[1] |
Adams A, Arkani-Hamed N, Dubovsky S, et al. Causality, analyticity and an IR obstruction to UV completion. Journal of High Energy Physics, 2006, 2006: 014. doi: 10.1088/1126-6708/2006/10/014
|
[2] |
de Rham C, Melville S, Tolley A J, et al. Positivity bounds for scalar field theories. Physical Review D, 2017, 96: 081702. doi: 10.1103/physrevd.96.081702
|
[3] |
de Rham C, Melville S, Tolley A J, et al. UV complete me: Positivity bounds for particles with spin. Journal of High Energy Physics, 2018, 2018: 11. doi: 10.1007/jhep03(2018)011
|
[4] |
Arkani-Hamed N, Huang T C, Huang Y T. The EFT-hedron. Journal of High Energy Physics, 2021, 2021: 259. doi: 10.1007/jhep05(2021)259
|
[5] |
Bellazzini B, Miró J E, Rattazzi R, et al. Positive moments for scattering amplitudes. Physical Review D, 2021, 104: 036006. doi: 10.1103/physrevd.104.036006
|
[6] |
Tolley A J, Wang Z Y, Zhou S Y. New positivity bounds from full crossing symmetry. Journal of High Energy Physics, 2021, 2021: 255. doi: 10.1007/jhep05(2021)255
|
[7] |
Caron-Huot S, Van Duong V. Extremal effective field theories. Journal of High Energy Physics, 2021, 2021: 280. doi: 10.1007/jhep05(2021)280
|
[8] |
Chiang L Y, Huang Y T, Li W, et al. Into the EFThedron and UV constraints from IR consistency. Journal of High Energy Physics, 2022, 2021: 63. doi: 10.1007/jhep03(2022)063
|
[9] |
Sinha A, Zahed A. Crossing symmetric dispersion relations in quantum field theories. Physical Review Letters, 2021, 126: 181601. doi: 10.1103/physrevlett.126.181601
|
[10] |
Zhang C, Zhou S Y. Convex geometry perspective on the (standard model) effective field theory space. Physical Review Letters, 2020, 125: 201601. doi: 10.1103/physrevlett.125.201601
|
[11] |
Li X, Xu H, Yang C, et al. Positivity in multifield effective field theories. Physical Review Letters, 2021, 127: 121601. doi: 10.1103/physrevlett.127.121601
|
[12] |
Bellazzini B, Martucci L, Torre R. Symmetries, sum rules and constraints on effective field theories. Journal of High Energy Physics, 2014, 2014: 100. doi: 10.1007/jhep09(2014)100
|
[13] |
Bellazzini B. Softness and amplitudes’ positivity for spinning particles. Journal of High Energy Physics, 2017, 2017: 34. doi: 10.1007/jhep02(2017)034
|
[14] |
Bern Z, Kosmopoulos D, Zhiboedov A. Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude. Journal of Physics A:Mathematical and Theoretical, 2021, 54: 344002. doi: 10.1088/1751-8121/ac0e51
|
[15] |
Alberte L, de Rham C, Jaitly S, et al. Positivity bounds and the massless spin-2 pole. Physical Review D, 2020, 102: 125023. doi: 10.1103/physrevd.102.125023
|
[16] |
Tokuda J, Aoki K, Hirano S. Gravitational positivity bounds. Journal of High Energy Physics,, 2020, 2020: 54. doi: 10.1007/jhep11(2020)054
|
[17] |
Caron-Huot S, Mazáč D, Rastelli L, et al. Sharp boundaries for the swampland. Journal of High Energy Physics, 2021, 2021: 110. doi: 10.1007/jhep07(2021)110
|
[18] |
Grall T, Melville S. Positivity bounds without boosts: New constraints on low energy effective field theories from the UV. Physical Review D, 2022, 105: L121301. doi: 10.1103/physrevd.105.l121301
|
[19] |
Du Z Z, Zhang C, Zhou S Y. Triple crossing positivity bounds for multi-field theories. Journal of High Energy Physics, 2021, 2021: 115. doi: 10.1007/jhep12(2021)115
|
[20] |
Alberte L, de Rham C, Jaitly S, et al. Reverse bootstrapping: IR lessons for UV physics. Physical Review Letters, 2022, 128: 051602. doi: 10.1103/physrevlett.128.051602
|
[21] |
Bellazzini B, Riembau M, Riva F. IR side of positivity bounds. Physical Review D, 2022, 106: 105008. doi: 10.1103/physrevd.106.105008
