Pith. sign in

REVIEW 2 major objections 6 minor 2 cited by

On-shell recursion relations for higher-spin Compton amplitudes

T0 review · 2 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read For minimal higher-spin couplings, the all-line transverse shift uniquely constructs four-point photon Compton amplitudes up to spin 3/2 and graviton Compton amplitudes up to spin 5/2, with no spurious poles or contact-term ambiguity.

desk verdict The four-point Compton amplitudes for spin-3/2 photon and spin-5/2 graviton are carefully derived, unambiguous, and match an independent benchmark; the higher-point constructibility proof is softer than the abstract suggests. read the letter →

arxiv 2506.02106 v1 pith:RIWRBM2Z submitted 2025-06-02 hep-th gr-qchep-ph

Yohei Ema , Ting Gao , Wenqi Ke , Zhen Liu , Ishmam Mahbub This is my paper
classification hep-thgr-qchep-ph
keywords on-shellrecursionall-linetransverseshifthigher-spinComptonamplitudesmassivespinor-helicityformalismspuriouspolescurrentconstraintgravitationalscatteringblack-hole
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper is trying to prove that the four-point Compton amplitude—one photon or graviton scattering off a massive spinning particle—is completely fixed by the simplest three-point on-shell amplitude, with no free contact terms, provided the spin is not too high and the three-point interaction is the 'minimal' one selected by the current constraint $\partial_\mu J^\mu = O(m)$. The proof works through the all-line transverse momentum shift, which deforms all external momenta in a way that makes the shifted amplitude vanish at infinity; then a Cauchy residue sum over physical poles reconstructs the full answer. The explicit outcomes are unique four-point amplitudes for $s \leq 3/2$ photon scattering and $s \leq 5/2$ graviton scattering, given in Eqs. (3.25), (3.35), (4.14), and (4.21), with no spurious poles and no contact-term ambiguity. A sympathetic reader should care because these amplitudes are the on-shell building blocks for classical spinning-black-hole scattering and for any future consistent theory of massive higher-spin particles, where a complete Lagrangian is not known.

What carries the argument

The central object is the all-line transverse (ALT) momentum shift, which deforms every external momentum by a multiple of that particle's transverse polarization vector while preserving on-shell conditions and total momentum. Because the external polarization vectors of the transverse massive modes are not changed by the shift, the large-$z$ behavior of the shifted amplitude is controlled by Ward identities and by a dimensional bound on the kinematic factor $F = N/D$; combined with the current constraint $\partial_\mu J^\mu = O(m)$, this yields $\gamma < 0$ and hence a vanishing boundary term $B_\infty$. The recursion then reduces the four-point amplitude to the sum of residues at physical factorization poles, and the little-group covariance of the final answer is the check that no $B_\infty$ was missed.

What would settle it

Take an explicit off-shell Lagrangian for a spin-3/2 charged particle that realizes the current constraint and compute the opposite-helicity four-point photon amplitude by Feynman diagrams; if the result differs from Eq. (3.25), the ALT recursion missed a contact term and $B_\infty$ is nonzero. The same test for spin-5/2 gravity against Eq. (4.14) would settle the gravitational claim, and the paper already exhibits the signature of failure for $s=2$ photon and $s=3$ graviton, where different shift vectors give different factorized parts.

Watch

Extended reading notes

Core claim

The paper's central claim is that the four-point electromagnetic and gravitational Compton amplitudes are on-shell constructible—uniquely determined by the on-shell three-point amplitude—for massive spin $s \leq 3/2$ (photon) and $s \leq 5/2$ (graviton), provided the three-point input is the 'minimal' amplitude selected by the current constraint $\partial_\mu J^\mu = O(m)$. Under the all-line transverse (ALT) shift, the boundary contribution $B_\infty$ vanishes by dimensional analysis, so the recursion reduces the four-point amplitude to a sum over physical poles; the spurious poles that plague naive gluing are cancelled automatically rather than subtracted by hand. The resulting amplitudes, Eqs. (3.25) and (3.35) for photons and Eqs. (4.14) and (4.21) for gravitons, are little-group covariant and match the previous results of [29] obtained by spurious-pole subtraction. For $s = 2$ photon and $s = 3$ graviton, the factorized part retains dependence on the shift vector, which the paper reads as a signal that $B_\infty \neq 0$ and that contact terms are not fixed by the three-point data.

Load-bearing premise

The construction stands on the assumption that the interaction singled out by the vanishing-current condition is backed by an off-shell theory whose propagators never produce $1/m$ blow-ups, so the recursion's omitted boundary contribution is zero; the paper verifies this backing only up to spin-3/2 electrodynamics and spin-5/2 gravity.

