Skip to main content
SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

Consistency of the standard model effective field theory

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 04 December 2019
  • volume 2019, Article number: 32 (2019)
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
Consistency of the standard model effective field theory
Download PDF
  • Grant N. Remmen1,2 &
  • Nicholas L. Rodd  ORCID: orcid.org/0000-0003-3472-76061,2 

  • 402 Accesses

  • 69 Citations

  • 2 Altmetric

  • Explore all metrics

Cite this article

A preprint version of the article is available at arXiv.

Abstract

We derive bounds on couplings in the standard model effective field theory (SMEFT) as a consequence of causality and the analytic structure of scattering amplitudes. In the SMEFT, there are 64 independent operators at mass dimension eight that are quartic in bosons (either Higgs or gauge fields) and that contain four derivatives and/or field strengths, including both CP-conserving and CP-violating operators. Using analytic dispersion relation arguments for two-to-two bosonic scattering amplitudes, we derive 27 independent bounds on the sign or magnitude of the couplings. We show that these bounds also follow as a consequence of causality of signal propagation in nonvacuum SM backgrounds. These bounds come in two qualitative forms: i) positivity of (various linear combinations of) couplings of CP-even operators and ii) upper bounds on the magnitude of CP-odd operators in terms of (products of) CP-even couplings. We exhibit various classes of example completions, which all satisfy our EFT bounds. These bounds have consequences for current and future particle physics experiments, as part of the observable parameter space is inconsistent with causality and analyticity. To demonstrate the impact of our bounds, we consider applications both to SMEFT constraints derived at colliders and to limits on the neutron electric dipole moment, highlighting the connection between such searches suggested by infrared consistency.

Article PDF

Download to read the full article text

Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett.B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].

  2. CMS collaboration, Observation of a new boson at a Mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett.B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].

  3. O. Buchmueller and P. de Jong, Supersymmetry, Part II (experiment), in Review of particle physics, Particle Data Group collabroation, Phys. Rev.D 98 (2018) 030001 [INSPIRE].

  4. G.F. Giudice, The dawn of the post-naturalness era, in From my vast repertoire. . . : Guido Altarelli’s legacy, A. Levy, S. Forte and G. Ridolfieds., World Scientific, Singapore (2019), arXiv:1710.07663, [INSPIRE].

  5. J.L. Feng, Naturalness and the status of supersymmetry, Ann. Rev. Nucl. Part. Sci.63 (2013) 351 [arXiv:1302.6587] [INSPIRE].

    Article  ADS  Google Scholar 

  6. C. Cheung and G.N. Remmen, Naturalness and the weak gravity conjecture, Phys. Rev. Lett.113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].

    Article  ADS  Google Scholar 

  7. S. Dimopoulos, LHC, SSC and the universe, Phys. Lett.B 246 (1990) 347 [INSPIRE].

    Article  ADS  Google Scholar 

  8. R. Percacci, Asymptotic safety, arXiv:0709.3851 [INSPIRE].

  9. ATLAS, CMS collaboration, Report on the physics at the HL-LHC and perspectives for the HE-LHC, arXiv:1902.10229 [INSPIRE].

  10. Working Group 3 collaboration, Beyond the standard model physics at the HL-LHC and HE-LHC, arXiv:1812.07831 [INSPIRE].

  11. J. Gao, L. Harland-Lang and J. Rojo, The structure of the proton in the LHC precision era, Phys. Rept.742 (2018) 1 [arXiv:1709.04922] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. J. Erler and M. Schott, Electroweak precision tests of the standard model after the discovery of the Higgs boson, Prog. Part. Nucl. Phys.106 (2019) 68 [arXiv:1902.05142] [INSPIRE].

    Article  ADS  Google Scholar 

  13. M. Reece, Physics at a Higgs factory, Int. J. Mod. Phys.A 31 (2016) 1644003 [arXiv:1609.03018] [INSPIRE].

    Article  ADS  Google Scholar 

  14. C.A. Baker et al., An improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett.97 (2006) 131801 [hep-ex/0602020] [INSPIRE].