|
[22] |
Dutta Chowdhury S, Ghosh K, Haldar P, et al. Crossing symmetric spinning S-matrix bootstrap: EFT bounds. SciPost Physics, 2022, 13: 51. doi: 10.21468/scipostphys.13.3.051
|
[23] |
Chiang L Y, Huang Y T, Rodina L, et al. De-projecting the EFThedron. Journal of High Energy Physics, 2024, 2024: 102. doi: 10.1007/jhep05(2024)102
|
[24] |
Caron-Huot S, Li Y Z, Parra-Martinez J, et al. Causality constraints on corrections to Einstein gravity. Journal of High Energy Physics, 2023, 2023: 122. doi: 10.1007/jhep05(2023)122
|
[25] |
Caron-Huot S, Li Y Z, Parra-Martinez J, et al. Graviton partial waves and causality in higher dimensions. Physical Review D, 2023, 108: 026007. doi: 10.1103/physrevd.108.026007
|
[26] |
Henriksson J, McPeak B, Russo F, et al. Bounding violations of the weak gravity conjecture. Journal of High Energy Physics, 2022, 2022: 184. doi: 10.1007/jhep08(2022)184
|
[27] |
Li-Yuan Chiang, Yu-tin Huang, Wei Li, Laurentiu Rodina, and He-Chen Weng. (Non)-projective bounds on gravitational EFT. arXiv: 2201. 07177, 2022.
|
[28] |
Albert J, Rastelli L. Bootstrapping pions at large N. Journal of High Energy Physics, 2022, 2022: 151. doi: 10.1007/jhep08(2022)151
|
[29] |
Carrillo González M, de Rham C, Jaitly S, et al. Positivity-causality competition: A road to ultimate EFT consistency constraints. Journal of High Energy Physics, 2024, 2024: 146. doi: 10.1007/jhep06(2024)146
|
[30] |
Hong D Y, Wang Z H, Zhou S Y. Causality bounds on scalar-tensor EFTs. Journal of High Energy Physics, 2023, 2023: 135. doi: 10.1007/jhep10(2023)135
|
[31] |
Li Y Z. Effective field theory bootstrap, large-N χPT and holographic QCD. Journal of High Energy Physics, 2024, 2024: 72. doi: 10.1007/jhep01(2024)072
|
[32] |
Paulos M F, Penedones J, Toledo J, et al. The S-matrix bootstrap II: Two dimensional amplitudes. Journal of High Energy Physics, 2017, 2017: 143. doi: 10.1007/jhep11(2017)143
|
[33] |
Paulos M F, Penedones J, Toledo J, et al. The S-matrix bootstrap. Part III:Higher dimensional amplitudes. Journal of High Energy Physics, 2019, 2019: 40. doi: 10.1007/jhep12(2019)040
|
[34] |
He Y, Irrgang A, Kruczenski M. A note on the S-matrix bootstrap for the 2d O(N) bosonic model. Journal of High Energy Physics, 2018, 2018: 93. doi: 10.1007/jhep11(2018)093
|
[35] |
He Y, Kruczenski M. S-matrix bootstrap in 3+1 dimensions: Regularization and dual convex problem. Journal of High Energy Physics, 2021, 2021: 125. doi: 10.1007/jhep08(2021)125
|
[36] |
Karateev D, Kuhn S, Penedones J. Bootstrapping massive quantum field theories. Journal of High Energy Physics, 2020, 2020: 35. doi: 10.1007/jhep07(2020)035
|
[37] |
Guerrieri A L, Penedones J, Vieira P. S-matrix bootstrap for effective field theories: Massless pions. Journal of High Energy Physics, 2021, 2021: 88. doi: 10.1007/jhep06(2021)088
|
[38] |
Kruczenski M, Murali H. The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary. Journal of High Energy Physics, 2021, 2021: 97. doi: 10.1007/jhep04(2021)097
|
[39] |
Guerrieri A, Sever A. Rigorous bounds on the analytic S matrix . Physical Review Letters, 2021, 127: 251601. doi: 10.1103/physrevlett.127.251601
|
[40] |
Guerrieri A, Penedones J, Vieira P. Where is string theory in the space of scattering amplitudes. Physical Review Letters, 2021, 127: 081601. doi: 10.1103/physrevlett.127.081601
|
[41] |
Albert J, Rastelli L. Bootstrapping pions at large N. Part II: background gauge fields and the chiral anomaly. arXiv: 2307. 01246, 2023.
