Abstract
We match the seesaw model for generating neutrino masses onto the Standard Model Effective Field Theory (SMEFT). We perform this matching at tree level up to dimension seven in the operator expansion. We explain how some of the perturbations of the neutrino mass matrix due to operators of mass dimension greater than five are tied to integrating out the heavy Majorana mass eigenstates in sequence. We demonstrate that the low energy limit of seesaw models are well described by the SMEFT, particularly when constructed using a flavour space expansion. Flavour space expansions of seesaw models are of interest as the coupling of the heavy states to the Standard Model, that are integrated out to generate neutrino masses, are through flavour space vectors ∈ \( {\mathbb{C}}^3 \). We point out that neutrino phenomenology can be systematically developed as a perturbation around the unknown eigenvectors diagonalizing the charged lepton mass matrix using the fact that these eigenvectors also form a basis of \( {\mathbb{C}}^3 \). This point holds in seesaw models and can also be applied to other models of neutrino mass generation to develop systematic expansions. We develop the algebra for this flavour space and discuss some phenomenology to illustrate this approach.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Lehman, Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators, Phys. Rev. D 90 (2014) 125023 [arXiv:1410.4193] [INSPIRE].
S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].
F. Wilczek and A. Zee, Operator Analysis of Nucleon Decay, Phys. Rev. Lett. 43 (1979) 1571 [INSPIRE].
W. Buchmüller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys. B 268 (1986) 621 [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].
L.F. Abbott and M.B. Wise, The Effective Hamiltonian for Nucleon Decay, Phys. Rev. D 22 (1980) 2208 [INSPIRE].
L. Lehman and A. Martin, Hilbert Series for Constructing Lagrangians: expanding the phenomenologist’s toolbox, Phys. Rev. D 91 (2015) 105014 [arXiv:1503.07537] [INSPIRE].
L. Lehman and A. Martin, Low-derivative operators of the Standard Model effective field theory via Hilbert series methods, JHEP 02 (2016) 081 [arXiv:1510.00372] [INSPIRE].
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].
S. Willenbrock, Symmetries of the standard model, hep-ph/0410370 [INSPIRE].
A. de Gouvêa, J. Herrero-Garcia and A. Kobach, Neutrino Masses, Grand Unification and Baryon Number Violation, Phys. Rev. D 90 (2014) 016011 [arXiv:1404.4057] [INSPIRE].
A. Kobach, Baryon Number, Lepton Number and Operator Dimension in the Standard Model, Phys. Lett. B 758 (2016) 455 [arXiv:1604.05726] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001.
P. Minkowski, μ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. 67B (1977) 421 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
T. Yanagida, Horizontal symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
A. Broncano, M.B. Gavela and E.E. Jenkins, The Effective Lagrangian for the seesaw model of neutrino mass and leptogenesis, Phys. Lett. B 552 (2003) 177 [Erratum ibid. B 636 (2006) 332] [hep-ph/0210271] [INSPIRE].
M.B. Gavela, T. Hambye, D. Hernandez and P. Hernández, Minimal Flavour Seesaw Models, JHEP 09 (2009) 038 [arXiv:0906.1461] [INSPIRE].
M.B. Gavela, D. Hernandez, T. Ota and W. Winter, Large gauge invariant non-standard neutrino interactions, Phys. Rev. D 79 (2009) 013007 [arXiv:0809.3451] [INSPIRE].
A. Abada, C. Biggio, F. Bonnet, M.B. Gavela and T. Hambye, Low energy effects of neutrino masses, JHEP 12 (2007) 061 [arXiv:0707.4058] [INSPIRE].
A. Broncano, M.B. Gavela and E.E. Jenkins, Neutrino physics in the seesaw model, Nucl. Phys. B 672 (2003) 163 [hep-ph/0307058] [INSPIRE].
F. Bonnet, M. Hirsch, T. Ota and W. Winter, Systematic study of the D = 5 Weinberg operator at one-loop order, JHEP 07 (2012) 153 [arXiv:1204.5862] [INSPIRE].
F. Bonnet, D. Hernandez, T. Ota and W. Winter, Neutrino masses from higher than D = 5 effective operators, JHEP 10 (2009) 076 [arXiv:0907.3143] [INSPIRE].