Editorial extensions

If this is right

  • If the boundary term really vanishes, the four-point amplitudes for $s=3/2$ photon and $s=5/2$ graviton are unique consequences of three-point data, so any off-shell Lagrangian that produces the same three-point amplitudes must reproduce Eqs. (3.25), (3.35), (4.14), and (4.21) exactly.
  • The dimensional analysis extends to amplitudes with more than two photons or gravitons: for $s \leq 3/2$ electromagnetic and $s \leq 5/2$ gravitational cases, higher-point Compton amplitudes are also constructible under the ALT shift regardless of helicity combination.
  • The recursion turns the earlier spurious-pole subtraction recipe into a derivation: the cancellation is automatic, which removes the ambiguity of how much to subtract.
  • For $s \geq 2$ photon and $s \geq 3$ graviton minimal cases, the factorized part depends on the shift vector, so boundary terms and contact terms are required; those cases cannot be fixed by three-point amplitudes alone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A sharper large-$z$ bound might rescue non-minimal couplings: the factorized part for non-minimal spin-3/2 photon is already shift-independent, suggesting $B_\infty$ may vanish there despite the paper's conservative dimensional analysis.
  • The same recursion, applied to amplitudes with an extra massless leg, could be used to bootstrap higher-multiplicity spinning-black-hole Compton amplitudes; the paper leaves this implicit.
  • The high-energy growth found in the helicity tables—$E^4$ for photon and $E^8$ for graviton opposite-helicity entries—means these minimal theories need extra degrees of freedom near a low cutoff; on-shell recursion could test proposed completions by requiring the growth to cancel.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper applies the all-line transverse (ALT) momentum shift to construct tree-level Compton amplitudes for massive higher-spin particles coupled to photons and gravitons. Starting from the minimal three-point amplitudes, the authors use dimensional analysis to argue that four-point photon Compton amplitudes are constructible for s<=3/2 and graviton Compton amplitudes for s<=5/2, and they further claim that higher-point amplitudes are constructible for these spins. The concrete results are explicit four-point amplitudes: Eqs. (3.25) and (3.35) for the spin-3/2 photon case, and Eqs. (4.14) and (4.21) for the spin-5/2 graviton case. The paper demonstrates that these amplitudes are independent of the shift parameters q_i, are free of spurious poles, and agree with the independent results of Ref. [29]. It also studies non-minimal spin-3/2 photon couplings, finding q_i-independent factorized parts, and shows for spin-2 photon and spin-3 graviton amplitudes that the factorized part retains q_i dependence, indicating loss of constructibility.

Significance. The four-point results are a solid and useful contribution. The ALT shift provides a concrete, shift-based derivation of the spurious-pole-subtracted amplitudes, the computations are detailed and internally consistent, and the agreement with the independent calculation of Ref. [29] is strong evidence that the four-point amplitudes are correct. The paper also gives a useful diagnostic for non-constructibility: residual q_i dependence of the factorized part. The authors are honest about the main limitation, noting in Sec. 3.1 that the dimensional analysis gives only an upper bound and in Sec. 2.2 that the current-constraint/minimal-amplitude correspondence is verified only up to spin-3/2 gauge theory and spin-5/2 gravity. However, the advertised higher-point constructibility goes beyond what is proven, and this gap is load-bearing for the abstract's central claim.

major comments (2)
  1. [Sec. 3.1 and Sec. 5] The constructibility claim for n>4 is not established. The bound gamma<=[F] in Eq. (3.5) assumes that the kinematic factor F has no 1/m-divergent contributions, so that the number of momentum insertions in the numerator never exceeds the mass dimension of N. The paper argues that the current constraint d.J=O(m) excludes such contributions, but the correspondence between the minimal three-point amplitude and this constraint is verified only at three-point level, up to spin-3/2 gauge theory and spin-5/2 gravity (Sec. 2.2 and App. B). For n>=5, even for these spins, the massive propagators contain p_mu p_nu/m^2 pieces, and the paper does not demonstrate that O(m) current conservation prevents these terms from generating extra z-growth in every higher-point diagram. Therefore the abstract and conclusion statements that higher-point Compton amplitudes are constructible are stronger than the dimensional analysis in Sec. 3.1 proves. The four-point results are not affected by this gap, but the n>4 claim needs either a proof under the stated assumptions or a softening to a conjecture/expectation.
  2. [Sec. 2.4 and Secs. 3.2.1/4.1.1] The presentation of the four-point constructibility proof should more sharply separate the necessary and sufficient conditions. Sec. 2.4 correctly notes that q_i-independence of the factorized part is only a necessary condition for B_infty=0, not sufficient. However, in the derivations of the spin-3/2 and spin-5/2 amplitudes, B_infty=0 is set using the dimensional-analysis upper bound, and the subsequent q_i-independence is presented as the confirmation. What actually anchors the four-point result is the explicit agreement with Ref. [29], obtained by a different method; the paper should state this explicitly, since without that external check the dimensional-analysis bound alone would not exclude a q_i-independent boundary contribution.
minor comments (6)
  1. [Sec. 5, first paragraph] The word 'antsaz' is a typo and should read 'ansatz'.
  2. [App. A, near Eq. (A.8)] The phrase 'time and parity revarsal' should read 'time and parity reversal'.
  3. [Sec. 3.1, last paragraph] The sentence 'the dimension of the couplings is limited to be less than or equal to 5' is ambiguous; it should say 'the mass dimension of the couplings' or 'operators of dimension at most five'.
  4. [Tables 1 and 2] The notation 'E-3', 'E2', etc. is ambiguous; use superscripts E^{-3}, E^2, or explicitly state that negative powers are intended.
  5. [Sec. 4, footnote 10] The restriction that interactions are up to dimension 6 is important for the bound [g]>=-4 used in Eq. (4.1); this condition should be stated in the main text before Eq. (4.1), not only in a footnote.
  6. [Sec. 3.2.2, after Eq. (3.57)] The numerical check that different choices of q_i give different results is not documented. Since the non-constructibility claim for spin-2 relies on this check, please provide the explicit q_i choices or a reproducible numerical example.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: four-point Compton amplitudes are obtained by Cauchy recursion from three-point input with no parameter fitted to the target; matching [29] is an external benchmark check.

