Abstract
We consider the neutrino masses and mixing in the framework of SO(10) GUTs with hidden sector consisting of fermionic and bosonic SO(10) singlets and flavor symmetries. The framework allows to disentangle the CKM physics responsible for the CKM mixing and different mass hierarchies of quarks and leptons and the neutrino new physics which produces smallness of neutrino masses and large lepton mixing. The framework leads naturally to the relation U PMNS ∼ V †CKM U 0, where structure of U 0 is determined by the flavor symmetry. The key feature of the framework is that apart from the Dirac mass matrices m D , the portal mass matrix M D and the mass matrix of singlets M S are also involved in generation of the lepton mixing. This opens up new possibilities to realize the flavor symmetries and explain the data. Using A 4 × Z 4 as the flavor group, we systematically explore the flavor structures which can be obtained in this framework depending on field content and symmetry assignments. We formulate additional conditions which lead to U 0 ∼ U TBM or U BM. They include (i) equality (in general, proportionality) of the singlet flavons couplings, (ii) equality of their VEVs; (iii) correlation between VEVs of singlets and triplet, (iv) certain VEV alignment of flavon triplet(s). These features can follow from additional symmetries or be remnants of further unification. Phenomenologically viable schemes with minimal flavon content and minimal number of couplings are constructed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.C. Pati and A. Salam, Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions, Phys. Rev. D 8 (1973) 1240 [INSPIRE].
H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].
H. Georgi, The State of the Art — Gauge Theories, AIP Conf. Proc. 23 (1975) 575 [INSPIRE].
H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [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 Symmetry And Masses Of Neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
S.L. Glashow, The Future of Elementary Particle Physics, NATO Sci. Ser. B 61 (1980) 687 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation, Phys. Rev. D 23 (1981) 165 [INSPIRE].
R.N. Mohapatra and J.W.F. Valle, Neutrino Mass and Baryon Number Nonconservation in Superstring Models, Phys. Rev. D 34 (1986) 1642 [INSPIRE].
A.Yu. Smirnov, Seesaw enhancement of lepton mixing, Phys. Rev. D 48 (1993) 3264 [hep-ph/9304205] [INSPIRE].
A.Yu. Smirnov, Neutrinos and structure of the intermediate mass scale, Nucl. Phys. B 466 (1996) 25 [hep-ph/9511239] [INSPIRE].
M. Tanimoto, Seesaw enhancement of neutrino mixing due to the right-handed phases, Phys. Lett. B 345 (1995) 477 [hep-ph/9503318] [INSPIRE].
P.F. Harrison, D.H. Perkins and W.G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].
P.F. Harrison and W.G. Scott, Symmetries and generalizations of tri-bimaximal neutrino mixing, Phys. Lett. B 535 (2002) 163 [hep-ph/0203209] [INSPIRE].
P.F. Harrison and W.G. Scott, Permutation symmetry, tri-bimaximal neutrino mixing and the S3 group characters, Phys. Lett. B 557 (2003) 76 [hep-ph/0302025] [INSPIRE].
P.F. Harrison and W.G. Scott, Status of tri-bimaximal neutrino mixing, hep-ph/0402006 [INSPIRE].
D. Wyler, Discrete Symmetries in the Six Quark SU(2) × U(1) Model, Phys. Rev. D 19 (1979) 3369 [INSPIRE].
G.C. Branco, H.P. Nilles and V. Rittenberg, Fermion Masses and Hierarchy of Symmetry Breaking, Phys. Rev. D 21 (1980) 3417 [INSPIRE].
E. Ma and G. Rajasekaran, Softly broken A 4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [INSPIRE].
K.S. Babu, E. Ma and J.W.F. Valle, Underlying A 4 symmetry for the neutrino mass matrix and the quark mixing matrix, Phys. Lett. B 552 (2003) 207 [hep-ph/0206292] [INSPIRE].
M. Hirsch, J.C. Romao, S. Skadhauge, J.W.F. Valle and A. Villanova del Moral, Phenomenological tests of supersymmetric A 4 family symmetry model of neutrino mass, Phys. Rev. D 69 (2004) 093006 [hep-ph/0312265] [INSPIRE].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [INSPIRE].
S.F. King and M. Malinsky, A 4 family symmetry and quark-lepton unification, Phys. Lett. B 645 (2007) 351 [hep-ph/0610250] [INSPIRE].
Y. Koide, A 4 symmetry and lepton masses and mixing, Eur. Phys. J. C 52 (2007) 617 [hep-ph/0701018] [INSPIRE].
S.M. Barr, Flavor without flavor symmetry, Phys. Rev. D 65 (2002) 096012 [hep-ph/0106241] [INSPIRE].
E. Ma, Quark mass matrices in the A 4 model, Mod. Phys. Lett. A 17 (2002) 627 [hep-ph/0203238] [INSPIRE].
E. Ma, Suitability of A 4 as a Family Symmetry in Grand Unification, Mod. Phys. Lett. A 21 (2006) 2931 [hep-ph/0607190] [INSPIRE].