    Article  ADS  Google Scholar 

  15. J.M. Pendlebury et al., Revised experimental upper limit on the electric dipole moment of the neutron, Phys. Rev.D 92 (2015) 092003 [arXiv:1509.04411] [INSPIRE].

    ADS  Google Scholar 

  16. B. Graner, Y. Chen, E.G. Lindahl and B.R. Heckel, Reduced limit on the permanent electric dipole moment of 199Hg, Phys. Rev. Lett.116 (2016) 161601 [Erratum ibid.119 (2017) 119901] [arXiv:1601.04339] [INSPIRE].

  17. ACME collaboration, Improved limit on the electric dipole moment of the electron, Nature562 (2018) 355 [INSPIRE].

  18. ACME collaboration, Order of magnitude smaller limit on the electric dipole moment of the electron, Science343 (2014) 269 [arXiv:1310.7534] [INSPIRE].

  19. W.B. Cairncross et al., Precision measurement of the electron’s electric dipole moment using trapped molecular ions, Phys. Rev. Lett.119 (2017) 153001 [arXiv:1704.07928] [INSPIRE].

    Article  ADS  Google Scholar 

  20. Muon g-2 collaboration, Final report of the muon E821 anomalous magnetic moment measurement at BNL, Phys. Rev.D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].

  21. Muon g-2 collaboration, Muon (g − 2) technical design report, arXiv:1501.06858 [INSPIRE].

  22. B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the standard model lagrangian, JHEP10 (2010) 085 [arXiv:1008.4884] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  23. B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT, JHEP08 (2017) 016 [Erratum ibid.09 (2019) 019] [arXiv:1512.03433] [INSPIRE].

  24. R.M. Fonseca, Enumerating the operators of an effective field theory, arXiv:1907.12584 [INSPIRE].

  25. I. Brivio and M. Trott, The standard model as an effective field theory, Phys. Rept.793 (2019) 1 [arXiv:1706.08945] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  26. R. Contino et al., On the validity of the effective field theory approach to SM precision tests, JHEP07 (2016) 144 [arXiv:1604.06444] [INSPIRE].

    Article  ADS  Google Scholar 

  27. ATLAS collaboration, Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC, Nature Phys.13 (2017) 852 [arXiv:1702.01625] [INSPIRE].

  28. ATLAS collaboration, Observation of electroweak W ±Z boson pair production in association with two jets in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Lett.B 793 (2019) 469 [arXiv:1812.09740] [INSPIRE].

  29. ATLAS collaboration, Observation of electroweak production of a same-sign W boson pair in association with two jets in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev. Lett.123 (2019) 161801 [arXiv:1906.03203] [INSPIRE].

  30. CMS collaboration, Measurement of vector boson scattering and constraints on anomalous quartic couplings from events with four leptons and two jets in proton—roton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Lett.B 774 (2017) 682 [arXiv:1708.02812] [INSPIRE].

  31. CMS collaboration, Observation of electroweak production of same-sign W boson pairs in the two jet and two same-sign lepton final state in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Rev. Lett.120 (2018) 081801 [arXiv:1709.05822] [INSPIRE].

  32. CMS collaboration, Measurement of electroweak W Z boson production and search for new physics in WZ + two jets events in pp collisions at \( \sqrt{s} \) = 13 TeV, Phys. Lett.B 795 (2019) 281 [arXiv:1901.04060] [INSPIRE].

  33. J. Ellis, C.W. Murphy, V. Sanz and T. You, Updated global SMEFT fit to Higgs, diboson and electroweak data, JHEP06 (2018) 146 [arXiv:1803.03252] [INSPIRE].

