Abstract
In models with discrete flavour symmetries, flavons are critical to realise specific flavour structures. Leptonic flavour mixing originates from the misalignment of flavon vacuum expectation values which respect different residual symmetries in the charged lepton and neutrino sectors. Flavon cross couplings are usually forbidden, in order to protect these symmetries. Contrary to this approach, we show that cross couplings can play a key role and give raise to necessary corrections to flavour-mixing patterns, including a non-zero value for the reactor angle and CP violation. For definiteness, we present two models based on A 4. In the first model, all flavons are assumed to be real or pseudo-real, with 7 real degrees of freedom in the flavon sector in total. A sizable reactor angle associated with nearly maximal CP violation is achieved, and, as both originate from the same cross coupling, a sum rule results with a precise prediction for the value of the Dirac CP-violating phase. In the second model, the flavons are taken to be complex scalars, which can be connected with supersymmetric models and multi-Higgs models. The complexity properties of flavons provide new sources for generating the reactor angle. Models in this new approach introduce very few degrees of freedom beyond the Standard Model and can be more economical than those in the framework of extra dimension or supersymmetry.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Super-Kamiokande collaboration, Y. Fukuda et al., Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003] [INSPIRE].
Super-Kamiokande collaboration, S. Fukuda et al., Solar 8 B and hep neutrino measurements from 1258 days of Super-Kamiokande data, Phys. Rev. Lett. 86 (2001) 5651 [hep-ex/0103032] [INSPIRE].
SNO collaboration, Q.R. Ahmad et al., Measurement of the rate of ν e + d → p + p + e − interactions produced by 8 B solar neutrinos at the Sudbury Neutrino Observatory, Phys. Rev. Lett. 87 (2001) 071301 [nucl-ex/0106015] [INSPIRE].
SNO collaboration, Q.R. Ahmad et al., Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89 (2002) 011301 [nucl-ex/0204008] [INSPIRE].
K2K collaboration, M.H. Ahn et al., Indications of neutrino oscillation in a 250 km long baseline experiment, Phys. Rev. Lett. 90 (2003) 041801 [hep-ex/0212007] [INSPIRE].
T2K collaboration, K. Abe et al., Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam, Phys. Rev. Lett. 107 (2011) 041801 [arXiv:1106.2822] [INSPIRE].
KamLAND collaboration, K. Eguchi et al., First results from KamLAND: Evidence for reactor anti-neutrino disappearance, Phys. Rev. Lett. 90 (2003) 021802 [hep-ex/0212021] [INSPIRE].
Daya Bay collaboration, F.P. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].
RENO collaboration, J.K. Ahn et al., Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
J. Bergstrom, M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Bayesian global analysis of neutrino oscillation data, JHEP 09 (2015) 200 [arXiv:1507.04366] [INSPIRE].
F. Capozzi, G.L. Fogli, E. Lisi, A. Marrone, D. Montanino and A. Palazzo, Status of three-neutrino oscillation parameters, circa 2013, Phys. Rev. D 89 (2014) 093018 [arXiv:1312.2878] [INSPIRE].
D.V. Forero, M. Tortola and J.W.F. Valle, Neutrino oscillations refitted, Phys. Rev. D 90 (2014) 093006 [arXiv:1405.7540] [INSPIRE].
M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Updated fit to three neutrino mixing: status of leptonic CP-violation, JHEP 11 (2014) 052 [arXiv:1409.5439] [INSPIRE].
T2K collaboration, K. Abe et al., Measurement of Neutrino Oscillation Parameters from Muon Neutrino Disappearance with an Off-axis Beam, Phys. Rev. Lett. 111 (2013) 211803 [arXiv:1308.0465] [INSPIRE].
T2K collaboration, K. Abe et al., Precise Measurement of the Neutrino Mixing Parameter θ 23 from Muon Neutrino Disappearance in an Off-Axis Beam, Phys. Rev. Lett. 112 (2014) 181801 [arXiv:1403.1532] [INSPIRE].
Daya Bay collaboration, F.P. An et al., Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay, Phys. Rev. Lett. 112 (2014) 061801 [arXiv:1310.6732] [INSPIRE].