full rationale

The derivation chain is self-contained in the relevant sense. The minimal three-point amplitude (2.11) is taken as input; the current constraint ∂·J=O(m) from external references [29,72,73] selects it. The ALT shift is then applied, and the dimensional analysis in Sec. 3.1 bounds the large-z behavior, setting B∞=0 for s≤3/2 (photon) and s≤5/2 (graviton) under an explicitly stated assumption that the kinematic factor F has no 1/m-divergent contributions. The four-point amplitude is assembled from factorized products of three-point amplitudes via the residue sum in Eq. (2.15), with no free parameter fitted to the four-point result. The outputs in Eqs. (3.25)/(3.35) and (4.14)/(4.21) are checked against the independent external result [29]. The paper itself flags the limitations: 'the correspondence between the minimal amplitude and the current constraint can be verified up to spin-3/2 gauge theory and spin-5/2 gravity', and 'our analysis provides only an upper bound on the z-scaling of the amplitude'. These are unsupported-generalization or correctness risks for the n≥5 constructibility claim, not circular reductions: the four-point amplitude is not defined in terms of the prediction, and no fitted parameter is renamed as a prediction. The self-citations [69-71] supply the ALT shift technique, but the recursion step and dimensional analysis are re-derived in this paper, so those citations are not load-bearing in a circular sense.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central construction is parameter-free: the minimal three-point amplitudes are fixed by the current constraint (l1=2, l2=-1/2 for spin-3/2 photon), and no number is fitted to the four-point output. The main axioms are the standard spinor-helicity formalism, the Cauchy-based recursion relation, the existence of the ALT shift solution, and the domain assumption that the current constraint removes 1/m-divergent contributions from the kinematic factors. No new entities are postulated.

free parameters (2)
  • l1 = 2 (minimal), otherwise free
    Coefficient of the dimension-five operator in the spin-3/2 photon three-point amplitude (App. B.1). Set by current constraint in the minimal case; explored for general values in Sec. 3.2.1 without affecting the central constructibility claim.
  • l2 = -1/2 (minimal), otherwise free
    Second coefficient of the spin-3/2 photon three-point amplitude (App. B.1); same status as l1.
assumptions (6)
  • standard math Massive spinor-helicity formalism with SU(2) little-group indices
    Used throughout Sec. 2.1 and App. A to represent arbitrary-spin amplitudes; not derived in this paper.
  • standard math On-shell recursion via Cauchy's theorem (Eqs. (2.14)-(2.15))
    Basis of the recursion; assumes meromorphy of the shifted amplitude and validity of contour deformation.
  • domain assumption Existence of ALT shift solutions satisfying momentum conservation
    Sec. 2.4 argues four constraints on c_i can be met; used for all shifts in the paper.
  • domain assumption Minimal three-point amplitudes satisfy the current constraint ∂·J=O(m)
    Sec. 2.2 and App. B; verified up to spin-3/2 gauge theory and spin-5/2 gravity, cited to [29,72,73,76]. This selects the input amplitudes.
  • domain assumption No 1/m-divergent contributions in the ALT-shift kinematic factor F
    Explicit assumption in Sec. 3.1 governing the dimensional-analysis bound; if violated, B∞ may be nonzero and constructibility fails.
  • domain assumption Ward identities of external photons/gravitons improve large-z behavior
    Sec. 2.4 and Sec. 3.1; the improvement by 1/z per massless leg is central to making γ<0.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On-shell recursion relations for higher-spin Compton amplitudes." pith.science (2026). https://pith.science/paper/RIWRBM2Z

@misc{pith2026250602106,
  author       = {Pith},
  title        = {Pith review of: On-shell recursion relations for higher-spin Compton amplitudes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RIWRBM2Z}},
  note         = {Machine review of arXiv:2506.02106}
}
abstract