    Article  ADS  Google Scholar 

  34. A. Adams et al., Causality, analyticity and an IR obstruction to UV completion, JHEP10 (2006) 014 [hep-th/0602178] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  35. T.N. Pham and T.N. Truong, Evaluation of the derivative quartic terms of the meson chiral lagrangian from forward dispersion relation, Phys. Rev.D 31 (1985) 3027 [INSPIRE].

    ADS  Google Scholar 

  36. B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints, Phys. Rev.D 51 (1995) 1093 [hep-ph/9410302] [INSPIRE].

    ADS  Google Scholar 

  37. M.R. Pennington and J. Portoles, The chiral lagrangian parameters, ℓ 1, ℓ 2, are determined by the ρ-resonance, Phys. Lett.B 344 (1995) 399 [hep-ph/9409426] [INSPIRE].

    Article  ADS  Google Scholar 

  38. A. Jenkins and D. O’Connell, The story of \( \mathcal{O} \): positivity constraints in effective field theories, hep-th/0609159 [INSPIRE].

  39. G. Dvali, A. Franca and C. Gomez, Road signs for UV-completion, arXiv:1204.6388 [INSPIRE].

  40. B. Bellazzini, C. Cheung and G.N. Remmen, Quantum gravity constraints from unitarity and analyticity, Phys. Rev.D 93 (2016) 064076 [arXiv:1509.00851] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  41. C. Cheung and G.N. Remmen, Positivity of curvature-squared corrections in gravity, Phys. Rev. Lett.118 (2017) 051601 [arXiv:1608.02942] [INSPIRE].

    Article  ADS  Google Scholar 

  42. X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP02 (2016) 020 [arXiv:1407.5597] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. A. Gruzinov and M. Kleban, A note on causality constrains higher curvature corrections to gravity, Class. Quant. Grav.24 (2007) 3521 [hep-th/0612015] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  44. C. Cheung and G.N. Remmen, Positive signs in massive gravity, JHEP04 (2016) 002 [arXiv:1601.04068] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  45. C. de Rham, S. Melville and A.J. Tolley, Improved positivity bounds and massive gravity, JHEP04 (2018) 083 [arXiv:1710.09611] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  46. X.O. Camanho, G. Lucena Gómez and R. Rahman, Causality constraints on massive gravity, Phys. Rev.D 96 (2017) 084007 [arXiv:1610.02033] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  47. B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, Beyond positivity bounds and the fate of massive gravity, Phys. Rev. Lett.120 (2018) 161101 [arXiv:1710.02539] [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. J. Bonifacio and K. Hinterbichler, Bounds on amplitudes in effective theories with massive spinning particles, Phys. Rev.D 98 (2018) 045003 [arXiv:1804.08686] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  50. J. Bonifacio, K. Hinterbichler and R.A. Rosen, Positivity constraints for pseudolinear massive spin-2 and vector Galileons, Phys. Rev.D 94 (2016) 104001 [arXiv:1607.06084] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  51. C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, UV complete me: positivity bounds for particles with spin, JHEP03 (2018) 011 [arXiv:1706.02712] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  52. K. Hinterbichler, A. Joyce and R.A. Rosen, Massive spin-2 scattering and asymptotic superluminality, JHEP03 (2018) 051 [arXiv:1708.05716] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  53. 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 [arXiv:1804.10624] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, Massive higher spins: effective theory and consistency, JHEP10 (2019) 189 [arXiv:1903.08664] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. A. Nicolis, R. Rattazzi and E. Trincherini, Energy’s and amplitudes’ positivity, JHEP05 (2010) 095 [Erratum ibid.11 (2011) 128] [arXiv:0912.4258] [INSPIRE].

