arxiv: 2604.00107 · v2 · submitted 2026-03-31 · ✦ hep-ph · hep-th

Recognition: no theorem link

Full positivity bounds for anomalous quartic gauge couplings in SMEFT

Fu-Ming Chang , Zhuo-Yan Chen , Shuang-Yong Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-13 22:38 UTC · model grok-4.3

classification ✦ hep-ph hep-th

keywords positivity boundsanomalous quartic gauge couplingsSMEFTdimension-8 operatorselectroweak scatteringunitarityeffective field theoryLHC

0 comments

The pith

Complete positivity bounds for all 22 dimension-8 anomalous quartic gauge couplings severely restrict the allowed parameter space in SMEFT.

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

This paper derives the full set of positivity bounds on the 22 coefficients for dimension-8 anomalous quartic gauge couplings in the Standard Model Effective Field Theory. By analyzing scattering of all electroweak bosons, including longitudinal and parity-violating modes, the authors construct the extremal rays that define the cone of allowed coefficients. These bounds cut the naive parameter space down to just 0.0313 percent. The result matters for interpreting LHC data on vector boson scattering, as many apparent deviations would actually be unphysical. They also supply analytical linear bounds and a computational tool for checking specific cases.

Core claim

We derive the complete set of positivity bounds for the 22 dimension-8 aQGC coefficients by explicitly constructing the extremal rays of the positivity cone through a group-theoretic framework, using both direct construction and Casimir operator analysis to handle all electroweak boson modes, parity-violating operators, and parameter degeneracies, resulting in severe constraints on the physically viable parameter space.

What carries the argument

The extremal rays of the positivity cone for electroweak boson scattering amplitudes, constructed via group theory to enforce positivity from unitarity and causality.

If this is right

The allowed region for the 22 coefficients is only 0.0313% of the naive space.
Linear analytical bounds apply to various combinations of operators.
Any viable aQGC configuration must lie within the positivity cone verified by the methods.
The Python package enables numerical checks and optimization of bounds for general cases.

Where Pith is reading between the lines

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

These bounds could be applied to interpret potential signals in vector boson scattering experiments at the LHC and future colliders.
Extensions might include higher-dimensional operators or other sectors of the SMEFT.
Violations could indicate the need for new physics beyond the effective theory assumptions.

Load-bearing premise

The group-theoretic construction of extremal rays via direct construction and Casimir operator analysis fully captures the positivity cone for all electroweak boson modes, including parity-violating operators and continuous degeneracies.

What would settle it

A precise measurement in electroweak boson scattering that yields a combination of aQGC coefficients lying outside the derived positivity cone, such as exceeding one of the linear bounds, would falsify the completeness of these bounds.

read the original abstract

Electroweak boson scattering at the LHC provides a crucial avenue for probing physics beyond the Standard Model, particularly regarding deviations in quartic gauge couplings. We derive the complete set of positivity bounds for the $22$ dimension-$8$ anomalous quartic gauge coupling (aQGC) coefficients within the Standard Model Effective Field Theory (SMEFT). Moving beyond previous studies limited to transverse vector bosons, our analysis incorporates all electroweak boson modes, explicitly constructing the extremal rays (ERs) of the positivity cone through a group theoretic framework. We utilize two independent methods--direct construction and Casimir operator analysis--to determine these rays, addressing complexities such as parity-violating operators and continuous parameter degeneracies. Our results indicate that the positivity bounds impose severe constraints, restricting the physically viable parameter space to approximately $0.0313\%$ of the naive total space. Furthermore, we derive linear analytical bounds for various operator combinations and provide an easy-to-use Python package, {\tt SMEFTaQGC}, which implements algorithms to numerically verify positivity and compute the optimized positivity bounds for general aQGC configurations.

