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arxiv: 2606.28245 · v1 · pith:74Z6GQFWnew · submitted 2026-06-26 · ✦ hep-th

Spinor-helicity formalism for continuous-spin particles

Thomas Basile , Xavier Bekaert , Felipe Figueroa , Evgeny Skvortsov This is my paper

Pith reviewed 2026-06-29 03:04 UTC · model grok-4.3

classification ✦ hep-th
keywords continuous-spin particlesspinor-helicity formalismscattering amplitudesinfinite-spin limitcollinear amplitudeshelicity states
0
0 comments X

The pith

A single two-component spinor builds asymptotic states for continuous-spin particles and yields their scattering amplitudes directly.

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

The paper introduces a formulation for continuous-spin particles that uses one two-component spinor to define their asymptotic states. This approach permits writing scattering amplitudes in a direct manner, mirroring the standard spinor-helicity method for massless particles. Helicity states appear naturally when the states are decomposed according to their homogeneity degree. The formulation also establishes that continuous-spin particle amplitudes arise as the infinite-spin limit of those for massive particles, with a universal factor that exponentiates in the process. Additionally, it identifies nontrivial collinear amplitudes for these particles, where the collinear momentum fractions are fixed by the particles' characteristic dimensionful parameter.

Core claim

Continuous-spin particles admit a spinor-helicity description in which a single two-component spinor constructs the asymptotic states. Amplitudes follow in the same straightforward manner as in the massless case. Helicity states arise upon decomposing into components of fixed homogeneity degree. The continuous-spin amplitudes are recovered as the infinite-spin limit of massive-particle amplitudes, with a universal factor that exponentiates. Nontrivial collinear amplitudes exist in which the momentum fractions are constrained by the dimensionful parameter that labels each continuous-spin particle.

What carries the argument

The single two-component spinor that constructs asymptotic states for continuous-spin particles, from which helicity components are extracted by homogeneity degree and amplitudes are obtained via the infinite-spin limit.

If this is right

  • Scattering amplitudes involving continuous-spin particles can be written using the same spinor techniques as massless particles.
  • A universal factor in the amplitudes exponentiates, in the same manner observed for black-hole scattering.
  • Collinear limits of continuous-spin amplitudes are nontrivial, with the splitting fractions fixed by the particles' dimensionful parameter.
  • Helicity states for continuous-spin particles emerge directly from the homogeneity decomposition of the spinor states.

Where Pith is reading between the lines

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

  • The formalism may simplify the construction of higher-point or loop amplitudes involving continuous-spin particles.
  • The constrained collinear fractions could impose new selection rules on allowed scattering channels.
  • Similar spinor methods might be applied to other exotic particle types whose states are not labeled by ordinary spin.

Load-bearing premise

That the infinite-spin limit of massive-particle amplitudes produces consistent continuous-spin amplitudes in which a universal factor exponentiates without inconsistencies or extra regularization.

What would settle it

An explicit calculation of a three-point or four-point amplitude in the infinite-spin limit that fails to reproduce the proposed spinor-helicity expression or violates collinear factorization.

read the original abstract

We propose a new formulation of continuous-spin particles (CSP) with the help of a single two-component spinor to build asymptotic states. This formulation allows to write down amplitudes in a straightforward way, similar to the massless spinor-helicity approach. The helicity states naturally emerge upon decomposing into components of a fixed homogeneity degree. We show that CSP amplitudes can be understood as the infinite-spin limit of amplitudes of massive particles and, similarly to the scattering of black holes, a certain universal factor exponentiates. In analogy with the recent discovery of collinear amplitudes in self-dual theories, we find nontrivial CSP collinear amplitudes where the collinear fractions are constrained by the dimensionful parameter characterising the various continuous-spin particles.

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

2 major / 2 minor

Summary. The paper proposes a spinor-helicity formalism for continuous-spin particles (CSP) constructed from a single two-component spinor to define asymptotic states. It claims this allows amplitudes to be written in a manner analogous to the massless spinor-helicity formalism, with helicity states emerging from fixed-homogeneity components; that CSP amplitudes arise as the infinite-spin limit of massive-particle amplitudes in which a universal factor exponentiates (analogous to black-hole scattering); and that nontrivial collinear amplitudes exist whose fractions are constrained by the dimensionful CSP parameter.