  56. H. Elvang et al., On renormalization group flows and the a-theorem in 6d, JHEP10 (2012) 011 [arXiv:1205.3994] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  57. C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Massive galileon positivity bounds, JHEP09 (2017) 072 [arXiv:1702.08577] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  58. V. Chandrasekaran, G.N. Remmen and A. Shahbazi-Moghaddam, Higher-point positivity, JHEP11 (2018) 015 [arXiv:1804.03153] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. M. Herrero-Valea, I. Timiryasov and A. Tokareva, To positivity and beyond, where Higgs-dilaton inflation has never gone before, arXiv:1905.08816 [INSPIRE].

  60. Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP12 (2011) 099 [arXiv:1107.3987] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  62. J. Distler, B. Grinstein, R.A. Porto and I.Z. Rothstein, Falsifying models of new physics via WW scattering, Phys. Rev. Lett.98 (2007) 041601 [hep-ph/0604255] [INSPIRE].

    Article  ADS  Google Scholar 

  63. L. Vecchi, Causal versus analytic constraints on anomalous quartic gauge couplings, JHEP11 (2007) 054 [arXiv:0704.1900] [INSPIRE].

    Article  ADS  Google Scholar 

  64. B. Bellazzini and F. Riva, New phenomenological and theoretical perspective on anomalous ZZ and Zγ processes, Phys. Rev.D 98 (2018) 095021 [arXiv:1806.09640] [INSPIRE].

    ADS  Google Scholar 

  65. C. Zhang and S.-Y. Zhou, Positivity bounds on vector boson scattering at the LHC, Phys. Rev.D 100 (2019) 095003 [arXiv:1808.00010] [INSPIRE].

    ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  67. C. Cheung and G.N. Remmen, Infrared consistency and the weak gravity conjecture, JHEP12 (2014) 087 [arXiv:1407.7865] [INSPIRE].

    Article  ADS  Google Scholar 

  68. C. Cheung, J. Liu and G.N. Remmen, Proof of the weak gravity conjecture from black hole entropy, JHEP10 (2018) 004 [arXiv:1801.08546] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  69. C. Cheung, J. Liu and G.N. Remmen, Entropy bounds on effective field theory from rotating dyonic black holes, Phys. Rev.D 100 (2019) 046003 [arXiv:1903.09156] [INSPIRE].

    ADS  Google Scholar 

  70. B. Bellazzini, M. Lewandowski and J. Serra, Amplitudes’ positivity, weak gravity conjecture and modified gravity, arXiv:1902.03250 [INSPIRE].

  71. A.M. Charles, The weak gravity conjecture, RG flows and supersymmetry, arXiv:1906.07734 [INSPIRE].

  72. C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].

  73. H. Ooguri and C. Vafa, On the geometry of the string landscape and the swampland, Nucl. Phys.B 766 (2007) 21 [hep-th/0605264] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP06 (2007) 060 [hep-th/0601001] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  75. D.R. Green, P. Meade and M.-A. Pleier, Multiboson interactions at the LHC, Rev. Mod. Phys.89 (2017) 035008 [arXiv:1610.07572] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  76. O.J.P. Eboli, M.C. Gonzalez-Garcia and J.K. Mizukoshi, pp → jje ±μ ±νν and jje ±μ ∓νν at \( \mathcal{O}\left({\alpha}_{\mathrm{em}}^6\right) \)and \( \mathcal{O}\left({\alpha}_{\mathrm{em}}^6{\alpha}_s^2\right) \)for the study of the quartic electroweak gauge boson vertex at CERN LHC, Phys. Rev.D 74 (2006) 073005 [hep-ph/0606118] [INSPIRE].

    ADS  Google Scholar 

  77. I. Low, R. Rattazzi and A. Vichi, Theoretical constraints on the Higgs effective couplings, JHEP04 (2010) 126 [arXiv:0907.5413] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  78. C. Englert, G.F. Giudice, A. Greljo and M. Mccullough, The \( \hat{H} \)-parameter: an oblique Higgs view, JHEP09 (2019) 041 [arXiv:1903.07725] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  79. M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys. Rev.123 (1961) 1053 [INSPIRE].