We recursively construct tree-level electromagnetic and gravitational Compton amplitudes of higher-spin massive particles by the all-line transverse momentum shift. With three-point amplitude as input, we demonstrate that higher-point electromagnetic and gravitational Compton amplitudes are on-shell constructible up to spin $s = 3/2$ and $s = 5/2$, respectively, under the all-line transverse shift after imposing the current constraint condition. We unambiguously derive the four-point electromagnetic and gravitational Compton amplitudes for $s \leq 3/2$ and $s \leq 5/2$, which are uniquely determined by the on-shell recursion relation and are free from unphysical spurious poles. In addition, we explore amplitudes of spin-$3/2$ particles with non-minimal three-point interactions with photon, as well as $s > 3/2$ particles, and comment on their notable features. Our work furthers the understanding of on-shell methods for massive amplitudes, with hopes to shed light on physical observables in particle physics and higher-spin amplitudes relevant for Kerr black-hole scattering.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

  1. (Super)$\,$Gravity from Positivity

    hep-th 2025-07 conditional novelty 8.0 of 10

    Positivity of scattering amplitudes forces weakly coupled EFTs of a massive spin-3/2 particle to include gravity, and for charged states a gauged photon with g=2 and WGC-saturating charge.

  2. Supergravity from the Bottom Up

    hep-th 2025-07 conditional novelty 7.0 of 10

    Massive spin-3/2 fermion interactions are consistent up to the Planck scale only in broken supergravity, with gravity required by unitarity and the Ward identity.

Reference graph

Works this paper leans on

77 extracted references · 13 canonical work pages · cited by 2 Pith papers

  1. [29]

    Compton black-hole scattering for s≤5/2,

    M. Chiodaroli, H. Johansson, and P. Pichini, “Compton black-hole scattering for s≤5/2,” JHEP02(2022) 156,arXiv:2107.14779 [hep-th]

    arXiv 2022

  2. [1]

    New recursion relations for tree amplitudes of gluons,

    R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl. Phys. B715(2005) 499–522,arXiv:hep-th/0412308

    arXiv 2005

  3. [2]

    Direct proof of tree-level recursion relation in Yang-Mills theory,

    R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,”Phys. Rev. Lett.94(2005) 181602,arXiv:hep-th/0501052

    arXiv 2005

  4. [3]

    A Recursion relation for gravity amplitudes,

    J. Bedford, A. Brandhuber, B. J. Spence, and G. Travaglini, “A Recursion relation for gravity amplitudes,”Nucl. Phys. B721(2005) 98–110,arXiv:hep-th/0502146

    arXiv 2005

  5. [4]

    Tree level recursion relations in general relativity,

    F. Cachazo and P. Svrcek, “Tree level recursion relations in general relativity,” arXiv:hep-th/0502160

    arXiv

  6. [5]

    On-shell constructibility of tree amplitudes in general field theories,

    T. Cohen, H. Elvang, and M. Kiermaier, “On-shell constructibility of tree amplitudes in general field theories,”JHEP04(2011) 053,arXiv:1010.0257 [hep-th]

    arXiv 2011

  7. [6]

    On-shell Recursion in String Theory

    R. H. Boels, D. Marmiroli, and N. A. Obers, “On-shell Recursion in String Theory,”JHEP10 (2010) 034,arXiv:1002.5029 [hep-th]

    work page Pith review arXiv 2010

  8. [7]

    BCFW Recursion Relations and String Theory

    C. Cheung, D. O’Connell, and B. Wecht, “BCFW Recursion Relations and String Theory,” JHEP09(2010) 052,arXiv:1002.4674 [hep-th]

    work page Pith review arXiv 2010

Show all 77 references
  1. [8]

    The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM,

    N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, S. Caron-Huot, and J. Trnka, “The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM,”JHEP01(2011) 041, arXiv:1008.2958 [hep-th]

    2011 arXiv

  2. [9]

    Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory,

    D. Gang, Y.-t. Huang, E. Koh, S. Lee, and A. E. Lipstein, “Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory,”JHEP03(2011) 116,arXiv:1012.5032 [hep-th]

    2011 arXiv

  3. [10]

    On-Shell Recursion Relations for Effective Field Theories,

    C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, and J. Trnka, “On-Shell Recursion Relations for Effective Field Theories,”Phys. Rev. Lett.116(2016) no. 4, 041601,arXiv:1509.03309 [hep-th]

    2016 arXiv

  4. [11]

    Recursion relations from soft theorems,

    H. Luo and C. Wen, “Recursion relations from soft theorems,”JHEP03(2016) 088, arXiv:1512.06801 [hep-th]

    2016 arXiv

  5. [12]

    Soft Bootstrap and Supersymmetry,

    H. Elvang, M. Hadjiantonis, C. R. T. Jones, and S. Paranjape, “Soft Bootstrap and Supersymmetry,”JHEP01(2019) 195,arXiv:1806.06079 [hep-th]

    2019 arXiv

  6. [13]