F. del Aguila, S. Bar-Shalom, A. Soni and J. Wudka, Heavy Majorana Neutrinos in the Effective Lagrangian Description: Application to Hadron Colliders, Phys. Lett. B 670 (2009) 399 [arXiv:0806.0876] [INSPIRE].
F. del Aguila, A. Aparici, S. Bhattacharya, A. Santamaria and J. Wudka, Effective Lagrangian approach to neutrinoless double beta decay and neutrino masses, JHEP 06 (2012) 146 [arXiv:1204.5986] [INSPIRE].
S. Bhattacharya and J. Wudka, Dimension-seven operators in the standard model with right handed neutrinos, Phys. Rev. D 94 (2016) 055022 [Erratum ibid. D 95 (2017) 039904] [arXiv:1505.05264] [INSPIRE].
P.W. Angel, N.L. Rodd and R.R. Volkas, Origin of neutrino masses at the LHC: ΔL = 2 effective operators and their ultraviolet completions, Phys. Rev. D 87 (2013) 073007 [arXiv:1212.6111] [INSPIRE].
B. Grinstein and M. Trott, An Expansion for Neutrino Phenomenology, JHEP 09 (2012) 005 [arXiv:1203.4410] [INSPIRE].
B. Pontecorvo, Mesonium and anti-mesonium, Sov. Phys. JETP 6 (1957) 429 [Zh. Eksp. Teor. Fiz. 33 (1957) 549] [INSPIRE].
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].
E. Majorana, Teoria simmetrica dell’elettrone e del positrone, Nuovo Cim. 14 (1937) 171 [INSPIRE].
Y. Liao and X.-D. Ma, Renormalization Group Evolution of Dimension-seven Baryon- and Lepton-number-violating Operators, JHEP 11 (2016) 043 [arXiv:1607.07309] [INSPIRE].
Y. Liao and X.-D. Ma, Operators up to Dimension Seven in Standard Model Effective Field Theory Extended with Sterile Neutrinos, Phys. Rev. D 96 (2017) 015012 [arXiv:1612.04527] [INSPIRE].
A. Broncano, M.B. Gavela and E.E. Jenkins, Renormalization of lepton mixing for Majorana neutrinos, Nucl. Phys. B 705 (2005) 269 [hep-ph/0406019] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, On Gauge Invariance and Minimal Coupling, JHEP 09 (2013) 063 [arXiv:1305.0017] [INSPIRE].
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].
H.K. Dreiner, H.E. Haber and S.P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1 [arXiv:0812.1594] [INSPIRE].
S.F. King, Atmospheric and solar neutrinos with a heavy singlet, Phys. Lett. B 439 (1998) 350 [hep-ph/9806440] [INSPIRE].
S.F. King, Atmospheric and solar neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 562 (1999) 57 [hep-ph/9904210] [INSPIRE].
S.F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576 (2000) 85 [hep-ph/9912492] [INSPIRE].
S.F. King, Constructing the large mixing angle MNS matrix in seesaw models with right-handed neutrino dominance, JHEP 09 (2002) 011 [hep-ph/0204360] [INSPIRE].
A. Cayley, Xxviii. on Jacobi’s elliptic functions, in reply to the rev. brice bronwin; and on quaternions, Philos. Mag. Ser. 3 26 (1845) 208.
J.C. Baez, The Octonions, Bull. Am. Math. Soc. 39 (2002) 145 [math/0105155] [INSPIRE].
E.E. Jenkins and A.V. Manohar, Rephasing Invariants of Quark and Lepton Mixing Matrices, Nucl. Phys. B 792 (2008) 187 [arXiv:0706.4313] [INSPIRE].
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].
C. Jarlskog, A Basis Independent Formulation of the Connection Between Quark Mass Matrices, CP-violation and Experiment, Z. Phys. C 29 (1985) 491 [INSPIRE].
A. Kusenko and R. Shrock, General determination of phases in leptonic mass matrices, Phys. Lett. B 323 (1994) 18 [hep-ph/9311307] [INSPIRE].
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
Corresponding author
Additional information
ArXiv ePrint: 1703.04415
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/.
About this article
Cite this article
Elgaard-Clausen, G., Trott, M. On expansions in neutrino effective field theory. J. High Energ. Phys. 2017, 88 (2017). https://doi.org/10.1007/JHEP11(2017)088
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2017)088