansatz to reconstruct the single-soft theorems for YM and the double-soft theorems for NLSM. They conclude that these principles determine the full amplitudes because prior literature has established that the (standard) soft theorems fix the complete tree-level expressions.

Significance. If the derived soft theorems match those used in the cited constructions and no additional constraints are required, the result would establish that locality, unitarity, and hidden zeros form a closed set of axioms sufficient for these amplitudes. This offers a compact perspective on amplitude determination and could motivate similar analyses in other theories. The explicit reconstruction step from the three principles to the soft factors is a concrete technical contribution, though the overall significance hinges on closing the link to the external results.

major comments (1)

The load-bearing step of the argument (abstract and concluding paragraph) identifies the reconstructed single-soft (YM) and double-soft (NLSM) factors with those shown in prior work to determine the full amplitudes, yet the manuscript supplies no explicit matching of the soft factors, normalizations, or higher-order terms. Without this verification, any discrepancy would invalidate the completeness claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for identifying a key point that strengthens the completeness argument. We address the major comment below.

read point-by-point responses

Referee: The load-bearing step of the argument (abstract and concluding paragraph) identifies the reconstructed single-soft (YM) and double-soft (NLSM) factors with those shown in prior work to determine the full amplitudes, yet the manuscript supplies no explicit matching of the soft factors, normalizations, or higher-order terms. Without this verification, any discrepancy would invalidate the completeness claim.

Authors: We agree that an explicit matching is necessary to close the logical chain. Our derivation produces specific soft factors from locality, unitarity, and hidden zeros, but the manuscript does not include a direct comparison (including overall normalizations and O(soft^2) and higher terms) against the expressions used in the cited works that reconstruct the full amplitudes. In the revised version we will add a dedicated subsection that performs this verification for both the single-soft YM and double-soft NLSM cases, confirming agreement to all orders in the soft expansion. This addition will make the completeness claim fully rigorous. revision: yes

Circularity Check

0 steps flagged

No circularity; soft theorems derived independently and linked via external literature.

full rationale

The paper reconstructs single-soft theorems for YM and double-soft theorems for NLSM by imposing locality, unitarity, and hidden zeros on an amplitude ansatz. It then cites prior studies showing that these soft theorems determine the full tree amplitudes, leading to the conclusion that the three principles suffice. No step reduces the claimed result to its inputs by construction: the soft-theorem derivation stands on its own, the cited constructions are external (not self-referential or redefined within the paper), and no fitted parameters, ansatz smuggling, or renaming of known results occurs. The argument is therefore non-circular, though its completeness claim depends on the accuracy of the external references.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The argument rests on the standard axioms of locality and unitarity plus the newly observed hidden zeros, together with the external claim that soft theorems determine the full amplitudes.

axioms (2)

domain assumption Locality and unitarity are sufficient to constrain soft behavior when combined with hidden zeros.
Invoked in the reconstruction of soft theorems from the three principles.
domain assumption Full tree amplitudes are uniquely determined by their soft theorems.
Cited as established by prior studies; this is the bridge to the final conclusion.

pith-pipeline@v0.9.0 · 5378 in / 1241 out tokens · 52104 ms · 2026-05-10T18:32:11.022458+00:00 · methodology

discussion (0)

Forward citations

Cited by 2 Pith papers

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

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

Reference graph

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