Journal of High Energy Physics

, 2019:51 | Cite as

Effective field theories in Rξ gauges

  • M. MisiakEmail author
  • M. Paraskevas
  • J. Rosiek
  • K. Suxho
  • B. Zglinicki
Open Access
Regular Article - Theoretical Physics


In effective quantum field theories, higher dimensional operators can affect the canonical normalization of kinetic terms at tree level. These contributions for scalars and gauge bosons should be carefully included in the gauge fixing procedure, in order to end up with a convenient set of Feynman rules. We develop such a setup for the linear Rξ-gauges. It involves a suitable reduction of the operator basis, a generalized gauge fixing term, and a corresponding ghost sector. Our approach extends previous results for the dimension-six Standard Model Effective Field Theory to a generic class of effective theories with operators of arbitrary dimension.


Effective Field Theories Gauge Symmetry Spontaneous Symmetry Breaking 


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]
    Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
  2. [2]
    W. Buchmüller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    B. Grzadkowski, M. Iskrzyński, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  4. [4]
    B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, …: Higher dimension operators in the SM EFT, JHEP 08 (2017) 016 [arXiv:1512.03433] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    R.H. Parker, C. Yu, W. Zhong, B. Estey and H. Müller, Measurement of the fine-structure constant as a test of the Standard Model, Science 365 (2018) 191.ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    J. Aebischer, J. Kumar, P. Stangl and D.M. Straub, A Global Likelihood for Precision Constraints and Flavour Anomalies, arXiv:1810.07698 [INSPIRE].
  7. [7]
    A. Dedes, W. Materkowska, M. Paraskevas, J. Rosiek and K. Suxho, Feynman rules for the Standard Model Effective Field Theory in R ξ -gauges, JHEP 06 (2017) 143 [arXiv:1704.03888] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    A. Helset, M. Paraskevas and M. Trott, Gauge fixing the Standard Model Effective Field Theory, Phys. Rev. Lett. 120 (2018) 251801 [arXiv:1803.08001] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    T. Appelquist and J. Carazzone, Infrared Singularities and Massive Fields, Phys. Rev. D 11 (1975) 2856 [INSPIRE].ADSGoogle Scholar
  10. [10]
    H.D. Politzer, Power Corrections at Short Distances, Nucl. Phys. B 172 (1980) 349 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    H. Kluberg-Stern and J.B. Zuber, Renormalization of Nonabelian Gauge Theories in a Background Field Gauge. 2. Gauge Invariant Operators, Phys. Rev. D 12 (1975) 3159 [INSPIRE].ADSGoogle Scholar
  12. [12]
    C. Grosse-Knetter, Effective Lagrangians with higher derivatives and equations of motion, Phys. Rev. D 49 (1994) 6709 [hep-ph/9306321] [INSPIRE].
  13. [13]
    C. Arzt, Reduced effective Lagrangians, Phys. Lett. B 342 (1995) 189 [hep-ph/9304230] [INSPIRE].
  14. [14]
    H. Simma, Equations of motion for effective Lagrangians and penguins in rare B decays, Z. Phys. C 61 (1994) 67 [hep-ph/9307274] [INSPIRE].
  15. [15]
    J. Wudka, Electroweak effective Lagrangians, Int. J. Mod. Phys. A 9 (1994) 2301 [hep-ph/9406205] [INSPIRE].
  16. [16]
    A.V. Manohar, Introduction to Effective Field Theories, in Les Houches summer school: EFT in Particle Physics and Cosmology Les Houches, Chamonix Valley, France, July 3–28, 2017, 2018, arXiv:1804.05863 [INSPIRE].
  17. [17]
    J.C. Criado and M. Pérez-Victoria, Field redefinitions in effective theories at higher orders, arXiv:1811.09413 [INSPIRE].
  18. [18]
    M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Perseus Books Publishing, L.L.C. (1995).Google Scholar
  19. [19]
    C. Becchi, A. Rouet and R. Stora, Renormalization of Gauge Theories, Annals Phys. 98 (1976) 287 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    M.Z. Iofa and I.V. Tyutin, Gauge Invariance of Spontaneously Broken Nonabelian Theories in the Bogolyubov-Parasiuk-HEPP-Zimmerman Method, Teor. Mat. Fiz. 27 (1976) 38 [Theor. Math. Phys. 27 (1976) 316] [INSPIRE].
  21. [21]
    M. Iskrzynski, Classification of higher-dimensional operators in the Standard Model (in Polish), MSc Thesis, University of Warsaw, Poland, (2010).Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • M. Misiak
    • 1
    Email author
  • M. Paraskevas
    • 1
    • 2
  • J. Rosiek
    • 1
  • K. Suxho
    • 2
  • B. Zglinicki
    • 1
  1. 1.Institute of Theoretical Physics, Faculty of PhysicsUniversity of WarsawWarsawPoland
  2. 2.Department of PhysicsUniversity of IoanninaIoanninaGreece

Personalised recommendations