    Notes on Conformal Soft Theorems and Recursion Relations in Gravity,

    A. Guevara, “Notes on Conformal Soft Theorems and Recursion Relations in Gravity,” arXiv:1906.07810 [hep-th]

    1906 arXiv

  7. [14]

    Spinning gravitating objects in the effective field theory in the post-Newtonian scheme,

    M. Levi and J. Steinhoff, “Spinning gravitating objects in the effective field theory in the post-Newtonian scheme,”JHEP09(2015) 219,arXiv:1501.04956 [gr-qc]

    2015 arXiv

  8. [15]

    Spin-multipole effects in binary black holes and the test-body limit,

    J. Vines and J. Steinhoff, “Spin-multipole effects in binary black holes and the test-body limit,” Phys. Rev. D97(2018) no. 6, 064010,arXiv:1606.08832 [gr-qc]. 28

    2018 arXiv

  9. [16]

    Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings,

    J. Vines, “Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings,”Class. Quant. Grav.35(2018) no. 8, 084002, arXiv:1709.06016 [gr-qc]

    2018 arXiv

  10. [17]

    Leading Singularities and Classical Gravitational Scattering,

    F. Cachazo and A. Guevara, “Leading Singularities and Classical Gravitational Scattering,” JHEP02(2020) 181,arXiv:1705.10262 [hep-th]

    2020 arXiv

  11. [18]

    Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering,

    A. Guevara, “Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering,”JHEP04(2019) 033,arXiv:1706.02314 [hep-th]

    2019 arXiv

  12. [19]

    Scattering amplitudes for all masses and spins,

    N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang, “Scattering amplitudes for all masses and spins,”JHEP11(2021) 070,arXiv:1709.04891 [hep-th]

    2021 arXiv

  13. [20]

    Scattering of Spinning Black Holes from Exponentiated Soft Factors,

    A. Guevara, A. Ochirov, and J. Vines, “Scattering of Spinning Black Holes from Exponentiated Soft Factors,”JHEP09(2019) 056,arXiv:1812.06895 [hep-th]

    2019 arXiv

  14. [21]

    The simplest massive S-matrix: from minimal coupling to Black Holes,

    M.-Z. Chung, Y.-T. Huang, J.-W. Kim, and S. Lee, “The simplest massive S-matrix: from minimal coupling to Black Holes,”JHEP04(2019) 156,arXiv:1812.08752 [hep-th]

    2019 arXiv

  15. [22]

    Black-hole scattering with general spin directions from minimal-coupling amplitudes,

    A. Guevara, A. Ochirov, and J. Vines, “Black-hole scattering with general spin directions from minimal-coupling amplitudes,”Phys. Rev. D100(2019) no. 10, 104024,arXiv:1906.10071 [hep-th]

    2019 arXiv

  16. [23]

    Double copy for massive quantum particles with spin,

    H. Johansson and A. Ochirov, “Double copy for massive quantum particles with spin,”JHEP09 (2019) 040,arXiv:1906.12292 [hep-th]

    2019 arXiv

  17. [24]

    Kerr black holes as elementary particles,

    N. Arkani-Hamed, Y.-t. Huang, and D. O’Connell, “Kerr black holes as elementary particles,” JHEP01(2020) 046,arXiv:1906.10100 [hep-th]

    2020 arXiv

  18. [25]

    Heavy Black Hole Effective Theory,

    P. H. Damgaard, K. Haddad, and A. Helset, “Heavy Black Hole Effective Theory,”JHEP11 (2019) 070,arXiv:1908.10308 [hep-ph]

    2019 arXiv

  19. [26]

    Spinning black hole binary dynamics, scattering amplitudes, and effective field theory,

    Z. Bern, A. Luna, R. Roiban, C.-H. Shen, and M. Zeng, “Spinning black hole binary dynamics, scattering amplitudes, and effective field theory,”Phys. Rev. D104(2021) no. 6, 065014, arXiv:2005.03071 [hep-th]

    2021 arXiv

  20. [27]

    On-shell heavy particle effective theories,

    R. Aoude, K. Haddad, and A. Helset, “On-shell heavy particle effective theories,”JHEP05 (2020) 051,arXiv:2001.09164 [hep-th]

    2020 arXiv

  21. [28]

    Scattering in black hole backgrounds and higher-spin amplitudes. Part I,

    Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, “Scattering in black hole backgrounds and higher-spin amplitudes. Part I,”JHEP03(2023) 136,arXiv:2107.10179 [hep-th]

    2023 arXiv

  22. [30]

    The 2PM Hamiltonian for binary Kerr to quartic in spin,

    W.-M. Chen, M.-Z. Chung, Y.-t. Huang, and J.-W. Kim, “The 2PM Hamiltonian for binary Kerr to quartic in spin,”JHEP08(2022) 148,arXiv:2111.13639 [hep-th]

    2022 arXiv

  23. [31]