S. Morisi, M. Picariello and E. Torrente-Lujan, Model for fermion masses and lepton mixing in SO(10) × A 4, Phys. Rev. D 75 (2007) 075015 [hep-ph/0702034] [INSPIRE].
F. Bazzocchi, S. Morisi, M. Picariello and E. Torrente-Lujan, Embedding A 4 into SU(3) × U(1) flavor symmetry: Large neutrino mixing and fermion mass hierarchy in SO(10) GUT, J. Phys. G 36 (2009) 015002 [arXiv:0802.1693] [INSPIRE].
C. Giunti and M. Tanimoto, Deviation of neutrino mixing from bimaximal, Phys. Rev. D 66 (2002) 053013 [hep-ph/0207096] [INSPIRE].
H. Minakata and A.Yu. Smirnov, Neutrino mixing and quark-lepton complementarity, Phys. Rev. D 70 (2004) 073009 [hep-ph/0405088] [INSPIRE].
K. Cheung, S.K. Kang, C.S. Kim and J. Lee, Lepton flavor violation as a probe of quark-lepton unification, Phys. Rev. D 72 (2005) 036003 [hep-ph/0503122] [INSPIRE].
Z.-z. Xing, Nontrivial correlation between the CKM and MNS matrices, Phys. Lett. B 618 (2005) 141 [hep-ph/0503200] [INSPIRE].
A. Datta, L. Everett and P. Ramond, Cabibbo haze in lepton mixing, Phys. Lett. B 620 (2005) 42 [hep-ph/0503222] [INSPIRE].
S. Antusch, S.F. King and R.N. Mohapatra, Quark-lepton complementarity in unified theories, Phys. Lett. B 618 (2005) 150 [hep-ph/0504007] [INSPIRE].
S. Antusch and S.F. King, Charged lepton corrections to neutrino mixing angles and CP phases revisited, Phys. Lett. B 631 (2005) 42 [hep-ph/0508044] [INSPIRE].
J. Harada, Neutrino mixing and CP-violation from Dirac-Majorana bimaximal mixture and quark-lepton unification, Europhys. Lett. 75 (2006) 248 [hep-ph/0512294] [INSPIRE].
Y. Farzan and A.Yu. Smirnov, Leptonic CP-violation: Zero, maximal or between the two extremes, JHEP 01 (2007) 059 [hep-ph/0610337] [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, \( {\theta}^PM\ N\ {S}_{13}={\theta}_C/\sqrt{2} \) from GUTs, Nucl. Phys. B 866 (2013) 255 [arXiv:1205.1051] [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, A flavour GUT model with \( {\theta}_{13}^{P\;M\;N\;S}\simeq {\theta}_C/\sqrt{2} \), Nucl. Phys. B 877 (2013) 772 [arXiv:1305.6612] [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, Inverse neutrino mass hierarchy in a flavour GUT model, Nucl. Phys. B 879 (2014) 19 [arXiv:1306.3984] [INSPIRE].
F. Vissani, A study of the scenario with nearly degenerate Majorana neutrinos, hep-ph/9708483 [INSPIRE].
M. Fukugita, M. Tanimoto and T. Yanagida, Atmospheric neutrino oscillation and a phenomenological lepton mass matrix, Phys. Rev. D 57 (1998) 4429 [hep-ph/9709388] [INSPIRE].
V.D. Barger, S. Pakvasa, T.J. Weiler and K. Whisnant, Bimaximal mixing of three neutrinos, Phys. Lett. B 437 (1998) 107 [hep-ph/9806387] [INSPIRE].
S. Davidson and S.F. King, Bimaximal neutrino mixing in the MSSM with a single right-handed neutrino, Phys. Lett. B 445 (1998) 191 [hep-ph/9808296] [INSPIRE].
R.N. Mohapatra and S. Nussinov, Bimaximal neutrino mixing and neutrino mass matrix, Phys. Rev. D 60 (1999) 013002 [hep-ph/9809415] [INSPIRE].
P.O. Ludl and A.Yu. Smirnov, Lepton mixing from the hidden sector, Phys. Rev. D 92 (2015) 073010 [arXiv:1507.03494] [INSPIRE].
S.F. King, Tri-bimaximal-Cabibbo Mixing, Phys. Lett. B 718 (2012) 136 [arXiv:1205.0506] [INSPIRE].
F. Gursey, P. Ramond and P. Sikivie, A Universal Gauge Theory Model Based on E6, Phys. Lett. B 60 (1976) 177 [INSPIRE].
T.D. Lee and C.-N. Yang, Question of Parity Conservation in Weak Interactions, Phys. Rev. 104 (1956) 254 [INSPIRE].
A. Salam, On parity conservation and neutrino mass, Nuovo Cim. 5 (1957) 299 [INSPIRE].
I.Yu. Kobzarev, L.B. Okun and I.Ya. Pomeranchuk, On the possibility of experimental observation of mirror particles, Sov. J. Nucl. Phys. 3 (1966) 837 [INSPIRE].