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

They deliver the full positivity bounds on all 22 aQGC coefficients across every boson polarization with a usable code package, but the completeness of the extremal-ray list for continuous degeneracies is the part that still needs verification.

read the letter

The core result is that Chang, Chen, and Zhou have produced positivity bounds on the complete set of 22 dimension-8 aQGC operators in SMEFT, now including longitudinal modes and parity-odd pieces that earlier transverse-only studies left out. The allowed volume shrinks to roughly 0.0313 percent of the naive space, and they supply explicit linear combinations plus the SMEFTaQGC Python package for numerical checks on arbitrary coefficient choices. That package and the analytic bounds are the parts most people will actually use.

Referee Report

2 major / 2 minor

Summary. The manuscript derives the complete set of positivity bounds for the 22 dimension-8 anomalous quartic gauge coupling coefficients in SMEFT. It constructs the extremal rays of the positivity cone via two group-theoretic methods (direct construction and Casimir operator analysis), incorporates all electroweak boson modes including parity-violating operators and continuous degeneracies, reports that the bounds restrict the viable parameter space to 0.0313% of the total, derives linear analytical bounds for operator combinations, and supplies the SMEFTaQGC Python package for numerical verification.

Significance. If the extremal-ray enumeration is exhaustive, the work substantially strengthens constraints on aQGCs relative to prior transverse-only analyses, supplying concrete linear bounds and a practical verification tool that could directly inform LHC searches and SMEFT fits.

major comments (2)

[Abstract and extremal-ray construction sections] The completeness claim for the positivity cone (Abstract) rests on the union of rays from direct construction and Casimir analysis fully spanning the boundary in the 22-dimensional space. Because continuous degeneracies exist among parity-violating operators, any missed ray would enlarge the reported 0.0313% viable volume; the manuscript provides no SDP relaxation, exhaustive numerical sampling of amplitude matrices, or other independent cross-check to confirm exhaustiveness.
[Results on parameter-space volume] The numerical fraction 0.0313% (Abstract) is presented as a concrete result of the enumerated rays, yet the text does not detail how degeneracies are resolved or how error propagation is controlled when optimizing over the cone; this directly affects the reliability of the quoted volume.

minor comments (2)

Clarify in the methods section whether the two ray-construction procedures are fully independent or share the same group-theoretic decomposition of four-boson amplitudes.
Add explicit documentation or examples in the SMEFTaQGC package description showing how users can reproduce the extremal-ray list and the 0.0313% volume.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and will revise the manuscript to improve clarity on the completeness of the bounds and the details of the volume calculation.

read point-by-point responses

Referee: [Abstract and extremal-ray construction sections] The completeness claim for the positivity cone (Abstract) rests on the union of rays from direct construction and Casimir analysis fully spanning the boundary in the 22-dimensional space. Because continuous degeneracies exist among parity-violating operators, any missed ray would enlarge the reported 0.0313% viable volume; the manuscript provides no SDP relaxation, exhaustive numerical sampling of amplitude matrices, or other independent cross-check to confirm exhaustiveness.

Authors: Our two independent group-theoretic methods—direct construction enumerating all helicity and polarization configurations of the electroweak bosons, and Casimir operator analysis identifying boundaries via Lorentz and gauge representations—are designed to be exhaustive, with continuous degeneracies among parity-violating operators handled by explicit parameterization of the degenerate directions. We acknowledge that an independent numerical cross-check would further strengthen the claim. In the revised manuscript we will add a short subsection describing Monte Carlo sampling over random amplitude matrices to verify that no additional extremal rays appear beyond those found by the two analytic methods. revision: partial
Referee: [Results on parameter-space volume] The numerical fraction 0.0313% (Abstract) is presented as a concrete result of the enumerated rays, yet the text does not detail how degeneracies are resolved or how error propagation is controlled when optimizing over the cone; this directly affects the reliability of the quoted volume.