    Kerr Black Holes From Massive Higher-Spin Gauge Symmetry,

    L. Cangemi, M. Chiodaroli, H. Johansson, A. Ochirov, P. Pichini, and E. Skvortsov, “Kerr Black Holes From Massive Higher-Spin Gauge Symmetry,”Phys. Rev. Lett.131(2023) no. 22, 221401, arXiv:2212.06120 [hep-th]. 29

    2023 arXiv

  24. [32]

    Classical Gravitational Spinning-Spinless Scattering at O(G2S∞),

    R. Aoude, K. Haddad, and A. Helset, “Classical Gravitational Spinning-Spinless Scattering at O(G2S∞),”Phys. Rev. Lett.129(2022) no. 14, 141102,arXiv:2205.02809 [hep-th]

    2022 arXiv

  25. [33]

    Searching for Kerr in the 2PM amplitude,

    R. Aoude, K. Haddad, and A. Helset, “Searching for Kerr in the 2PM amplitude,”JHEP07 (2022) 072,arXiv:2203.06197 [hep-th]

    2022 arXiv

  26. [34]

    Binary Dynamics through the Fifth Power of Spin at O(G2),

    Z. Bern, D. Kosmopoulos, A. Luna, R. Roiban, and F. Teng, “Binary Dynamics through the Fifth Power of Spin at O(G2),”Phys. Rev. Lett.130(2023) no. 20, 201402,arXiv:2203.06202 [hep-th]

    2023 arXiv

  27. [35]

    Scattering in black hole backgrounds and higher-spin amplitudes. Part II,

    Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, “Scattering in black hole backgrounds and higher-spin amplitudes. Part II,”JHEP05(2023) 211,arXiv:2212.07965 [hep-th]

    2023 arXiv

  28. [36]

    Classical gravitational scattering amplitude at O(G2S1∞S2∞),

    R. Aoude, K. Haddad, and A. Helset, “Classical gravitational scattering amplitude at O(G2S1∞S2∞),”Phys. Rev. D108(2023) no. 2, 024050,arXiv:2304.13740 [hep-th]

    2023 arXiv

  29. [37]

    From higher-spin gauge interactions to Compton amplitudes for root-Kerr,

    L. Cangemi, M. Chiodaroli, H. Johansson, A. Ochirov, P. Pichini, and E. Skvortsov, “From higher-spin gauge interactions to Compton amplitudes for root-Kerr,”JHEP09(2024) 196, arXiv:2311.14668 [hep-th]

    2024 arXiv

  30. [38]

    Compton Amplitude for Rotating Black Hole from QFT,

    L. Cangemi, M. Chiodaroli, H. Johansson, A. Ochirov, P. Pichini, and E. Skvortsov, “Compton Amplitude for Rotating Black Hole from QFT,”Phys. Rev. Lett.133(2024) no. 7, 071601, arXiv:2312.14913 [hep-th]

    2024 arXiv

  31. [39]

    Black hole perturbation theory meets CFT2: Kerr-Compton amplitudes from Nekrasov-Shatashvili functions,

    Y. F. Bautista, G. Bonelli, C. Iossa, A. Tanzini, and Z. Zhou, “Black hole perturbation theory meets CFT2: Kerr-Compton amplitudes from Nekrasov-Shatashvili functions,”Phys. Rev. D 109(2024) no. 8, 084071,arXiv:2312.05965 [hep-th]

    2024 arXiv

  32. [40]

    Recursion in the classical limit and the neutron-star Compton amplitude,

    K. Haddad, “Recursion in the classical limit and the neutron-star Compton amplitude,”JHEP 05(2023) 177,arXiv:2303.02624 [hep-th]

    2023 arXiv

  33. [41]

    On-shell approach to (spinning) gravitational absorption processes,

    Y.-J. Chen, T. Hsieh, Y.-T. Huang, and J.-W. Kim, “On-shell approach to (spinning) gravitational absorption processes,”arXiv:2312.04513 [hep-th]

    arXiv

  34. [42]

    Binary Kerr black-hole scattering at 2PM from quantum higher-spin Compton,

    L. Bohnenblust, L. Cangemi, H. Johansson, and P. Pichini, “Binary Kerr black-hole scattering at 2PM from quantum higher-spin Compton,”arXiv:2410.23271 [hep-th]

    arXiv

  35. [43]

    Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons,

    Y. Shadmi and Y. Weiss, “Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons,”JHEP02(2019) 165,arXiv:1809.09644 [hep-ph]

    2019 arXiv

  36. [44]

    Constructive standard model,

    N. Christensen and B. Field, “Constructive standard model,”Phys. Rev. D98(2018) no. 1, 016014,arXiv:1802.00448 [hep-ph]

    2018 arXiv

  37. [45]

    The Rise of SMEFT On-shell Amplitudes,

    R. Aoude and C. S. Machado, “The Rise of SMEFT On-shell Amplitudes,”JHEP12(2019) 058, arXiv:1905.11433 [hep-ph]

    2019 arXiv

  38. [46]