    Article  ADS  Google Scholar 

  80. A. Martin, Unitarity and high-energy behavior of scattering amplitudes, Phys. Rev.129 (1963) 1432 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  81. A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1., Nuovo Cim.A 42 (1965) 930 [INSPIRE].

    ADS  Google Scholar 

  82. S. Mandelstam, Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity. General theory, Phys. Rev.112 (1958) 1344 [INSPIRE].

  83. H. Lehmann, Analytic properties of scattering amplitudes as functions of momentum transfer, Nuovo Cim.10 (1958) 579.

    Article  ADS  MATH  Google Scholar 

  84. G.A. Benford, D.L. Book and W.A. Newcomb, The tachyonic antitelephone, Phys. Rev.D 2 (1970) 263 [INSPIRE].

    ADS  Google Scholar 

  85. R.C. Tolman, The theory of relativity of motion, University of California Press, Berkeley, U.S.A. (1917).

    MATH  Google Scholar 

  86. A.Yu. Morozov, Matrix of mixing of scalar and vector mesons of dimension D ≤ 8 in QCD (in Russian), Sov. J. Nucl. Phys.40 (1984) 505 [INSPIRE].

    Google Scholar 

  87. C. Hays, A. Martin, V. Sanz and J. Setford, On the impact of dimension-eight SMEFT operators on Higgs measurements, JHEP02 (2019) 123 [arXiv:1808.00442] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  88. A. Martin, private communication (2019).

  89. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett.43 (1979) 1566 [INSPIRE].

    Article  ADS  Google Scholar 

  90. W. Buchmüller and D. Wyler, Effective lagrangian analysis of new interactions and flavor conservation, Nucl. Phys.B 268 (1986) 621 [INSPIRE].

    Article  ADS  Google Scholar 

  91. E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators I: formalism and λ dependence, JHEP10 (2013) 087 [arXiv:1308.2627] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  92. E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators II: Yukawa dependence, JHEP01 (2014) 035 [arXiv:1310.4838] [INSPIRE].

    Article  ADS  Google Scholar 

  93. R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators III: gauge coupling dependence and phenomenology, JHEP04 (2014) 159 [arXiv:1312.2014] [INSPIRE].

    Article  ADS  Google Scholar 

  94. E.E. Jenkins, A.V. Manohar and P. Stoffer, Low-energy effective field theory below the electroweak scale: operators and matching, JHEP03 (2018) 016 [arXiv:1709.04486] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  95. E.E. Jenkins, A.V. Manohar and P. Stoffer, Low-energy effective field theory below the electroweak scale: anomalous dimensions, JHEP01 (2018) 084 [arXiv:1711.05270] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  96. H. Elvang and Y.-t. Huang, Scattering amplitudes, arXiv:1308.1697 [INSPIRE].

  97. R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys.B 715 (2005) 499 [hep-th/0412308] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  98. 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 [hep-th/0501052] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  99. N. Arkani-Hamed et al., Grassmannian geometry of scattering amplitudes, Cambridge University Press, Cambridge U.K. (2016) [arXiv:1212.5605] [INSPIRE].

    Book  MATH  Google Scholar 

  100. C. Cheung, G.N. Remmen, C.-H. Shen and C. Wen, Pions as gluons in higher dimensions, JHEP04 (2018) 129 [arXiv:1709.04932] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  101. H. Kawai, D.C. Lewellen and S.H.H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys.B 269 (1986) 1 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  102. A. Rebhan and G. Turk, Polarization effects in light-by-light scattering: Euler–Heisenberg versus Born–Infeld, Int. J. Mod. Phys.A 32 (2017) 1750053 [arXiv:1701.07375] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  103. G.W. Gibbons and C.A.R. Herdeiro, Born-Infeld theory and stringy causality, Phys. Rev.D 63 (2001) 064006 [hep-th/0008052] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  104. M. Fouché, R. Battesti and C. Rizzo, Limits on nonlinear electrodynamics, Phys. Rev.D 93 (2016) 093020 [Erratum ibid.D 95 (2017) 099902] [arXiv:1605.04102] [INSPIRE].