Authors: We agree that additional detail on the volume computation is warranted. The quoted fraction is obtained by exact linear programming over the polyhedral cone after reducing the effective dimension by fixing degenerate parameters to their boundary values that produce the tightest constraints. Because the procedure uses deterministic exact arithmetic with no stochastic sampling, there is no statistical error propagation. In the revision we will insert a dedicated paragraph in the results section that outlines the numerical algorithm, the handling of degeneracies, and the implementation within the SMEFTaQGC package. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained via dispersion relations and group theory.

full rationale

The paper derives the positivity bounds from standard dispersion relations applied to four-boson scattering amplitudes, then enumerates extremal rays via direct construction and Casimir analysis in the electroweak group representation. These steps do not reduce to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations. The two methods are presented as independent checks on the same amplitude decomposition, with no evidence that completeness is assumed by construction or imported from prior author work as an unverified uniqueness theorem. The resulting bounds are external constraints on the 22-dimensional coefficient space rather than tautological rearrangements of the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard EFT positivity assumptions plus a paper-specific group-theoretic method for identifying extremal rays; no free parameters or new entities are introduced in the abstract.

axioms (2)

domain assumption Positivity bounds derived from forward dispersion relations and unitarity apply to all SMEFT dimension-8 aQGC operators.
Standard assumption in the EFT positivity literature invoked to justify the cone construction.
ad hoc to paper The group-theoretic framework together with Casimir operator analysis identifies the complete set of extremal rays for the positivity cone including parity-violating cases.
Method-specific assumption required for the completeness claim.

pith-pipeline@v0.9.0 · 5499 in / 1460 out tokens · 38934 ms · 2026-05-13T22:38:13.954072+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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

Analytic Bootstrap of the Veneziano Amplitude
hep-th 2026-05 unverdicted novelty 7.0

The Veneziano amplitude is the unique outcome of an analytic dual bootstrap from dispersive sum rules, unitarity, and either string monodromy or splitting and hidden-zero conditions.

Reference graph

Works this paper leans on

117 extracted references · 117 canonical work pages · cited by 1 Pith paper · 7 internal anchors

[1]

Weinberg,Phenomenological Lagrangians,Physica A96(1979) 327

S. Weinberg,Phenomenological Lagrangians,Physica A96(1979) 327

work page 1979
[2]

Buchmuller and D

W. Buchmuller and D. Wyler,Effective Lagrangian Analysis of New Interactions and Flavor Conservation,Nucl. Phys. B268(1986) 621

work page 1986
[3]

Leung, S.T

C.N. Leung, S.T. Love and S. Rao,Low-Energy Manifestations of a New Interaction Scale: Operator Analysis,Z. Phys. C31(1986) 433

work page 1986
[4]

Brivio and M

I. Brivio and M. Trott,The Standard Model as an Effective Field Theory,Phys. Rept.793 (2019) 1 [1706.08945]. – 41 –

work page arXiv 2019
[5]

de Blas, Y

J. de Blas, Y. Du, C. Grojean, J. Gu, V. Miralles, M.E. Peskin et al.,Global SMEFT Fits at Future Colliders, inSnowmass 2021, 6, 2022 [2206.08326]

work page arXiv 2021
[6]

Contino, M

R. Contino, M. Ghezzi, C. Grojean, M. Muhlleitner and M. Spira,Effective Lagrangian for a light Higgs-like scalar,JHEP07(2013) 035 [1303.3876]

work page arXiv 2013
[7]

Zhang and S.-Y

C. Zhang and S.-Y. Zhou,Positivity bounds on vector boson scattering at the LHC,Phys. Rev. D100(2019) 095003 [1808.00010]

work page arXiv 2019
[8]

I. Low, R. Rattazzi and A. Vichi,Theoretical Constraints on the Higgs Effective Couplings, JHEP04(2010) 126 [0907.5413]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[9]

Bellazzini and F

B. Bellazzini and F. Riva,New phenomenological and theoretical perspective on anomalous ZZ and Zγprocesses,Phys. Rev. D98(2018) 095021 [1806.09640]

work page arXiv 2018
[10]

Gomez-Ambrosio,Studies of Dimension-Six EFT effects in Vector Boson Scattering,Eur

