Journal of High Energy Physics

, 2019:31 | Cite as

Complete one-loop matching for a singlet scalar in the Standard Model EFT

  • Minyuan Jiang
  • Nathaniel Craig
  • Ying-Ying Li
  • Dave SutherlandEmail author
Open Access
Regular Article - Theoretical Physics


We present the results of the first complete one-loop matching calculation between the real singlet scalar extension of the Standard Model and the Standard Model effective field theory (SMEFT) at dimension six. Beyond their immediate relevance to the precision calculation of observables in singlet extensions of the Standard Model, our results illustrate a variety of general features of one-loop matching. We explore the interplay between non-supersymmetric non-renormalization theorems, the logarithmic dependence of Wilson coefficients, and the relevance of mixed diagrams in theories with large scale separation. In addition, we highlight some of the subtleties involved in computing observables at next-to-leading order in SMEFT by mapping our results to the T parameter at one loop.


Beyond Standard Model Effective Field Theories 


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.


  1. [1]
    I. Brivio and M. Trott, The Standard Model as an Effective Field Theory, arXiv:1706.08945 [INSPIRE].
  2. [2]
    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  3. [3]
    C. Grojean, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Scaling of Higgs Operators and Γ(hγγ), JHEP 04 (2013) 016 [arXiv:1301.2588] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  5. [5]
    E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence, JHEP 01 (2014) 035 [arXiv:1310.4838] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    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, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector, arXiv:1610.07922 [INSPIRE].
  8. [8]
    G. Passarino and M. Trott, The Standard Model Effective Field Theory and Next to Leading Order, arXiv:1610.08356 [INSPIRE].
  9. [9]
    J. de Blas, J.C. Criado, M. Pérez-Victoria and J. Santiago, Effective description of general extensions of the Standard Model: the complete tree-level dictionary, JHEP 03 (2018) 109 [arXiv:1711.10391] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP 01 (2016) 023 [arXiv:1412.1837] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    M.K. Gaillard, The Effective One Loop Lagrangian With Derivative Couplings, Nucl. Phys. B 268 (1986) 669 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    L.-H. Chan, Derivative Expansion for the One Loop Effective Actions With Internal Symmetry, Phys. Rev. Lett. 57 (1986) 1199 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    O. Cheyette, Effective Action for the Standard Model With Large Higgs Mass, Nucl. Phys. B 297 (1988) 183 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    A. Drozd, J. Ellis, J. Quevillon and T. You, The Universal One-Loop Effective Action, JHEP 03 (2016) 180 [arXiv:1512.03003] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    F. del Aguila, Z. Kunszt and J. Santiago, One-loop effective lagrangians after matching, Eur. Phys. J. C 76 (2016) 244 [arXiv:1602.00126] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    M. Boggia, R. Gomez-Ambrosio and G. Passarino, Low energy behaviour of standard model extensions, JHEP 05 (2016) 162 [arXiv:1603.03660] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    B. Henning, X. Lu and H. Murayama, One-loop Matching and Running with Covariant Derivative Expansion, JHEP 01 (2018) 123 [arXiv:1604.01019] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    S.A.R. Ellis, J. Quevillon, T. You and Z. Zhang, Mixed heavy-light matching in the Universal One-Loop Effective Action, Phys. Lett. B 762 (2016) 166 [arXiv:1604.02445] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  19. [19]