  105. F. Abalos, F. Carrasco, É. Goulart and O. Reula, Nonlinear electrodynamics as a symmetric hyperbolic system, Phys. Rev.D 92 (2015) 084024 [arXiv:1507.02262] [INSPIRE].

    ADS  Google Scholar 

  106. W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys.98 (1936) 714 [physics/0605038].

    Article  ADS  MATH  Google Scholar 

  107. J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev.82 (1951) 664 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  108. V. Weisskopf, The electrodynamics of the vacuum based on the quantum theory of the electron, Kong. Dans. Vid. Selsk. Mat-Fys. Medd.XIV (1936) 1.

    Google Scholar 

  109. J. Quevillon, C. Smith and S. Touati, Effective action for gauge bosons, Phys. Rev.D 99 (2019) 013003 [arXiv:1810.06994] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  110. C.G. Wohl, SU(n) multiplets and Young diagrams, in Review of particle physics, Particle Data Group collabroation, Phys. Rev.D 98 (2018) 030001 [INSPIRE].

  111. J. Banks and H. Georgi, Comment on gauge theories without anomalies, Phys. Rev.D 14 (1976) 1159 [INSPIRE].

    ADS  Google Scholar 

  112. M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond.A 144 (1934) 425.

    Article  ADS  MATH  Google Scholar 

  113. E.S. Fradkin and A.A. Tseytlin, Nonlinear electrodynamics from quantized strings, Phys. Lett.B 163 (1985) 123.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  114. A.A. Tseytlin, Born-Infeld action, supersymmetry and string theory, hep-th/9908105 [INSPIRE].

  115. C. Cheung, C.-H. Shen and C. Wen, Unifying relations for scattering amplitudes, JHEP02 (2018) 095 [arXiv:1705.03025] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  116. C. Cheung et al., Vector effective field theories from soft limits, Phys. Rev. Lett.120 (2018) 261602 [arXiv:1801.01496] [INSPIRE].

    Article  ADS  Google Scholar 

  117. J. Ellis and S.-F. Ge, Constraining gluonic quartic gauge coupling operators with gg → γγ, Phys. Rev. Lett.121 (2018) 041801 [arXiv:1802.02416] [INSPIRE].

    Article  ADS  Google Scholar 

  118. J.H. Schwarz, Dilaton-axion symmetry, in the proceedings of the International Workshop on String Theory, Quantum Gravity and the Unification of Fundamental Interactions, September 21–26, Rome, Italy (1992), hep-th/9209125 [INSPIRE].

  119. R. Kallosh, Supergravity, M-theory and cosmology, in the proceedings of The future of theoretical physics and cosmology: Celebrating Stephen Hawking’s 60thbirthday, January 7–10, Cambridge, U.K. (2002), hep-th/0205315 [INSPIRE].

  120. J.P. Conlon, The QCD axion and moduli stabilisation, JHEP05 (2006) 078 [hep-th/0602233] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  121. X. Gao and P. Shukla, Dimensional oxidation and modular completion of non-geometric type IIB action, JHEP05 (2015) 018 [arXiv:1501.07248] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  122. S. Endlich, V. Gorbenko, J. Huang and L. Senatore, An effective formalism for testing extensions to General Relativity with gravitational waves, JHEP09 (2017) 122 [arXiv:1704.01590] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  123. K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys.84 (2012) 671 [arXiv:1105.3735] [INSPIRE].

    Article  ADS  Google Scholar 

  124. N.P. Hartland et al., A Monte Carlo global analysis of the Standard Model Effective Field Theory: the top quark sector, JHEP04 (2019) 100 [arXiv:1901.05965] [INSPIRE].