R. Gomez-Ambrosio,Studies of Dimension-Six EFT effects in Vector Boson Scattering,Eur. Phys. J. C79(2019) 389 [1809.04189]

work page arXiv 2019
[11]

Q. Bi, C. Zhang and S.-Y. Zhou,Positivity constraints on aQGC: carving out the physical parameter space,JHEP06(2019) 137 [1902.08977]

work page arXiv 2019
[12]

Remmen and N.L

G.N. Remmen and N.L. Rodd,Consistency of the Standard Model Effective Field Theory, JHEP12(2019) 032 [1908.09845]

work page arXiv 2019
[13]

Zhang and S.-Y

C. Zhang and S.-Y. Zhou,Convex Geometry Perspective on the (Standard Model) Effective Field Theory Space,Phys. Rev. Lett.125(2020) 201601 [2005.03047]

work page arXiv 2020
[14]

Yamashita, C

K. Yamashita, C. Zhang and S.-Y. Zhou,Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings,JHEP01(2021) 095 [2009.04490]

work page arXiv 2021
[15]

Trott,Causality, unitarity and symmetry in effective field theory,JHEP07(2021) 143, [2011.10058]

T. Trott,Causality, unitarity and symmetry in effective field theory,JHEP07(2021) 143 [2011.10058]

work page arXiv 2021
[16]

Remmen and N.L

G.N. Remmen and N.L. Rodd,Flavor Constraints from Unitarity and Analyticity,Phys. Rev. Lett.125(2020) 081601 [2004.02885]

work page arXiv 2020
[17]

Remmen and N.L

G.N. Remmen and N.L. Rodd,Signs, spin, SMEFT: Sum rules at dimension six,Phys. Rev. D 105(2022) 036006 [2010.04723]

work page arXiv 2022
[18]

Gu and L.-T

J. Gu and L.-T. Wang,Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes,JHEP03(2021) 149 [2008.07551]

work page arXiv 2021
[19]

B. Fuks, Y. Liu, C. Zhang and S.-Y. Zhou,Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states,Chin. Phys. C45(2021) 023108 [2009.02212]

work page arXiv 2021
[20]

Gu, L.-T

J. Gu, L.-T. Wang and C. Zhang,Unambiguously Testing Positivity at Lepton Colliders,Phys. Rev. Lett.129(2022) 011805 [2011.03055]

work page arXiv 2022
[21]

Bonnefoy, E

Q. Bonnefoy, E. Gendy and C. Grojean,Positivity bounds on Minimal Flavor Violation,JHEP 04(2021) 115 [2011.12855]

work page arXiv 2021
[22]

X. Li, H. Xu, C. Yang, C. Zhang and S.-Y. Zhou,Positivity in Multifield Effective Field Theories,Phys. Rev. Lett.127(2021) 121601 [2101.01191]. – 42 –

work page arXiv 2021
[23]

Davighi, S

J. Davighi, S. Melville and T. You,Natural selection rules: new positivity bounds for massive spinning particles,JHEP02(2022) 167 [2108.06334]

work page arXiv 2022
[24]

Chala and J

M. Chala and J. Santiago,Positivity bounds in the standard model effective field theory beyond tree level,Phys. Rev. D105(2022) L111901 [2110.01624]

work page arXiv 2022
[25]

Zhang,SMEFTs living on the edge: determining the UV theories from positivity and extremality,JHEP12(2022) 096 [2112.11665]

C. Zhang,SMEFTs living on the edge: determining the UV theories from positivity and extremality,JHEP12(2022) 096 [2112.11665]

work page arXiv 2022
[26]

Chala, G

M. Chala, G. Guedes, M. Ramos and J. Santiago,Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I,SciPost Phys. 11(2021) 065 [2106.05291]

work page arXiv 2021
[27]

Boughezal, E

R. Boughezal, E. Mereghetti and F. Petriello,Dilepton production in the SMEFT at O(1/Λ4), Phys. Rev. D104(2021) 095022 [2106.05337]

work page arXiv 2021
[28]

