Abstract
We present a general framework for models in which the lepton mixing matrix is the product of the maximal mixing matrix U ω times a matrix constrained by a well-defined \( {{\mathbb{Z}}_2} \) symmetry. Our framework relies on neither supersymmetry nor non-renormalizable Lagrangians nor higher dimensions; it relies instead on the double seesaw mechanism and on the soft breaking of symmetries. The framework may be used to construct models for virtually all the lepton mixing matrices of the type mentioned above which have been proposed in the literature.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
DOUBLE-CHOOZ collaboration, Y. Abe et al., Indication for the disappearance of reactor electron antineutrinos in the Double CHOOZ experiment, Phys. Rev. Lett. 108 (2012) 131801 [arXiv:1112.6353] [INSPIRE].
DAYA-BAY collaboration, F. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].
RENO collaboration, J. Ahn et al., Observation of reactor electron antineutrino disappearance in the RENO experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].
D. Forero, M. Tórtola and J. Valle, Global status of neutrino oscillation parameters after Neutrino-2012, Phys. Rev. D 86 (2012) 073012 [arXiv:1205.4018] [INSPIRE].
G. Fogli et al., Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP-violation searches, Phys. Rev. D 86 (2012) 013012 [arXiv:1205.5254] [INSPIRE].
M. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global fit to three neutrino mixing: critical look at present precision, JHEP 12 (2012) 123 [arXiv:1209.3023] [INSPIRE].
P. Harrison, D. Perkins and W. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].
C.H. Albright and W. Rodejohann, Comparing trimaximal mixing and its variants with deviations from tri-bimaximal mixing, Eur. Phys. J. C 62 (2009) 599 [arXiv:0812.0436] [INSPIRE].
C.H. Albright, A. Dueck and W. Rodejohann, Possible alternatives to tri-bimaximal mixing, Eur. Phys. J. C 70 (2010) 1099 [arXiv:1004.2798] [INSPIRE].
C. Lam, Determining horizontal symmetry from neutrino mixing, Phys. Rev. Lett. 101 (2008) 121602 [arXiv:0804.2622] [INSPIRE].
C. Lam, The unique horizontal symmetry of leptons, Phys. Rev. D 78 (2008) 073015 [arXiv:0809.1185] [INSPIRE].
C. Lam, A bottom-up analysis of horizontal symmetry, arXiv:0907.2206 [INSPIRE].
S.-F. Ge, D.A. Dicus and W.W. Repko, \( {{\mathbb{Z}}_2} \) symmetry prediction for the leptonic Dirac CP phase, Phys. Lett. B 702 (2011) 220 [arXiv:1104.0602] [INSPIRE].
H.-J. He and F.-R. Yin, Common origin of μ − τ and CP breaking in neutrino seesaw, baryon asymmetry and hidden flavor symmetry, Phys. Rev. D 84 (2011) 033009 [arXiv:1104.2654] [INSPIRE].
R.d.A. Toorop, F. Feruglio and C. Hagedorn, Discrete flavour symmetries in light of T2K, Phys. Lett. B 703 (2011) 447 [arXiv:1107.3486] [INSPIRE].
S.-F. Ge, D.A. Dicus and W.W. Repko, Residual symmetries for neutrino mixing with a large θ 13 and nearly maximal δD , Phys. Rev. Lett. 108 (2012) 041801 [arXiv:1108.0964] [INSPIRE].
R. de Adelhart Toorop, F. Feruglio and C. Hagedorn, Finite modular groups and lepton mixing, Nucl. Phys. B 858 (2012) 437 [arXiv:1112.1340] [INSPIRE].
H.-J. He and X.-J. Xu, Octahedral symmetry with geometrical breaking: new prediction for neutrino mixing angle θ 13 and CP-violation, Phys. Rev. D 86 (2012) 111301 [arXiv:1203.2908] [INSPIRE].
D. Hernandez and A.Y. Smirnov, Lepton mixing and discrete symmetries, Phys. Rev. D 86 (2012) 053014 [arXiv:1204.0445] [INSPIRE].
C. Lam, Finite symmetry of leptonic mass matrices, Phys. Rev. D 87 (2013) 013001 [arXiv:1208.5527] [INSPIRE].
D. Hernandez and A.Y. Smirnov, Discrete symmetries and model-independent patterns of lepton mixing, Phys. Rev. D 87 (2013) 053005 [arXiv:1212.2149] [INSPIRE].
B. Hu, Neutrino mixing and discrete symmetries, Phys. Rev. D 87 (2013) 033002 [arXiv:1212.2819] [INSPIRE].
M. Holthausen, K.S. Lim and M. Lindner, Lepton mixing patterns from a scan of finite discrete groups, Phys. Lett. B 721 (2013) 61 [arXiv:1212.2411] [INSPIRE].
S. Antusch, S.F. King, C. Luhn and M. Spinrath, Trimaximal mixing with predicted θ 13 from a new type of constrained sequential dominance, Nucl. Phys. B 856 (2012) 328 [arXiv:1108.4278] [INSPIRE].