|
[42] |
Acanfora F, Guerrieri A, Häring K, et al. Bounds on scattering of neutral Goldstones. Journal of High Energy Physics, 2024, 2024: 28. doi: 10.1007/jhep03(2024)028
|
[43] |
Miró J E, Guerrieri A, Gumus M A. Extremal Higgs couplings. arXiv: 2311. 09283, 2023.
|
[44] |
de Rham C, Kundu S, Reece M, et al. Snowmass white paper: UV constraints on IR physics. arXiv: 2203. 06805, 2022.
|
[45] |
Zhang C, Zhou S Y. Positivity bounds on vector boson scattering at the LHC. Physical Review D, 2019, 100: 095003. doi: 10.1103/physrevd.100.095003
|
[46] |
Bi Q, Zhang C, Zhou S Y. Positivity constraints on aQGC: Carving out the physical parameter space. Journal of High Energy Physics, 2019, 2019: 137. doi: 10.1007/jhep06(2019)137
|
[47] |
Bellazzini B, Riva F. New phenomenological and theoretical perspective on anomalous ZZ and Zγ processes. Physical Review D, 2018, 98: 095021. doi: 10.1103/physrevd.98.095021
|
[48] |
Remmen G N, Rodd N L. Consistency of the standard model effective field theory. Journal of High Energy Physics, 2019, 2019: 32. doi: 10.1007/jhep12(2019)032
|
[49] |
Yamashita K, Zhang C, Zhou S Y. Elastic positivity vs extremal positivity bounds in SMEFT: A case study in transversal electroweak gauge-boson scatterings. Journal of High Energy Physics, 2021, 2021: 95. doi: 10.1007/jhep01(2021)095
|
[50] |
Trott T. Causality, unitarity and symmetry in effective field theory. Journal of High Energy Physics, 2021, 2021: 143. doi: 10.1007/jhep07(2021)143
|
[51] |
Remmen G N, Rodd N L. Flavor constraints from unitarity and analyticity. Physical Review Letters, 2020, 125: 081601. doi: 10.1103/physrevlett.125.081601
|
[52] |
Remmen G N, Rodd N L. Signs, spin, SMEFT: Sum rules at dimension six. Physical Review D, 2022, 105: 036006. doi: 10.1103/physrevd.105.036006
|
[53] |
Gu J, Wang L T. Sum rules in the standard model effective field theory from helicity amplitudes. Journal of High Energy Physics, 2021, 2021: 149. doi: 10.1007/jhep03(2021)149
|
[54] |
Fuks B, Liu Y, Zhang C, et al. Positivity in electron-positron scattering: Testing the axiomatic quantum field theory principles and probing the existence of UV states. Chinese Physics C, 2021, 45: 023108. doi: 10.1088/1674-1137/abcd8c
|
[55] |
Gu J, Wang L T, Zhang C. Unambiguously testing positivity at lepton colliders. Physical Review Letters, 2022, 129: 011805. doi: 10.1103/physrevlett.129.011805
|
[56] |
Bonnefoy Q, Gendy E, Grojean C. Positivity bounds onminimal flavor violation. Journal of High Energy Physics, 2021, 2021: 115. doi: 10.1007/jhep04(2021)115
|
[57] |
Davighi J, Melville S, You T. Natural selection rules: New positivity bounds for massive spinning particles. Journal of High Energy Physics, 2022, 2022: 167. doi: 10.1007/jhep02(2022)167
|
[58] |
Chala M, Santiago J. Positivity bounds in the standard model effective field theory beyond tree level. Physical Review D, 2022, 105: L111901. doi: 10.1103/physrevd.105.l111901
|
[59] |
Zhang C. SMEFTs living on the edge: Determining the UV theories from positivity and extremality. Journal of High Energy Physics, 2022, 2022: 96. doi: 10.1007/jhep12(2022)096