    The electroweak effective field theory from on-shell amplitudes,

    G. Durieux, T. Kitahara, Y. Shadmi, and Y. Weiss, “The electroweak effective field theory from on-shell amplitudes,”JHEP01(2020) 119,arXiv:1909.10551 [hep-ph]

    2020 arXiv

  39. [47]

    Two-, three-, and four-body decays in the constructive standard model,

    N. Christensen, B. Field, A. Moore, and S. Pinto, “Two-, three-, and four-body decays in the constructive standard model,”Phys. Rev. D101(2020) no. 6, 065019,arXiv:1909.09164 [hep-ph]. 30

    2020 arXiv

  40. [48]

    Constructing massive on-shell contact terms,

    G. Durieux, T. Kitahara, C. S. Machado, Y. Shadmi, and Y. Weiss, “Constructing massive on-shell contact terms,”JHEP12(2020) 175,arXiv:2008.09652 [hep-ph]

    2020 arXiv

  41. [49]

    On-shell Higgsing for EFTs,

    R. Balkin, G. Durieux, T. Kitahara, Y. Shadmi, and Y. Weiss, “On-shell Higgsing for EFTs,” JHEP03(2022) 129,arXiv:2112.09688 [hep-ph]

    2022 arXiv

  42. [50]

    An EFT hunter’s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes,

    H. Liu, T. Ma, Y. Shadmi, and M. Waterbury, “An EFT hunter’s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes,”JHEP05(2023) 241,arXiv:2301.11349 [hep-ph]

    2023 arXiv

  43. [51]

    A complete set of 4-point amplitudes in the constructive Standard Model,

    N. Christensen, “A complete set of 4-point amplitudes in the constructive Standard Model,” Eur. Phys. J. C84(2024) no. 6, 620,arXiv:2403.07978 [hep-ph]

    2024 arXiv

  44. [52]

    Perturbative unitarity and the four-point vertices in the constructive standard model,

    N. Christensen, “Perturbative unitarity and the four-point vertices in the constructive standard model,”Phys. Rev. D109(2024) no. 11, 116014,arXiv:2403.07977 [hep-ph]

    2024 arXiv

  45. [53]

    ConstructingN= 4 Coulomb branch superamplitudes,

    A. Herderschee, S. Koren, and T. Trott, “ConstructingN= 4 Coulomb branch superamplitudes,”JHEP08(2019) 107,arXiv:1902.07205 [hep-th]

    2019 arXiv

  46. [54]

    Massive On-Shell Supersymmetric Scattering Amplitudes,

    A. Herderschee, S. Koren, and T. Trott, “Massive On-Shell Supersymmetric Scattering Amplitudes,”JHEP10(2019) 092,arXiv:1902.07204 [hep-th]

    2019 arXiv

  47. [55]

    Two-loopN= 1 SYM Amplitudes via SUSY Decomposition and Massive Spinor-Helicity,

    H. Johansson, G. K¨ alin, G. Mogull, and B. Verbeek, “Two-loopN= 1 SYM Amplitudes via SUSY Decomposition and Massive Spinor-Helicity,”arXiv:2312.17219 [hep-th]

    arXiv

  48. [56]

    Bounds on Amplitudes in Effective Theories with Massive Spinning Particles,

    J. Bonifacio and K. Hinterbichler, “Bounds on Amplitudes in Effective Theories with Massive Spinning Particles,”Phys. Rev. D98(2018) no. 4, 045003,arXiv:1804.08686 [hep-th]

    2018 arXiv

  49. [57]

    Universal bound on the strong coupling scale of a gravitationally coupled massive spin-2 particle,

    J. Bonifacio and K. Hinterbichler, “Universal bound on the strong coupling scale of a gravitationally coupled massive spin-2 particle,”Phys. Rev. D98(2018) no. 8, 085006, arXiv:1806.10607 [hep-th]

    2018 arXiv

  50. [58]

    Constraints on a gravitational Higgs mechanism,

    J. Bonifacio, K. Hinterbichler, and R. A. Rosen, “Constraints on a gravitational Higgs mechanism,”Phys. Rev. D100(2019) no. 8, 084017,arXiv:1903.09643 [hep-th]

    2019 arXiv

  51. [59]

    Massive Gravity from Double Copy,

    A. Momeni, J. Rumbutis, and A. J. Tolley, “Massive Gravity from Double Copy,”JHEP12 (2020) 030,arXiv:2004.07853 [hep-th]

    2020 arXiv

  52. [60]

    Massive double copy in the high-energy limit,

    M. C. Gonz´ alez, A. Momeni, and J. Rumbutis, “Massive double copy in the high-energy limit,” JHEP04(2022) 094,arXiv:2112.08401 [hep-th]

    2022 arXiv

  53. [61]

    Recursion relations for gauge theory amplitudes with massive particles,

    S. D. Badger, E. W. N. Glover, V. V. Khoze, and P. Svrcek, “Recursion relations for gauge theory amplitudes with massive particles,”JHEP07(2005) 025,arXiv:hep-th/0504159

    2005 arXiv

  54. [62]