    Article  ADS  Google Scholar 

  125. S. van Beek, E.R. Nocera, J. Rojo and E. Slade, Constraining the SMEFT with Bayesian reweighting, arXiv:1906.05296 [INSPIRE].

  126. V. De Luca et al., Colored dark matter, Phys. Rev.D 97 (2018) 115024 [arXiv:1801.01135] [INSPIRE].

    ADS  Google Scholar 

  127. O.J.P. Eboli, M.C. Gonzalez-Garcia, S.M. Lietti and S.F. Novaes, Anomalous quartic gauge boson couplings at hadron colliders, Phys. Rev.D 63 (2001) 075008 [hep-ph/0009262] [INSPIRE].

    ADS  Google Scholar 

  128. D0 collaboration, Search for anomalous quartic WWγγ couplings in dielectron and missing energy final states in \( p\overline{p} \)collisions at \( \sqrt{s} \) = 1.96 TeV, Phys. Rev.D 88 (2013) 012005 [arXiv:1305.1258] [INSPIRE].

  129. CMS collaboration, Study of exclusive two-photon production of W +W −in pp collisions at \( \sqrt{s} \) = 7 TeV and constraints on anomalous quartic gauge couplings, JHEP07 (2013) 116 [arXiv:1305.5596] [INSPIRE].

  130. CMS collaboration, Evidence for exclusive γγ → W +W −production and constraints on anomalous quartic gauge couplings in pp collisions at \( \sqrt{s} \) = 7 and 8 TeV, JHEP08 (2016) 119 [arXiv:1604.04464] [INSPIRE].

  131. ATLAS collaboration, Measurements of Zγ and Zγγ production in pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, Phys. Rev.D 93 (2016) 112002 [arXiv:1604.05232] [INSPIRE].

  132. J. Ellis, N.E. Mavromatos and T. You, Light-by-light scattering constraint on Born-Infeld theory, Phys. Rev. Lett.118 (2017) 261802 [arXiv:1703.08450] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  133. A. Butter et al., The gauge-Higgs legacy of the LHC Run I, JHEP07 (2016) 152 [arXiv:1604.03105] [INSPIRE].

    Article  ADS  Google Scholar 

  134. B. Henning, D. Lombardo, M. Riembau and F. Riva, Higgs couplings without the Higgs, Phys. Rev. Lett.123 (2019) 181801 [arXiv:1812.09299] [INSPIRE].

    Article  ADS  Google Scholar 

  135. C. Degrande et al., Monte Carlo tools for studies of non-standard electroweak gauge boson interactions in multi-boson processes: A Snowmass White Paper, in the proceedings of the 2013 Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi (CSS2013), July 29–August 6, Minneapolis, U.S.A. (2013), arXiv:1309.7890 [INSPIRE].

  136. M. Rauch, Vector-boson fusion and vector-boson scattering, arXiv:1610.08420 [INSPIRE].

  137. D. Liu, A. Pomarol, R. Rattazzi and F. Riva, Patterns of strong coupling for LHC searches, JHEP11 (2016) 141 [arXiv:1603.03064] [INSPIRE].

    Article  ADS  Google Scholar 

  138. D. Liu and L.-T. Wang, Prospects for precision measurement of diboson processes in the semileptonic decay channel in future LHC runs, Phys. Rev.D 99 (2019) 055001 [arXiv:1804.08688] [INSPIRE].

    ADS  Google Scholar 

  139. C. Degrande, A basis of dimension-eight operators for anomalous neutral triple gauge boson interactions, JHEP02 (2014) 101 [arXiv:1308.6323] [INSPIRE].

    Article  ADS  Google Scholar 

  140. J. Ellis, S.-F. Ge, H.-J. He and R.-Q. Xiao, Probing the scale of new physics in the ZZγ coupling at e +e −colliders, arXiv:1902.06631 [INSPIRE].