|
[60] |
Ghosh D, Sharma R, Ullah F. Amplitude’s positivity vs. subluminality: Causality and unitarity constraints on dimension 6 & 8 gluonic operators in the SMEFT. Journal of High Energy Physics, 2023, 2023: 199. doi: 10.1007/jhep02(2023)199
|
[61] |
Remmen G N, Rodd N L. Spinning sum rules for the dimension-six SMEFT. Journal of High Energy Physics, 2022, 2022: 30. doi: 10.1007/jhep09(2022)030
|
[62] |
Li X, Zhou S. Origin of neutrino masses on the convex cone of positivity bounds. Physical Review D, 2023, 107: L031902. doi: 10.1103/physrevd.107.l031902
|
[63] |
Li X, Mimasu K, Yamashita K, et al. Moments for positivity: Using Drell-Yan data to test positivity bounds and reverse-engineer new physics. Journal of High Energy Physics, 2022, 2022: 107. doi: 10.1007/jhep10(2022)107
|
[64] |
Li X. Positivity bounds at one-loop level: The Higgs sector. Journal of High Energy Physics, 2023, 2023: 230. doi: 10.1007/jhep05(2023)230
|
[65] |
Altmannshofer W, Gori S, Lehmann B V, et al. UV physics from IR features: New prospects from top flavor violation. Physical Review D, 2023, 107: 095025. doi: 10.1103/physrevd.107.095025
|
[66] |
Davighi J, Melville S, Mimasu K, et al. Positivity and the electroweak hierarchy. Physical Review D, 2024, 109: 033009. doi: 10.1103/physrevd.109.033009
|
[67] |
Ellis J, Mimasu K, Zampedri F. Dimension-8 SMEFT analysis of minimal scalar field extensions of the Standard Model. Journal of High Energy Physics, 2023, 2023: 51. doi: 10.1007/jhep10(2023)051
|
[68] |
Chala M, Li X. Positivity restrictions on the mixing of dimension-eight SMEFT operators. Physical Review D, 2024, 109: 065015. doi: 10.1103/physrevd.109.065015
|
[69] |
Gu J, Shu C. Probing positivity at the LHC with exclusive photon-fusion processes. Journal of High Energy Physics, 2024, 2024: 183. doi: 10.1007/jhep05(2024)183
|
[70] |
Li H L, Ren Z, Shu J, et al. Complete set of dimension-eight operators in the standard model effective field theory. Physical Review D, 2021, 104: 015026. doi: 10.1103/physrevd.104.015026
|
[71] |
Murphy C W. Dimension-8 operators in the Standard Model Effective Field Theory. Journal of High Energy Physics, 2020, 2020: 174. doi: 10.1007/jhep10(2020)174
|
[72] |
Vecchi L. Causal vs. analytic constraints on anomalous quartic gauge couplings. Journal of High Energy Physics, 2007, 2007: 54. doi: 10.1088/1126-6708/2007/11/054
|
[73] |
Chen Q, Mimasu K, Wu T A, et al. Capping the positivity cone: Dimension-8 Higgs operators in the SMEFT. Journal of High Energy Physics, 2024, 2024: 180. doi: 10.1007/jhep03(2024)180
|
[74] |
Froissart M. Asymptotic behavior and subtractions in the mandelstam representation. Physical Review, 1961, 123: 1053–1057. doi: 10.1103/physrev.123.1053
|
[75] |
Martin A. Unitarity and high-energy behavior of scattering amplitudes. Physical Review, 1963, 129: 1432–1436. doi: 10.1103/physrev.129.1432
|
[76] |
Landry W, Simmons-Duffin D. Scaling the semidefinite program solver SDPB. arXiv: 1909. 09745, 2019.
|
Figure
1.