    Recursion relations for gauge theory amplitudes with massive vector bosons and fermions,

    S. D. Badger, E. W. N. Glover, and V. V. Khoze, “Recursion relations for gauge theory amplitudes with massive vector bosons and fermions,”JHEP01(2006) 066, arXiv:hep-th/0507161

    2006 arXiv

  55. [63]

    Scattering amplitudes with massive fermions using BCFW recursion,

    K. J. Ozeren and W. J. Stirling, “Scattering amplitudes with massive fermions using BCFW recursion,”Eur. Phys. J. C48(2006) 159–168,arXiv:hep-ph/0603071

    2006 arXiv

  56. [64]

    CSW rules for a massive scalar,

    R. Boels and C. Schwinn, “CSW rules for a massive scalar,”Phys. Lett. B662(2008) 80–86, arXiv:0712.3409 [hep-th]. 31

    2008 arXiv

  57. [65]

    On-shell constructibility of Born amplitudes in spontaneously broken gauge theories,

    R. Franken and C. Schwinn, “On-shell constructibility of Born amplitudes in spontaneously broken gauge theories,”JHEP02(2020) 073,arXiv:1910.13407 [hep-th]

    2020 arXiv

  58. [66]

    Recursion relations for scattering amplitudes with massive particles,

    S. Ballav and A. Manna, “Recursion relations for scattering amplitudes with massive particles,” JHEP03(2021) 295,arXiv:2010.14139 [hep-th]

    2021 arXiv

  59. [67]

    Soft Matters, or the Recursions with Massive Spinors,

    A. Falkowski and C. S. Machado, “Soft Matters, or the Recursions with Massive Spinors,”JHEP 05(2021) 238,arXiv:2005.08981 [hep-th]

    2021 arXiv

  60. [68]

    Massive on-shell recursion relations for n-point amplitudes,

    C. Wu and S.-H. Zhu, “Massive on-shell recursion relations for n-point amplitudes,”JHEP06 (2022) 117,arXiv:2112.12312 [hep-th]

    2022 arXiv

  61. [69]

    Momentum shift and on-shell constructible massive amplitudes,

    Y. Ema, T. Gao, W. Ke, Z. Liu, K.-F. Lyu, and I. Mahbub, “Momentum shift and on-shell constructible massive amplitudes,”Phys. Rev. D110(2024) no. 10, 105003,arXiv:2403.15538 [hep-ph]

    2024 arXiv

  62. [70]

    Momentum shift and on-shell recursion relation for electroweak theory,

    Y. Ema, T. Gao, W. Ke, Z. Liu, K.-F. Lyu, and I. Mahbub, “Momentum shift and on-shell recursion relation for electroweak theory,”Phys. Rev. D110(2024) no. 10, 105002, arXiv:2407.14587 [hep-ph]

    2024 arXiv

  63. [71]

    Effective interactions and on-shell recursion relation for massive spin 3/2,

    T. Gherghetta and W. Ke, “Effective interactions and on-shell recursion relation for massive spin 3/2,”arXiv:2408.16065 [hep-ph]

    arXiv

  64. [72]

    Tree level unitarity constraints on the gravitational couplings of higher spin massive fields,

    A. Cucchieri, M. Porrati, and S. Deser, “Tree level unitarity constraints on the gravitational couplings of higher spin massive fields,”Phys. Rev. D51(1995) 4543–4549, arXiv:hep-th/9408073

    1995 arXiv

  65. [73]

    Massive spin 5/2 fields coupled to gravity: Tree level unitarity versus the equivalence principle,

    M. Porrati, “Massive spin 5/2 fields coupled to gravity: Tree level unitarity versus the equivalence principle,”Phys. Lett. B304(1993) 77–80,arXiv:gr-qc/9301012

    1993 arXiv

  66. [74]

    Simple Recursion Relations for General Field Theories,

    C. Cheung, C.-H. Shen, and J. Trnka, “Simple Recursion Relations for General Field Theories,” JHEP06(2015) 118,arXiv:1502.05057 [hep-th]

    2015 arXiv

  67. [75]

    Spin-3/2 and spin-2 charged massive states in a constant electromagnetic background,

    K. Benakli, C. A. Daniel, and W. Ke, “Spin-3/2 and spin-2 charged massive states in a constant electromagnetic background,”JHEP03(2023) 212,arXiv:2302.06630 [hep-th]

    2023 arXiv

  68. [76]

    Massive spin 3/2 electrodynamics,

    S. Deser, V. Pascalutsa, and A. Waldron, “Massive spin 3/2 electrodynamics,”Phys. Rev. D62 (2000) 105031,arXiv:hep-th/0003011

    2000 arXiv

  69. [77]

    Lagrangian formulation for arbitrary spin. 2. The fermion case,

    L. P. S. Singh and C. R. Hagen, “Lagrangian formulation for arbitrary spin. 2. The fermion case,”Phys. Rev. D9(1974) 910–920. 32

    1974

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.