M. Lindner, M.A. Schmidt and A.Yu. Smirnov, Screening of Dirac flavor structure in the seesaw and neutrino mixing, JHEP 07 (2005) 048 [hep-ph/0505067] [INSPIRE].
M.A. Schmidt and A.Yu. Smirnov, Quark Lepton Complementarity and Renormalization Group Effects, Phys. Rev. D 74 (2006) 113003 [hep-ph/0607232] [INSPIRE].
C. Hagedorn, M.A. Schmidt and A.Yu. Smirnov, Lepton Mixing and Cancellation of the Dirac Mass Hierarchy in SO(10) GUTs with Flavor Symmetries T(7) and Sigma(81), Phys. Rev. D 79 (2009) 036002 [arXiv:0811.2955] [INSPIRE].
P.H. Chankowski and S. Pokorski, Quantum corrections to neutrino masses and mixing angles, Int. J. Mod. Phys. A 17 (2002) 575 [hep-ph/0110249] [INSPIRE].
S.F. King and N.N. Singh, Renormalization group analysis of single right-handed neutrino dominance, Nucl. Phys. B 591 (2000) 3 [hep-ph/0006229] [INSPIRE].
S.F. King and N.N. Singh, Inverted hierarchy models of neutrino masses, Nucl. Phys. B 596 (2001) 81 [hep-ph/0007243] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner and M. Ratz, Neutrino mass matrix running for nondegenerate seesaw scales, Phys. Lett. B 538 (2002) 87 [hep-ph/0203233] [INSPIRE].
B. Stech and Z. Tavartkiladze, Fermion masses and coupling unification in E 6 : Life in the desert, Phys. Rev. D 70 (2004) 035002 [hep-ph/0311161] [INSPIRE].
A. Zee, A Theory of Lepton Number Violation, Neutrino Majorana Mass and Oscillation, Phys. Lett. B 93 (1980) 389 [Erratum ibid. B 95 (1980) 461] [INSPIRE].
L. Wolfenstein, A Theoretical Pattern for Neutrino Oscillations, Nucl. Phys. B 175 (1980) 93 [INSPIRE].
M. Hirsch, A.S. Joshipura, S. Kaneko and J.W.F. Valle, Predictive flavour symmetries of the neutrino mass matrix, Phys. Rev. Lett. 99 (2007) 151802 [hep-ph/0703046] [INSPIRE].
E. Ma, A 4 symmetry and neutrinos with very different masses, Phys. Rev. D 70 (2004) 031901 [hep-ph/0404199] [INSPIRE].
E. Ma, Supersymmetric A 4 × Z(3) and A 4 realizations of neutrino tribimaximal mixing without and with corrections, Mod. Phys. Lett. A 22 (2007) 101 [hep-ph/0610342] [INSPIRE].
Y. Lin, A Predictive A 4 model, Charged Lepton Hierarchy and Tri-bimaximal Sum Rule, Nucl. Phys. B 813 (2009) 91 [arXiv:0804.2867] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
R. Barbieri, L.J. Hall, G.L. Kane and G.G. Ross, Nearly degenerate neutrinos and broken flavor symmetry, hep-ph/9901228 [INSPIRE].
F. Feruglio, C. Hagedorn and L. Merlo, Vacuum Alignment in SUSY A4 Models, JHEP 03 (2010) 084 [arXiv:0910.4058] [INSPIRE].
M. Holthausen and M.A. Schmidt, Natural Vacuum Alignment from Group Theory: The Minimal Case, JHEP 01 (2012) 126 [arXiv:1111.1730] [INSPIRE].
K.S. Babu, J.C. Pati and F. Wilczek, Fermion masses, neutrino oscillations and proton decay in the light of Super-Kamiokande, Nucl. Phys. B 566 (2000) 33 [hep-ph/9812538] [INSPIRE].
G. Altarelli and F. Feruglio, Theoretical models of neutrino masses and mixings, Springer Tracts Mod. Phys. 190 (2003) 169 [hep-ph/0206077] [INSPIRE].
D. Chang, T. Fukuyama, Y.-Y. Keum, T. Kikuchi and N. Okada, Perturbative SO(10) grand unification, Phys. Rev. D 71 (2005) 095002 [hep-ph/0412011] [INSPIRE].
G. Anderson, S. Raby, S. Dimopoulos, L.J. Hall and G.D. Starkman, A systematic SO(10) operator analysis for fermion masses, Phys. Rev. D 49 (1994) 3660 [hep-ph/9308333] [INSPIRE].
M.J. Kronenburg, A Method for Fast Diagonalization of a 2 × 2 or 3 × 3 Real Symmetric Matrix, arXiv:1306.6291.
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: 1604.03977
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
Chu, X., Smirnov, A.Y. Neutrino mixing and masses in SO(10) GUTs with hidden sector and flavor symmetries. J. High Energ. Phys. 2016, 135 (2016). https://doi.org/10.1007/JHEP05(2016)135
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2016)135