Positivity regions in the 2D subspaces of
[1] |
Adams A, Arkani-Hamed N, Dubovsky S, et al. Causality, analyticity and an IR obstruction to UV completion. Journal of High Energy Physics, 2006, 2006: 014. doi: 10.1088/1126-6708/2006/10/014
|
[2] |
de Rham C, Melville S, Tolley A J, et al. Positivity bounds for scalar field theories. Physical Review D, 2017, 96: 081702. doi: 10.1103/physrevd.96.081702
|
[3] |
de Rham C, Melville S, Tolley A J, et al. UV complete me: Positivity bounds for particles with spin. Journal of High Energy Physics, 2018, 2018: 11. doi: 10.1007/jhep03(2018)011
|
[4] |
Arkani-Hamed N, Huang T C, Huang Y T. The EFT-hedron. Journal of High Energy Physics, 2021, 2021: 259. doi: 10.1007/jhep05(2021)259
|
[5] |
Bellazzini B, Miró J E, Rattazzi R, et al. Positive moments for scattering amplitudes. Physical Review D, 2021, 104: 036006. doi: 10.1103/physrevd.104.036006
|
[6] |
Tolley A J, Wang Z Y, Zhou S Y. New positivity bounds from full crossing symmetry. Journal of High Energy Physics, 2021, 2021: 255. doi: 10.1007/jhep05(2021)255
|
[7] |
Caron-Huot S, Van Duong V. Extremal effective field theories. Journal of High Energy Physics, 2021, 2021: 280. doi: 10.1007/jhep05(2021)280
|
[8] |
Chiang L Y, Huang Y T, Li W, et al. Into the EFThedron and UV constraints from IR consistency. Journal of High Energy Physics, 2022, 2021: 63. doi: 10.1007/jhep03(2022)063
|
[9] |
Sinha A, Zahed A. Crossing symmetric dispersion relations in quantum field theories. Physical Review Letters, 2021, 126: 181601. doi: 10.1103/physrevlett.126.181601
|
[10] |
Zhang C, Zhou S Y. Convex geometry perspective on the (standard model) effective field theory space. Physical Review Letters, 2020, 125: 201601. doi: 10.1103/physrevlett.125.201601
|
[11] |
Li X, Xu H, Yang C, et al. Positivity in multifield effective field theories. Physical Review Letters, 2021, 127: 121601. doi: 10.1103/physrevlett.127.121601
|
[12] |
Bellazzini B, Martucci L, Torre R. Symmetries, sum rules and constraints on effective field theories. Journal of High Energy Physics, 2014, 2014: 100. doi: 10.1007/jhep09(2014)100
|
[13] |
Bellazzini B. Softness and amplitudes’ positivity for spinning particles. Journal of High Energy Physics, 2017, 2017: 34. doi: 10.1007/jhep02(2017)034
|
[14] |
Bern Z, Kosmopoulos D, Zhiboedov A. Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude. Journal of Physics A:Mathematical and Theoretical, 2021, 54: 344002. doi: 10.1088/1751-8121/ac0e51
|
[15] |
Alberte L, de Rham C, Jaitly S, et al. Positivity bounds and the massless spin-2 pole. Physical Review D, 2020, 102: 125023. doi: 10.1103/physrevd.102.125023
|
[16] |
Tokuda J, Aoki K, Hirano S. Gravitational positivity bounds. Journal of High Energy Physics,, 2020, 2020: 54. doi: 10.1007/jhep11(2020)054
|
[17] |
Caron-Huot S, Mazáč D, Rastelli L, et al. Sharp boundaries for the swampland. Journal of High Energy Physics, 2021, 2021: 110. doi: 10.1007/jhep07(2021)110
|
[18] |
Grall T, Melville S. Positivity bounds without boosts: New constraints on low energy effective field theories from the UV. Physical Review D, 2022, 105: L121301. doi: 10.1103/physrevd.105.l121301
|
[19] |
Du Z Z, Zhang C, Zhou S Y. Triple crossing positivity bounds for multi-field theories. Journal of High Energy Physics, 2021, 2021: 115. doi: 10.1007/jhep12(2021)115
|
[20] |
Alberte L, de Rham C, Jaitly S, et al. Reverse bootstrapping: IR lessons for UV physics. Physical Review Letters, 2022, 128: 051602. doi: 10.1103/physrevlett.128.051602
|
[21] |