    J. Fuentes-Martin, J. Portoles and P. Ruiz-Femenia, Integrating out heavy particles with functional methods: a simplified framework, JHEP 09 (2016) 156 [arXiv:1607.02142] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Z. Zhang, Covariant diagrams for one-loop matching, JHEP 05 (2017) 152 [arXiv:1610.00710] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    S.A.R. Ellis, J. Quevillon, T. You and Z. Zhang, Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients, JHEP 08 (2017) 054 [arXiv:1706.07765] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    V. Silveira and A. Zee, Scalar phantoms, Phys. Lett. 161B (1985) 136 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev. D 50 (1994) 3637 [hep-ph/0702143] [INSPIRE].
  24. [24]
    C.P. Burgess, M. Pospelov and T. ter Veldhuis, The Minimal model of nonbaryonic dark matter: A Singlet scalar, Nucl. Phys. B 619 (2001) 709 [hep-ph/0011335] [INSPIRE].
  25. [25]
    X.-G. He, T. Li, X.-Q. Li, J. Tandean and H.-C. Tsai, Constraints on Scalar Dark Matter from Direct Experimental Searches, Phys. Rev. D 79 (2009) 023521 [arXiv:0811.0658] [INSPIRE].ADSGoogle Scholar
  26. [26]
    M. Gonderinger, Y. Li, H. Patel and M.J. Ramsey-Musolf, Vacuum Stability, Perturbativity and Scalar Singlet Dark Matter, JHEP 01 (2010) 053 [arXiv:0910.3167] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  27. [27]
    Y. Mambrini, Higgs searches and singlet scalar dark matter: Combined constraints from XENON 100 and the LHC, Phys. Rev. D 84 (2011) 115017 [arXiv:1108.0671] [INSPIRE].ADSGoogle Scholar
  28. [28]
    A. Menon, D.E. Morrissey and C.E.M. Wagner, Electroweak baryogenesis and dark matter in the NMSSM, Phys. Rev. D 70 (2004) 035005 [hep-ph/0404184] [INSPIRE].
  29. [29]
    S.J. Huber, T. Konstandin, T. Prokopec and M.G. Schmidt, Electroweak Phase Transition and Baryogenesis in the NMSSM, Nucl. Phys. B 757 (2006) 172 [hep-ph/0606298] [INSPIRE].
  30. [30]
    S. Profumo, M.J. Ramsey-Musolf and G. Shaughnessy, Singlet Higgs phenomenology and the electroweak phase transition, JHEP 08 (2007) 010 [arXiv:0705.2425] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    V. Barger, D.J.H. Chung, A.J. Long and L.-T. Wang, Strongly First Order Phase Transitions Near an Enhanced Discrete Symmetry Point, Phys. Lett. B 710 (2012) 1 [arXiv:1112.5460] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    J.R. Espinosa, T. Konstandin and F. Riva, Strong Electroweak Phase Transitions in the Standard Model with a Singlet, Nucl. Phys. B 854 (2012) 592 [arXiv:1107.5441] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  33. [33]
    K. Fuyuto and E. Senaha, Improved sphaleron decoupling condition and the Higgs coupling constants in the real singlet-extended standard model, Phys. Rev. D 90 (2014) 015015 [arXiv:1406.0433] [INSPIRE].ADSGoogle Scholar
  34. [34]
    D. Curtin, P. Meade and C.-T. Yu, Testing Electroweak Baryogenesis with Future Colliders, JHEP 11 (2014) 127 [arXiv:1409.0005] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    N. Craig, C. Englert and M. McCullough, New Probe of Naturalness, Phys. Rev. Lett. 111 (2013) 121803 [arXiv:1305.5251] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    D. Curtin and P. Saraswat, Towards a No-Lose Theorem for Naturalness, Phys. Rev. D 93 (2016) 055044 [arXiv:1509.04284] [INSPIRE].ADSGoogle Scholar
  37. [37]
    A. Datta and A. Raychaudhuri, Next-to-minimal Higgs: Mass bounds and search prospects, Phys. Rev. D 57 (1998) 2940 [hep-ph/9708444] [INSPIRE].
  38. [38]
    O. Bahat-Treidel, Y. Grossman and Y. Rozen, Hiding the Higgs at the LHC, JHEP 05 (2007) 022 [hep-ph/0611162] [INSPIRE].
  39. [39]
    V. Barger, P. Langacker and G. Shaughnessy, Collider Signatures of Singlet Extended Higgs Sectors, Phys. Rev. D 75 (2007) 055013 [hep-ph/0611239] [INSPIRE].
  40. [40]