Ghosh, R

D. Ghosh, R. Sharma and F. Ullah,Amplitude’s positivity vs. subluminality: causality and unitarity constraints on dimension 6 & 8 gluonic operators in the SMEFT,JHEP02(2023) 199 [2211.01322]

work page arXiv 2023
[29]

Remmen and N.L

G.N. Remmen and N.L. Rodd,Spinning sum rules for the dimension-six SMEFT,JHEP09 (2022) 030 [2206.13524]

work page arXiv 2022
[30]

Li and S

X. Li and S. Zhou,Origin of neutrino masses on the convex cone of positivity bounds,Phys. Rev. D107(2023) L031902 [2202.12907]

work page arXiv 2023
[31]

X. Li, K. Mimasu, K. Yamashita, C. Yang, C. Zhang and S.-Y. Zhou,Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics,JHEP10 (2022) 107 [2204.13121]

work page arXiv 2022
[32]

Li,Positivity bounds at one-loop level: the Higgs sector,JHEP05(2023) 230 [2212.12227]

X. Li,Positivity bounds at one-loop level: the Higgs sector,JHEP05(2023) 230 [2212.12227]

work page arXiv 2023
[33]

Altmannshofer, S

W. Altmannshofer, S. Gori, B.V. Lehmann and J. Zuo,UV physics from IR features: New prospects from top flavor violation,Phys. Rev. D107(2023) 095025 [2303.00781]

work page arXiv 2023
[34]

C. Yang, Z. Ren and J.-H. Yu,Positivity from J-Basis operators in the standard model effective Field Theory,JHEP05(2024) 221 [2312.04663]

work page arXiv 2024
[35]

Davighi, S

J. Davighi, S. Melville, K. Mimasu and T. You,Positivity and the electroweak hierarchy,Phys. Rev. D109(2024) 033009 [2308.06226]

work page arXiv 2024
[36]

Chala and X

M. Chala and X. Li,Positivity restrictions on the mixing of dimension-eight SMEFT operators,Phys. Rev. D109(2024) 065015 [2309.16611]

work page arXiv 2024
[37]

Q. Chen, K. Mimasu, T.A. Wu, G.-D. Zhang and S.-Y. Zhou,Capping the positivity cone: dimension-8 Higgs operators in the SMEFT,JHEP03(2024) 180 [2309.15922]

work page arXiv 2024
[38]

Hong, Z.-H

D.-Y. Hong, Z.-H. Wang and S.-Y. Zhou,On Capped Higgs Positivity Cone, 4, 2024 [2404.04479]

work page arXiv 2024
[39]

Remmen and N.L

G.N. Remmen and N.L. Rodd,Positively Identifying HEFT or SMEFT,2412.07827

work page arXiv
[40]

Liu, K.-F

Z. Liu, K.-F. Lyu and T.A. Wu,LHC Shines on Positivity,2512.04336

work page arXiv
[41]

Causality, Analyticity and an IR Obstruction to UV Completion

A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi,Causality, analyticity and an IR obstruction to UV completion,JHEP10(2006) 014 [hep-th/0602178]. – 43 –

work page internal anchor Pith review Pith/arXiv arXiv 2006
[42]

Tolley, Z.-Y

A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou,New positivity bounds from full crossing symmetry, JHEP05(2021) 255 [2011.02400]

work page arXiv 2021
[43]

Caron-Huot and V

S. Caron-Huot and V. Van Duong,Extremal Effective Field Theories,JHEP05(2021) 280 [2011.02957]

work page arXiv 2021
[44]

de Rham, S

C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou,Positivity bounds for scalar field theories, Phys. Rev. D96(2017) 081702 [1702.06134]

work page arXiv 2017
[45]

de Rham, S

C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou,UV complete me: Positivity Bounds for Particles with Spin,JHEP03(2018) 011 [1706.02712]

work page arXiv 2018
[46]

Chiang, Y.-t

L.-Y. Chiang, Y.-t. Huang, L. Rodina and H.-C. Weng,De-projecting the EFThedron,JHEP 05(2024) 102 [2204.07140]

work page arXiv 2024
[47]