Bellazzini B, Riembau M, Riva F. IR side of positivity bounds. Physical Review D, 2022, 106: 105008. doi: 10.1103/physrevd.106.105008
|
[22] |
Dutta Chowdhury S, Ghosh K, Haldar P, et al. Crossing symmetric spinning S-matrix bootstrap: EFT bounds. SciPost Physics, 2022, 13: 51. doi: 10.21468/scipostphys.13.3.051
|
[23] |
Chiang L Y, Huang Y T, Rodina L, et al. De-projecting the EFThedron. Journal of High Energy Physics, 2024, 2024: 102. doi: 10.1007/jhep05(2024)102
|
[24] |
Caron-Huot S, Li Y Z, Parra-Martinez J, et al. Causality constraints on corrections to Einstein gravity. Journal of High Energy Physics, 2023, 2023: 122. doi: 10.1007/jhep05(2023)122
|
[25] |
Caron-Huot S, Li Y Z, Parra-Martinez J, et al. Graviton partial waves and causality in higher dimensions. Physical Review D, 2023, 108: 026007. doi: 10.1103/physrevd.108.026007
|
[26] |
Henriksson J, McPeak B, Russo F, et al. Bounding violations of the weak gravity conjecture. Journal of High Energy Physics, 2022, 2022: 184. doi: 10.1007/jhep08(2022)184
|
[27] |
Li-Yuan Chiang, Yu-tin Huang, Wei Li, Laurentiu Rodina, and He-Chen Weng. (Non)-projective bounds on gravitational EFT. arXiv: 2201. 07177, 2022.
|
[28] |
Albert J, Rastelli L. Bootstrapping pions at large N. Journal of High Energy Physics, 2022, 2022: 151. doi: 10.1007/jhep08(2022)151
|
[29] |
Carrillo González M, de Rham C, Jaitly S, et al. Positivity-causality competition: A road to ultimate EFT consistency constraints. Journal of High Energy Physics, 2024, 2024: 146. doi: 10.1007/jhep06(2024)146
|
[30] |
Hong D Y, Wang Z H, Zhou S Y. Causality bounds on scalar-tensor EFTs. Journal of High Energy Physics, 2023, 2023: 135. doi: 10.1007/jhep10(2023)135
|
[31] |
Li Y Z. Effective field theory bootstrap, large-N χPT and holographic QCD. Journal of High Energy Physics, 2024, 2024: 72. doi: 10.1007/jhep01(2024)072
|
[32] |
Paulos M F, Penedones J, Toledo J, et al. The S-matrix bootstrap II: Two dimensional amplitudes. Journal of High Energy Physics, 2017, 2017: 143. doi: 10.1007/jhep11(2017)143
|
[33] |
Paulos M F, Penedones J, Toledo J, et al. The S-matrix bootstrap. Part III:Higher dimensional amplitudes. Journal of High Energy Physics, 2019, 2019: 40. doi: 10.1007/jhep12(2019)040
|
[34] |
He Y, Irrgang A, Kruczenski M. A note on the S-matrix bootstrap for the 2d O(N) bosonic model. Journal of High Energy Physics, 2018, 2018: 93. doi: 10.1007/jhep11(2018)093
|
[35] |
He Y, Kruczenski M. S-matrix bootstrap in 3+1 dimensions: Regularization and dual convex problem. Journal of High Energy Physics, 2021, 2021: 125. doi: 10.1007/jhep08(2021)125
|
[36] |
Karateev D, Kuhn S, Penedones J. Bootstrapping massive quantum field theories. Journal of High Energy Physics, 2020, 2020: 35. doi: 10.1007/jhep07(2020)035
|
[37] |
Guerrieri A L, Penedones J, Vieira P. S-matrix bootstrap for effective field theories: Massless pions. Journal of High Energy Physics, 2021, 2021: 88. doi: 10.1007/jhep06(2021)088
|
[38] |
Kruczenski M, Murali H. The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary. Journal of High Energy Physics, 2021, 2021: 97. doi: 10.1007/jhep04(2021)097
|
[39] |
Guerrieri A, Sever A. Rigorous bounds on the analytic S matrix . Physical Review Letters, 2021, 127: 251601. doi: 10.1103/physrevlett.127.251601
|
[40] |
Guerrieri A, Penedones J, Vieira P. Where is string theory in the space of scattering amplitudes. Physical Review Letters, 2021, 127: 081601. doi: 10.1103/physrevlett.127.081601
|
[41] |
Albert J, Rastelli L. Bootstrapping pions at large N. Part II: background gauge fields and the chiral anomaly. arXiv: 2307. 01246, 2023.