    D. O’Connell, M.J. Ramsey-Musolf and M.B. Wise, Minimal Extension of the Standard Model Scalar Sector, Phys. Rev. D 75 (2007) 037701 [hep-ph/0611014] [INSPIRE].
  41. [41]
    V. Barger, P. Langacker, M. McCaskey, M.J. Ramsey-Musolf and G. Shaughnessy, LHC Phenomenology of an Extended Standard Model with a Real Scalar Singlet, Phys. Rev. D 77 (2008) 035005 [arXiv:0706.4311] [INSPIRE].ADSGoogle Scholar
  42. [42]
    V. Barger, P. Langacker, M. McCaskey, M. Ramsey-Musolf and G. Shaughnessy, Complex Singlet Extension of the Standard Model, Phys. Rev. D 79 (2009) 015018 [arXiv:0811.0393] [INSPIRE].ADSGoogle Scholar
  43. [43]
    J. de Blas, M. Chala, M. Pérez-Victoria and J. Santiago, Observable Effects of General New Scalar Particles, JHEP 04 (2015) 078 [arXiv:1412.8480] [INSPIRE].CrossRefGoogle Scholar
  44. [44]
    M. Gorbahn, J.M. No and V. Sanz, Benchmarks for Higgs Effective Theory: Extended Higgs Sectors, JHEP 10 (2015) 036 [arXiv:1502.07352] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    J. Brehmer, A. Freitas, D. Lopez-Val and T. Plehn, Pushing Higgs Effective Theory to its Limits, Phys. Rev. D 93 (2016) 075014 [arXiv:1510.03443] [INSPIRE].ADSGoogle Scholar
  46. [46]
    C.-W. Chiang and R. Huo, Standard Model Effective Field Theory: Integrating out a Generic Scalar, JHEP 09 (2015) 152 [arXiv:1505.06334] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    G. Buchalla, O. Catà, A. Celis and C. Krause, Standard Model Extended by a Heavy Singlet: Linear vs. Nonlinear EFT, Nucl. Phys. B 917 (2017) 209 [arXiv:1608.03564] [INSPIRE].
  48. [48]
    Y. Jiang and M. Trott, On the non-minimal character of the SMEFT, Phys. Lett. B 770 (2017) 108 [arXiv:1612.02040] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  49. [49]
    S. Dawson and C.W. Murphy, Standard Model EFT and Extended Scalar Sectors, Phys. Rev. D 96 (2017) 015041 [arXiv:1704.07851] [INSPIRE].ADSGoogle Scholar
  50. [50]
    T. Corbett, A. Joglekar, H.-L. Li and J.-H. Yu, Exploring Extended Scalar Sectors with Di-Higgs Signals: A Higgs EFT Perspective, JHEP 05 (2018) 061 [arXiv:1705.02551] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    R. Alonso, E.E. Jenkins and A.V. Manohar, Holomorphy without Supersymmetry in the Standard Model Effective Field Theory, Phys. Lett. B 739 (2014) 95 [arXiv:1409.0868] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    J. Elias-Miró, J.R. Espinosa, E. Masso and A. Pomarol, Renormalization of dimension-six operators relevant for the Higgs decays hγγ, γZ, JHEP 08 (2013) 033 [arXiv:1302.5661] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    J. Elias-Miro, J.R. Espinosa, E. Masso and A. Pomarol, Higgs windows to new physics through d = 6 operators: constraints and one-loop anomalous dimensions, JHEP 11 (2013) 066 [arXiv:1308.1879] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    J. Elias-Miró, C. Grojean, R.S. Gupta and D. Marzocca, Scaling and tuning of EW and Higgs observables, JHEP 05 (2014) 019 [arXiv:1312.2928] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    C. Cheung and C.-H. Shen, Nonrenormalization Theorems without Supersymmetry, Phys. Rev. Lett. 115 (2015) 071601 [arXiv:1505.01844] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    J.D. Wells and Z. Zhang, Effective theories of universal theories, JHEP 01 (2016) 123 [arXiv:1510.08462] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    E.E. Jenkins, A.V. Manohar and M. Trott, Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions, Phys. Lett. B 726 (2013) 697 [arXiv:1309.0819] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsNanjing UniversityNanjingChina
  2. 2.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  3. 3.Kavli Institute for Theoretical PhysicsSanta BarbaraU.S.A.
  4. 4.Department of PhysicsThe Hong Kong University of Science and TechnologyKowloonChina

Personalised recommendations