Significance. If the central construction is valid, the work supplies a concrete computational tool for CSP scattering that parallels established massless techniques and makes falsifiable predictions for collinear limits. The explicit link to the infinite-spin limit of massive amplitudes and the exponentiation statement, if accompanied by reproducible derivations, would constitute a useful bridge between massive and continuous-spin regimes.

major comments (2)
  1. [infinite-spin limit section] The central claim that CSP amplitudes are obtained as the infinite-spin limit of massive amplitudes with a universal factor that exponentiates without additional regularization is load-bearing for the entire formalism (§ on infinite-spin limit and collinear amplitudes). The manuscript must supply an explicit derivation or check that the limit commutes with the exponentiation and does not generate extra divergent terms from the continuous little-group parameter; absent this, the assertion that amplitudes can be written “in a straightforward way” remains unverified.
  2. [collinear amplitudes section] The statement that collinear fractions are constrained by the dimensionful CSP parameter (abstract and collinear-amplitudes section) requires an explicit formula or example showing how the constraint arises from the spinor construction and survives the infinite-spin limit. Without a concrete expression or numerical check, the nontriviality claim cannot be assessed.
minor comments (2)
  1. [asymptotic states section] Notation for the single two-component spinor and the homogeneity degree should be introduced with an explicit definition and comparison to the standard massless spinor-helicity variables.
  2. The abstract lists several results ('we show', 'we find') without pointers to the corresponding equations or sections; adding such cross-references would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The points raised highlight areas where additional explicit derivations will strengthen the presentation of the infinite-spin limit and collinear amplitudes. We address each major comment below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [infinite-spin limit section] The central claim that CSP amplitudes are obtained as the infinite-spin limit of massive amplitudes with a universal factor that exponentiates without additional regularization is load-bearing for the entire formalism (§ on infinite-spin limit and collinear amplitudes). The manuscript must supply an explicit derivation or check that the limit commutes with the exponentiation and does not generate extra divergent terms from the continuous little-group parameter; absent this, the assertion that amplitudes can be written “in a straightforward way” remains unverified.

    Authors: We agree that an explicit verification of the limit procedure is necessary to fully substantiate the claim. The manuscript derives the CSP amplitudes by taking the large-spin limit of the corresponding massive amplitudes, in which the universal factor exponentiates in direct analogy with black-hole scattering amplitudes. To address the referee's concern regarding commutation of the limit with exponentiation and possible divergences associated with the continuous little-group parameter, we will add a dedicated subsection (or appendix) containing the step-by-step limiting procedure. This will include an explicit check confirming that no additional regularization is required and that the limit yields the CSP amplitudes in a straightforward manner without extraneous divergent terms. revision: yes

  2. Referee: [collinear amplitudes section] The statement that collinear fractions are constrained by the dimensionful CSP parameter (abstract and collinear-amplitudes section) requires an explicit formula or example showing how the constraint arises from the spinor construction and survives the infinite-spin limit. Without a concrete expression or numerical check, the nontriviality claim cannot be assessed.

    Authors: The constraint on the collinear fractions originates from the fixed-homogeneity decomposition inherent to the single two-component spinor construction of the asymptotic states; the dimensionful CSP parameter enters as the scale that restricts the allowed momentum fractions in the collinear configuration. This structure is preserved under the infinite-spin limit because the massive amplitudes reduce to the CSP case while retaining the same homogeneity condition. We will expand the collinear-amplitudes section with an explicit formula for the constrained fractions together with a concrete example (including the infinite-spin limit) to demonstrate the nontriviality of the amplitudes. revision: yes

Circularity Check

0 steps flagged

No circularity: new formulation derived from spinor states, not reducing to inputs by construction

full rationale

The paper introduces a spinor-helicity construction for CSP asymptotic states using a single two-component spinor, from which amplitudes and helicity decomposition follow directly. The infinite-spin limit of massive amplitudes and exponentiation of a universal factor are presented as derived results (analogous to black-hole scattering), not as fitted parameters renamed as predictions. Collinear amplitudes are exhibited as a new consequence constrained by the CSP parameter. No self-definitional equations, fitted-input predictions, load-bearing self-citations, or ansatz smuggling appear in the abstract or described chain; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The formulation rests on the pre-existing spinor-helicity formalism for massless particles and the standard definition of continuous-spin representations; the dimensionful CSP parameter is introduced to label the particles and constrain collinear fractions.

free parameters (1)
  • dimensionful CSP parameter
    Characterises each continuous-spin particle and constrains allowed collinear momentum fractions; appears as an input rather than derived.
axioms (2)
  • domain assumption Standard spinor-helicity formalism applies to massless particles and can be extended to CSP states
    The new formulation is explicitly analogous to the massless case.
  • domain assumption Infinite-spin limit of massive amplitudes exists and yields well-defined CSP amplitudes
    Central to the claim that CSP amplitudes are the infinite-spin limit.

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discussion (0)

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Reference graph

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