|
[42] |
Acanfora F, Guerrieri A, Häring K, et al. Bounds on scattering of neutral Goldstones. Journal of High Energy Physics, 2024, 2024: 28. doi: 10.1007/jhep03(2024)028
|
[43] |
Miró J E, Guerrieri A, Gumus M A. Extremal Higgs couplings. arXiv: 2311. 09283, 2023.
|
[44] |
de Rham C, Kundu S, Reece M, et al. Snowmass white paper: UV constraints on IR physics. arXiv: 2203. 06805, 2022.
|
[45] |
Zhang C, Zhou S Y. Positivity bounds on vector boson scattering at the LHC. Physical Review D, 2019, 100: 095003. doi: 10.1103/physrevd.100.095003
|
[46] |
Bi Q, Zhang C, Zhou S Y. Positivity constraints on aQGC: Carving out the physical parameter space. Journal of High Energy Physics, 2019, 2019: 137. doi: 10.1007/jhep06(2019)137
|
[47] |
Bellazzini B, Riva F. New phenomenological and theoretical perspective on anomalous ZZ and Zγ processes. Physical Review D, 2018, 98: 095021. doi: 10.1103/physrevd.98.095021
|
[48] |
Remmen G N, Rodd N L. Consistency of the standard model effective field theory. Journal of High Energy Physics, 2019, 2019: 32. doi: 10.1007/jhep12(2019)032
|
[49] |
Yamashita K, Zhang C, Zhou S Y. Elastic positivity vs extremal positivity bounds in SMEFT: A case study in transversal electroweak gauge-boson scatterings. Journal of High Energy Physics, 2021, 2021: 95. doi: 10.1007/jhep01(2021)095
|
[50] |
Trott T. Causality, unitarity and symmetry in effective field theory. Journal of High Energy Physics, 2021, 2021: 143. doi: 10.1007/jhep07(2021)143
|
[51] |
Remmen G N, Rodd N L. Flavor constraints from unitarity and analyticity. Physical Review Letters, 2020, 125: 081601. doi: 10.1103/physrevlett.125.081601
|
[52] |
Remmen G N, Rodd N L. Signs, spin, SMEFT: Sum rules at dimension six. Physical Review D, 2022, 105: 036006. doi: 10.1103/physrevd.105.036006
|
[53] |
Gu J, Wang L T. Sum rules in the standard model effective field theory from helicity amplitudes. Journal of High Energy Physics, 2021, 2021: 149. doi: 10.1007/jhep03(2021)149
|
[54] |
Fuks B, Liu Y, Zhang C, et al. Positivity in electron-positron scattering: Testing the axiomatic quantum field theory principles and probing the existence of UV states. Chinese Physics C, 2021, 45: 023108. doi: 10.1088/1674-1137/abcd8c
|
[55] |
Gu J, Wang L T, Zhang C. Unambiguously testing positivity at lepton colliders. Physical Review Letters, 2022, 129: 011805. doi: 10.1103/physrevlett.129.011805
|
[56] |
Bonnefoy Q, Gendy E, Grojean C. Positivity bounds onminimal flavor violation. Journal of High Energy Physics, 2021, 2021: 115. doi: 10.1007/jhep04(2021)115
|
[57] |
Davighi J, Melville S, You T. Natural selection rules: New positivity bounds for massive spinning particles. Journal of High Energy Physics, 2022, 2022: 167. doi: 10.1007/jhep02(2022)167
|
[58] |
Chala M, Santiago J. Positivity bounds in the standard model effective field theory beyond tree level. Physical Review D, 2022, 105: L111901. doi: 10.1103/physrevd.105.l111901
|
[59] |
Zhang C. SMEFTs living on the edge: Determining the UV theories from positivity and extremality. Journal of High Energy Physics, 2022, 2022: 96. doi: 10.1007/jhep12(2022)096