Arkani-Hamed, T.-C

N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang,The EFT-Hedron,JHEP05(2021) 259 [2012.15849]

work page arXiv 2021
[48]

Bellazzini, J

B. Bellazzini, J. Elias Mir´ o, R. Rattazzi, M. Riembau and F. Riva,Positive moments for scattering amplitudes,Phys. Rev. D104(2021) 036006 [2011.00037]

work page arXiv 2021
[49]

Sinha and A

A. Sinha and A. Zahed,Crossing Symmetric Dispersion Relations in Quantum Field Theories, Phys. Rev. Lett.126(2021) 181601 [2012.04877]

work page arXiv 2021
[50]

Alberte, C

L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley,Positivity Bounds and the Massless Spin-2 Pole,Phys. Rev. D102(2020) 125023 [2007.12667]

work page arXiv 2020
[51]

Guerrieri and A

A. Guerrieri and A. Sever,Rigorous Bounds on the Analytic S Matrix,Phys. Rev. Lett.127 (2021) 251601 [2106.10257]

work page arXiv 2021
[52]

Alberte, C

L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley,Reverse Bootstrapping: IR Lessons for UV Physics,Phys. Rev. Lett.128(2022) 051602 [2111.09226]

work page arXiv 2022
[53]

Caron-Huot, D

S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin,Sharp boundaries for the swampland,JHEP07(2021) 110 [2102.08951]

work page arXiv 2021
[54]

Z.-Z. Du, C. Zhang and S.-Y. Zhou,Triple crossing positivity bounds for multi-field theories, JHEP12(2021) 115 [2111.01169]

work page arXiv 2021
[55]

Pham and T.N

T.N. Pham and T.N. Truong,Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation,Phys. Rev. D31(1985) 3027

work page 1985
[56]

The Chiral Lagrangian parameters, $\overline{\ell}_1$, $\overline{\ell}_2$, are determined by the $\rho$--resonance

M.R. Pennington and J. Portoles,The Chiral Lagrangian parameters, l1, l2, are determined by the rho resonance,Phys. Lett. B344(1995) 399 [hep-ph/9409426]

work page internal anchor Pith review Pith/arXiv arXiv 1995
[57]

Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints

B. Ananthanarayan, D. Toublan and G. Wanders,Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints,Phys. Rev. D51(1995) 1093 [hep-ph/9410302]

work page internal anchor Pith review Pith/arXiv arXiv 1995
[58]

Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities

J. Comellas, J.I. Latorre and J. Taron,Constraints on chiral perturbation theory parameters from QCD inequalities,Phys. Lett. B360(1995) 109 [hep-ph/9507258]

work page internal anchor Pith review Pith/arXiv arXiv 1995
[59]

Dispersion Relation Bounds for pi pi Scattering

A.V. Manohar and V. Mateu,Dispersion Relation Bounds for pi pi Scattering,Phys. Rev. D 77(2008) 094019 [0801.3222]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[60]

Chiang, Y.-t

L.-Y. Chiang, Y.-t. Huang, W. Li, L. Rodina and H.-C. Weng,Into the EFThedron and UV constraints from IR consistency,JHEP03(2022) 063 [2105.02862]. – 44 –

work page arXiv 2022
[61]

Sanz-Cillero, D.-L

J.J. Sanz-Cillero, D.-L. Yao and H.-Q. Zheng,Positivity constraints on the low-energy constants of the chiral pion-nucleon Lagrangian,Eur. Phys. J. C74(2014) 2763 [1312.0664]

work page arXiv 2014
[62]

Softness and Amplitudes' Positivity for Spinning Particles

B. Bellazzini,Softness and amplitudes’ positivity for spinning particles,JHEP02(2017) 034 [1605.06111]

work page Pith review arXiv 2017
[63]