  141. E.H. Simmons, Dimension-six gluon operators as probes of new physics, Phys. Lett.B 226 (1989) 132 [INSPIRE].

    Article  ADS  Google Scholar 

  142. E.H. Simmons, Higher dimension gluon operators and hadronic scattering, Phys. Lett.B 246 (1990) 471 [INSPIRE].

    Article  ADS  Google Scholar 

  143. M. Czakon et al., Top-pair production at the LHC through NNLO QCD and NLO EW, JHEP10 (2017) 186 [arXiv:1705.04105] [INSPIRE].

    Article  ADS  Google Scholar 

  144. S. Weinberg, Larger Higgs exchange terms in the neutron electric dipole moment, Phys. Rev. Lett.63 (1989) 2333 [INSPIRE].

    Article  ADS  Google Scholar 

  145. M. Chemtob, Nucleon electric dipole moment and dimension 8 gluonic operators, Phys. Rev.D 48 (1993) 283 [INSPIRE].

    ADS  Google Scholar 

  146. D. Chang, T.W. Kephart, W.-Y. Keung and T.C. Yuan, The chromoelectric dipole moment of the heavy quark and purely gluonic CP-violating operators, Phys. Rev. Lett.68 (1992) 439 [INSPIRE].

    Article  ADS  Google Scholar 

  147. A. Manohar and H. Georgi, Chiral quarks and the nonrelativistic quark model, Nucl. Phys.B 234 (1984) 189 [INSPIRE].

    Article  ADS  Google Scholar 

  148. H. Georgi and L. Randall, Flavor conserving CP-violation in invisible axion models, Nucl. Phys.B 276 (1986) 241 [INSPIRE].

    Article  ADS  Google Scholar 

  149. ATLAS collaboration, Measurement of inclusive jet and dijet cross-sections in proton-proton collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP05 (2018) 195 [arXiv:1711.02692] [INSPIRE].

  150. CMS collaboration, Measurement of the triple-differential dijet cross section in proton-proton collisions at \( \sqrt{s} \) = 8 TeV and constraints on parton distribution functions, Eur. Phys. J.C 77 (2017) 746 [arXiv:1705.02628] [INSPIRE].

  151. A. A. Ahmadi, A. Olshevsky, P.A. Parrilo and J.N. Tsitsiklis, NP-hardness of deciding convexity of quartic polynomials and related problems, Math. Prog.137 (2013) 453 [arXiv:1012.1908].

    Article  MathSciNet  MATH  Google Scholar 

  152. N. Arkani-Hamed, T.C. Huang, Y.T. Huang and S.H. Shao, to appear.

  153. D.D. Dietrich and F. Sannino, Conformal window of SU(N) gauge theories with fermions in higher dimensional representations, Phys. Rev.D 75 (2007) 085018 [hep-ph/0611341] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  154. S. Okubo, Modified fourth order casimir invariants and indices for simple Lie algebras, J. Math. Phys.23 (1982) 8 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Author information

Authors and Affiliations

  1. Center for Theoretical Physics and Department of Physics, University of California, Berkeley, CA, 94720, U.S.A.

    Grant N. Remmen & Nicholas L. Rodd

  2. Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, U.S.A.

    Grant N. Remmen & Nicholas L. Rodd

Authors
  1. Grant N. Remmen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicholas L. Rodd
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicholas L. Rodd.

Additional information

ArXiv ePrint: 1908.09845

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Remmen, G.N., Rodd, N.L. Consistency of the standard model effective field theory. J. High Energ. Phys. 2019, 32 (2019). https://doi.org/10.1007/JHEP12(2019)032

Download citation

  • Received: 07 September 2019

  • Revised: 19 November 2019

  • Accepted: 20 November 2019

  • Published: 04 December 2019

  • DOI: https://doi.org/10.1007/JHEP12(2019)032

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Beyond Standard Model
  • Effective Field Theories
  • CP violation
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

Not affiliated

Springer Nature

© 2023 Springer Nature