|
[60] |
Ghosh D, Sharma R, Ullah F. Amplitude’s positivity vs. subluminality: Causality and unitarity constraints on dimension 6 & 8 gluonic operators in the SMEFT. Journal of High Energy Physics, 2023, 2023: 199. doi: 10.1007/jhep02(2023)199
|
[61] |
Remmen G N, Rodd N L. Spinning sum rules for the dimension-six SMEFT. Journal of High Energy Physics, 2022, 2022: 30. doi: 10.1007/jhep09(2022)030
|
[62] |
Li X, Zhou S. Origin of neutrino masses on the convex cone of positivity bounds. Physical Review D, 2023, 107: L031902. doi: 10.1103/physrevd.107.l031902
|
[63] |
Li X, Mimasu K, Yamashita K, et al. Moments for positivity: Using Drell-Yan data to test positivity bounds and reverse-engineer new physics. Journal of High Energy Physics, 2022, 2022: 107. doi: 10.1007/jhep10(2022)107
|
[64] |
Li X. Positivity bounds at one-loop level: The Higgs sector. Journal of High Energy Physics, 2023, 2023: 230. doi: 10.1007/jhep05(2023)230
|
[65] |
Altmannshofer W, Gori S, Lehmann B V, et al. UV physics from IR features: New prospects from top flavor violation. Physical Review D, 2023, 107: 095025. doi: 10.1103/physrevd.107.095025
|
[66] |
Davighi J, Melville S, Mimasu K, et al. Positivity and the electroweak hierarchy. Physical Review D, 2024, 109: 033009. doi: 10.1103/physrevd.109.033009
|
[67] |
Ellis J, Mimasu K, Zampedri F. Dimension-8 SMEFT analysis of minimal scalar field extensions of the Standard Model. Journal of High Energy Physics, 2023, 2023: 51. doi: 10.1007/jhep10(2023)051
|
[68] |
Chala M, Li X. Positivity restrictions on the mixing of dimension-eight SMEFT operators. Physical Review D, 2024, 109: 065015. doi: 10.1103/physrevd.109.065015
|
[69] |
Gu J, Shu C. Probing positivity at the LHC with exclusive photon-fusion processes. Journal of High Energy Physics, 2024, 2024: 183. doi: 10.1007/jhep05(2024)183
|
[70] |
Li H L, Ren Z, Shu J, et al. Complete set of dimension-eight operators in the standard model effective field theory. Physical Review D, 2021, 104: 015026. doi: 10.1103/physrevd.104.015026
|
[71] |
Murphy C W. Dimension-8 operators in the Standard Model Effective Field Theory. Journal of High Energy Physics, 2020, 2020: 174. doi: 10.1007/jhep10(2020)174
|
[72] |
Vecchi L. Causal vs. analytic constraints on anomalous quartic gauge couplings. Journal of High Energy Physics, 2007, 2007: 54. doi: 10.1088/1126-6708/2007/11/054
|
[73] |
Chen Q, Mimasu K, Wu T A, et al. Capping the positivity cone: Dimension-8 Higgs operators in the SMEFT. Journal of High Energy Physics, 2024, 2024: 180. doi: 10.1007/jhep03(2024)180
|
[74] |
Froissart M. Asymptotic behavior and subtractions in the mandelstam representation. Physical Review, 1961, 123: 1053–1057. doi: 10.1103/physrev.123.1053
|
[75] |
Martin A. Unitarity and high-energy behavior of scattering amplitudes. Physical Review, 1963, 129: 1432–1436. doi: 10.1103/physrev.129.1432
|
[76] |
Landry W, Simmons-Duffin D. Scaling the semidefinite program solver SDPB. arXiv: 1909. 09745, 2019.
|