Positivity Bounds for Massive Spin-1 and Spin-2 Fields

C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou,Positivity Bounds for Massive Spin-1 and Spin-2 Fields,JHEP03(2019) 182 [1804.10624]

work page Pith review arXiv 2019
[64]

de Rham, S

C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou,Massive Galileon Positivity Bounds, JHEP09(2017) 072 [1702.08577]

work page arXiv 2017
[65]

Bonifacio, K

J. Bonifacio, K. Hinterbichler and R.A. Rosen,Positivity constraints for pseudolinear massive spin-2 and vector Galileons,Phys. Rev. D94(2016) 104001 [1607.06084]

work page arXiv 2016
[66]

Du, F.-K

M.-L. Du, F.-K. Guo, U.-G. Meißner and D.-L. Yao,Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons,Phys. Rev. D94(2016) 094037 [1610.02963]

work page arXiv 2016
[67]

Beyond Amplitudes' Positivity and the Fate of Massive Gravity

B. Bellazzini, F. Riva, J. Serra and F. Sgarlata,Beyond Positivity Bounds and the Fate of Massive Gravity,Phys. Rev. Lett.120(2018) 161101 [1710.02539]

work page Pith review arXiv 2018
[68]

Hinterbichler, A

K. Hinterbichler, A. Joyce and R.A. Rosen,Massive Spin-2 Scattering and Asymptotic Superluminality,JHEP03(2018) 051 [1708.05716]

work page arXiv 2018
[69]

Bellazzini, F

B. Bellazzini, F. Riva, J. Serra and F. Sgarlata,The other effective fermion compositeness, JHEP11(2017) 020 [1706.03070]

work page arXiv 2017
[70]

Bonifacio and K

J. Bonifacio and K. Hinterbichler,Bounds on Amplitudes in Effective Theories with Massive Spinning Particles,Phys. Rev. D98(2018) 045003 [1804.08686]

work page arXiv 2018
[71]

Bellazzini, M

B. Bellazzini, M. Lewandowski and J. Serra,Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity,Phys. Rev. Lett.123(2019) 251103 [1902.03250]

work page arXiv 2019
[72]

Melville and J

S. Melville and J. Noller,Positivity in the Sky: Constraining dark energy and modified gravity from the UV,Phys. Rev. D101(2020) 021502 [1904.05874]

work page arXiv 2020
[73]

Melville, D

S. Melville, D. Roest and D. Stefanyszyn,UV Constraints on Massive Spinning Particles: Lessons from the Gravitino,JHEP02(2020) 185 [1911.03126]

work page arXiv 2020
[74]

de Rham and A.J

C. de Rham and A.J. Tolley,Speed of gravity,Phys. Rev. D101(2020) 063518 [1909.00881]

work page arXiv 2020
[75]

Alberte, C

L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A.J. Tolley,Positivity Constraints on Interacting Spin-2 Fields,JHEP03(2020) 097 [1910.11799]

work page arXiv 2020
[76]

Alberte, C

L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A.J. Tolley,Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields,JHEP07(2020) 121 [1912.10018]

work page arXiv 2020
[77]

Ye and Y.-S

G. Ye and Y.-S. Piao,Positivity in the effective field theory of cosmological perturbations,Eur. Phys. J. C80(2020) 421 [1908.08644]

work page arXiv 2020
[78]

Huang, J.-Y

Y.-t. Huang, J.-Y. Liu, L. Rodina and Y. Wang,Carving out the Space of Open-String S-matrix,JHEP04(2021) 195 [2008.02293]

work page arXiv 2021
[79]

Wan and S.-Y

S.-L. Wan and S.-Y. Zhou,Matrix moment approach to positivity bounds and UV reconstruction from IR,JHEP02(2025) 168 [2411.11964]

work page arXiv 2025
[80]

Elias Miro, A

J. Elias Miro, A. Guerrieri and M.A. Gumus,Bridging positivity and S-matrix bootstrap bounds,JHEP05(2023) 001 [2210.01502]. – 45 –

work page arXiv 2023

Showing first 80 references.