Abstract
Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as a reference for one-loop matching calculations and to ease their automation. Here we present the fermionic universal one-loop effective action (UOLEA), resulting from integrating out heavy fermions (Dirac or Majorana) with scalar, pseudo-scalar, vector and axial-vector couplings. We also clarify the relation of the new terms computed here to terms previously computed in the literature and those that remain to complete the UOLEA. Our results can be readily used to efficiently obtain analytical expressions for effective operators arising from heavy fermion loops [13].
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.K. Gaillard, The Effective One Loop Lagrangian With Derivative Couplings, Nucl. Phys. B 268 (1986) 669 [INSPIRE].
L.-H. Chan, Derivative Expansion for the One Loop Effective Actions With Internal Symmetry, Phys. Rev. Lett. 57 (1986) 1199 [INSPIRE].
O. Cheyette, Effective Action for the Standard Model With Large Higgs Mass, Nucl. Phys. B 297 (1988) 183 [INSPIRE].
B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP 01 (2016) 023 [arXiv:1412.1837] [INSPIRE].
A. Drozd, J. Ellis, J. Quevillon and T. You, The Universal One-Loop Effective Action, JHEP 03 (2016) 180 [arXiv:1512.03003] [INSPIRE].
B. Henning, X. Lu and H. Murayama, One-loop Matching and Running with Covariant Derivative Expansion, JHEP 01 (2018) 123 [arXiv:1604.01019] [INSPIRE].
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].
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].
Z. Zhang, Covariant diagrams for one-loop matching, JHEP 05 (2017) 152 [arXiv:1610.00710] [INSPIRE].
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].
M. Krämer, B. Summ and A. Voigt, Completing the scalar and fermionic Universal One-Loop Effective Action, JHEP 01 (2020) 079 [arXiv:1908.04798] [INSPIRE].
T. Cohen, M. Freytsis and X. Lu, Functional Methods for Heavy Quark Effective Theory, JHEP 06 (2020) 164 [arXiv:1912.08814] [INSPIRE].
S.A.R. Ellis, J. Quevillon, P.N.H. Vuong, T. You and Z. Zhang, https://github.com/HoaVuong-lpsc/The-Fermionic-UOLEA-Mathematica-notebook.
M. Jiang, N. Craig, Y.-Y. Li and D. Sutherland, Complete One-Loop Matching for a Singlet Scalar in the Standard Model EFT, JHEP 02 (2019) 031 [arXiv:1811.08878] [INSPIRE].
R. Huo, Standard Model Effective Field Theory: Integrating out Vector-Like Fermions, JHEP 09 (2015) 037 [arXiv:1506.00840] [INSPIRE].
M.S. Chanowitz, M. Furman and I. Hinchliffe, The Axial Current in Dimensional Regularization, Nucl. Phys. B 159 (1979) 225 [INSPIRE].
F. Jegerlehner, Facts of life with gamma(5), Eur. Phys. J. C 18 (2001) 673 [hep-th/0005255] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
P. Breitenlohner and D. Maison, Dimensional Renormalization and the Action Principle, Commun. Math. Phys. 52 (1977) 11 [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading, U.S.A. (1995) [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, FeynCalc 9.3: New features and improvements, Comput. Phys. Commun. 256 (2020) 107478 [arXiv:2001.04407] [INSPIRE].
J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs Hunter’s Guide, Front. Phys. 80 (2000) 1 [INSPIRE].
M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Low-Energy Theorems for Higgs Boson Couplings to Photons, Sov. J. Nucl. Phys. 30 (1979) 711 [INSPIRE].
B.A. Kniehl and M. Spira, Low-energy theorems in Higgs physics, Z. Phys. C 69 (1995) 77 [hep-ph/9505225] [INSPIRE].
M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
A. Djouadi, The Anatomy of electro-weak symmetry breaking. II. The Higgs bosons in the minimal supersymmetric model, Phys. Rept. 459 (2008) 1 [hep-ph/0503173] [INSPIRE].
J.F. Gunion, H.E. Haber and C. Kao, Searching for the CP odd Higgs boson of the minimal supersymmetric model at hadron supercolliders, Phys. Rev. D 46 (1992) 2907 [INSPIRE].
J.C. Criado, MatchingTools: a Python library for symbolic effective field theory calculations, Comput. Phys. Commun. 227 (2018) 42 [arXiv:1710.06445] [INSPIRE].
S. Das Bakshi, J. Chakrabortty and S.K. Patra, CoDEx: Wilson coefficient calculator connecting SMEFT to UV theory, Eur. Phys. J. C 79 (2019) 21 [arXiv:1808.04403] [INSPIRE].
A. Angelescu and P. Huang, Integrating Out New Fermions at One Loop, to appear.
J.D. Wells and Z. Zhang, Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings, JHEP 05 (2018) 182 [arXiv:1711.04774] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2006.16260
Rights and permissions
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.
About this article
Cite this article
Ellis, S.A.R., Quevillon, J., Vuong, P.N.H. et al. The fermionic universal one-loop effective action. J. High Energ. Phys. 2020, 78 (2020). https://doi.org/10.1007/JHEP11(2020)078
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2020)078