Abstract
We calculate the order λ, λ2 and λy 2 terms of the 59 × 59 one-loop anomalous dimension matrix of dimension-six operators, where λ and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Grojean, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group scaling of Higgs operators and Γ(h− > γγ), JHEP 04 (2013) 016 [arXiv:1301.2588] [INSPIRE].
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].
W. Buchmüller and D. Wyler, Effective lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].
C. Arzt, M. Einhorn and J. Wudka, Patterns of deviation from the standard model, Nucl. Phys. B 433 (1995) 41 [hep-ph/9405214] [INSPIRE].
J. Elias-Miró, J. Espinosa, E. Masso and A. Pomarol, Renormalization of dimension-six operators relevant for the Higgs decays h → γγ, γZ, JHEP 08 (2013) 033 [arXiv:1302.5661] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, On gauge invariance and minimal coupling, JHEP 09 (2013) 063 [arXiv:1305.0017] [INSPIRE].
A.V. Manohar, An exactly solvable model for dimension six Higgs operators and h → γγ, arXiv:1305.3927 [INSPIRE].
H.D. Politzer, Power corrections at short distances, Nucl. Phys. B 172 (1980) 349 [INSPIRE].
H. Georgi, On-shell effective field theory, Nucl. Phys. B 361 (1991) 339 [INSPIRE].
A.V. Manohar, The HQET/NRQCD lagrangian to order \( {{{{\alpha_s}}} \left/ {{m_Q^3}} \right.} \), Phys. Rev. D 56 (1997) 230 [hep-ph/9701294] [INSPIRE].
A.V. Manohar, Effective field theories, hep-ph/9606222 [INSPIRE].
M.B. Einhorn and J. Wudka, Effective β-functions for effective field theory, JHEP 08 (2001) 025 [hep-ph/0105035] [INSPIRE].
F.J. Gilman and M.B. Wise, Effective hamiltonian for Δs = 1 weak nonleptonic decays in the six quark model, Phys. Rev. D 20 (1979) 2392 [INSPIRE].
H. Georgi, Weak interactions and modern particle theory, Dover Publications, U.S.A. (2009).
E.E. Jenkins and A.V. Manohar, Algebraic structure of lepton and quark flavor invariants and CP-violation, JHEP 10 (2009) 094 [arXiv:0907.4763] [INSPIRE].
A. Manohar and H. Georgi, Chiral quarks and the nonrelativistic quark model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].
J. Elias-Miro, J. Espinosa, E. Masso and A. Pomarol, Higgs windows to new physics through D=6 operators: Constraints and one-loop anomalous dimensions, arXiv:1308.1879 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1308.2627
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Jenkins, E.E., Manohar, A.V. & Trott, M. Renormalization group evolution of the standard model dimension six operators. I: formalism and λ dependence. J. High Energ. Phys. 2013, 87 (2013). https://doi.org/10.1007/JHEP10(2013)087
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2013)087