W. Rodejohann and H. Zhang, Simple two parameter description of lepton mixing, Phys. Rev. D 86 (2012) 093008 [arXiv:1207.1225] [INSPIRE].
E. Ma, Self-organizing neutrino mixing matrix, Phys. Rev. D 86 (2012) 117301 [arXiv:1209.3374] [INSPIRE].
C. Luhn, Trimaximal TM 1 neutrino mixing in S 4 with spontaneous CP-violation, Nucl. Phys. B 875 (2013) 80 [arXiv:1306.2358] [INSPIRE].
I. de Medeiros Varzielas and L. Lavoura, Flavour models for T M 1 lepton mixing, J. Phys. G 40 (2013) 085002 [arXiv:1212.3247] [INSPIRE].
R. Mohapatra, Mechanism for understanding small neutrino mass in superstring theories, Phys. Rev. Lett. 56 (1986) 561 [INSPIRE].
R. Mohapatra and J. Valle, Neutrino mass and baryon number nonconservation in superstring models, Phys. Rev. D 34 (1986) 1642 [INSPIRE].
S. Barr, A different seesaw formula for neutrino masses, Phys. Rev. Lett. 92 (2004) 101601 [hep-ph/0309152] [INSPIRE].
T. Fukuyama, A. Ilakovac, T. Kikuchi and K. Matsuda, Neutrino oscillations in a supersymmetric SO(10) model with Type-III see-saw mechanism, JHEP 06 (2005) 016 [hep-ph/0503114] [INSPIRE].
P.B. Dev and A. Pilaftsis, Minimal radiative neutrino mass mechanism for inverse seesaw models, Phys. Rev. D 86 (2012) 113001 [arXiv:1209.4051] [INSPIRE].
P. Minkowski, μ → eγ at a rate of one out of 109 muon decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, in Proceedings of the workshop on unified theory and baryon number in the universe, Tsukuba Japan (1979), O. Sawata and A. Sugamoto eds., KEK report 79-18, Tsukuba Japan (1979).
S.L. Glashow, The future of elementary particle physics, in Quarks and leptons, proceedings of the advanced study institute, Cargèse Corsica (1979), M. Lévy et al. eds., Plenum Press, New York U.S.A. (1980).
M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, in Supergravity, D.Z. Freedman and F. van Nieuwenhuizen eds., North Holland, Amsterdam The Netherlands (1979).
R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
W. Grimus and L. Lavoura, A model realizing the Harrison-Perkins-Scott lepton mixing matrix, JHEP 01 (2006) 018 [hep-ph/0509239] [INSPIRE].
W. Grimus and L. Lavoura, Tri-bimaximal lepton mixing from symmetry only, JHEP 04 (2009) 013 [arXiv:0811.4766] [INSPIRE].
W. Grimus, Discrete symmetries, roots of unity and lepton mixing, J. Phys. G 40 (2013) 075008 [arXiv:1301.0495] [INSPIRE].
W. Grimus and L. Lavoura, A model for trimaximal lepton mixing, JHEP 09 (2008) 106 [arXiv:0809.0226] [INSPIRE].
F. Feruglio, C. Hagedorn and R. Ziegler, Lepton mixing parameters from discrete and CP symmetries, JHEP 07 (2013) 027 [arXiv:1211.5560] [INSPIRE].
G.-J. Ding, S.F. King, C. Luhn and A.J. Stuart, Spontaneous CP-violation from vacuum alignment in S 4 models of leptons, JHEP 05 (2013) 084 [arXiv:1303.6180] [INSPIRE].
F. Feruglio, C. Hagedorn and R. Ziegler, A realistic pattern of lepton mixing and masses from S 4 and CP, Eur. Phys. J. C 74 (2014) 2753 [arXiv:1303.7178] [INSPIRE].
G.-J. Ding, S.F. King and A.J. Stuart, Generalised CP and A 4 family symmetry, JHEP 12 (2013) 006 [arXiv:1307.4212] [INSPIRE].
A. Bovier, M. Lüling and D. Wyler, Finite subgroups of SU(3), J. Math. Phys. 22 (1981) 1543 [INSPIRE].
J. Escobar and C. Luhn, The flavor group Δ(6n 2), J. Math. Phys. 50 (2009) 013524 [arXiv:0809.0639] [INSPIRE].
W. Grimus and P.O. Ludl, Finite flavour groups of fermions, J. Phys. A 45 (2012) 233001 [arXiv:1110.6376] [INSPIRE].
P. Ferreira, W. Grimus, L. Lavoura and P. Ludl, Maximal CP-violation in lepton mixing from a model with Δ(27) flavour symmetry, JHEP 09 (2012) 128 [arXiv:1206.7072] [INSPIRE].
Y. Chikashige, R.N. Mohapatra and R.D. Peccei, Are there real Goldstone bosons associated with broken lepton number?, Phys. Lett. B 98 (1981) 265 [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: 1309.3186
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Grimus, W., Lavoura, L. Double seesaw mechanism and lepton mixing. J. High Energ. Phys. 2014, 4 (2014). https://doi.org/10.1007/JHEP03(2014)004
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2014)004