Daya Bay collaboration, F.P. An et al., New Measurement of Antineutrino Oscillation with the Full Detector Configuration at Daya Bay, Phys. Rev. Lett. 115 (2015) 111802 [arXiv:1505.03456] [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].
Z.-z. Xing, Nearly tri bimaximal neutrino mixing and CP-violation, Phys. Lett. B 533 (2002) 85 [hep-ph/0204049] [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].
X.G. He and A. Zee, Some simple mixing and mass matrices for neutrinos, Phys. Lett. B 560 (2003) 87 [hep-ph/0301092] [INSPIRE].
S.F. King, Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing, Phys. Lett. B 659 (2008) 244 [arXiv:0710.0530] [INSPIRE].
S.F. King, Tri-bimaximal-Cabibbo Mixing, Phys. Lett. B 718 (2012) 136 [arXiv:1205.0506] [INSPIRE].
Z.-z. Xing and S. Zhou, Tri-bimaximal Neutrino Mixing and Flavor-dependent Resonant Leptogenesis, Phys. Lett. B 653 (2007) 278 [hep-ph/0607302] [INSPIRE].
C.S. Lam, Mass Independent Textures and Symmetry, Phys. Rev. D 74 (2006) 113004 [hep-ph/0611017] [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].
J.D. Bjorken, P.F. Harrison and W.G. Scott, Simplified unitarity triangles for the lepton sector, Phys. Rev. D 74 (2006) 073012 [hep-ph/0511201] [INSPIRE].
X.-G. He and A. Zee, Minimal modification to the tri-bimaximal neutrino mixing, Phys. Lett. B 645 (2007) 427 [hep-ph/0607163] [INSPIRE].
W. Grimus and L. Lavoura, A Model for trimaximal lepton mixing, JHEP 09 (2008) 106 [arXiv:0809.0226] [INSPIRE].
W. Grimus and L. Lavoura, A Three-parameter neutrino mass matrix with maximal CP-violation, Phys. Lett. B 671 (2009) 456 [arXiv:0810.4516] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino Mass and Mixing: from Theory to Experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [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].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A 4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [INSPIRE].
C.S. Lam, The Unique Horizontal Symmetry of Leptons, Phys. Rev. D 78 (2008) 073015 [arXiv:0809.1185] [INSPIRE].
I.K. Cooper, S.F. King and C. Luhn, A4 × SU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing, JHEP 06 (2012) 130 [arXiv:1203.1324] [INSPIRE].
G. Altarelli, F. Feruglio and L. Merlo, Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries, Fortsch. Phys. 61 (2013) 507 [arXiv:1205.5133] [INSPIRE].
Y. BenTov, X.-G. He and A. Zee, An A 4 × Z 4 model for neutrino mixing, JHEP 12 (2012) 093 [arXiv:1208.1062] [INSPIRE].
M.-C. Chen, J. Huang, J.-M. O’Bryan, A.M. Wijangco and F. Yu, Compatibility of θ 13 and the Type I Seesaw Model with A 4 Symmetry, JHEP 02 (2013) 021 [arXiv:1210.6982] [INSPIRE].
M. Holthausen, M. Lindner and M.A. Schmidt, Lepton flavor at the electroweak scale: A complete A 4 model, Phys. Rev. D 87 (2013) 033006 [arXiv:1211.5143] [INSPIRE].
N. Memenga, W. Rodejohann and H. Zhang, A 4 flavor symmetry model for Dirac neutrinos and sizable U e3, Phys. Rev. D 87 (2013) 053021 [arXiv:1301.2963] [INSPIRE].
J. Heeck, M. Holthausen, W. Rodejohann and Y. Shimizu, Higgs → μτ in Abelian and non-Abelian flavor symmetry models, Nucl. Phys. B 896 (2015) 281 [arXiv:1412.3671] [INSPIRE].
I. de Medeiros Varzielas, O. Fischer and V. Maurer, \( {\mathbb{A}}_4 \) symmetry at colliders and in the universe, JHEP 08 (2015) 080 [arXiv:1504.03955] [INSPIRE].
K.S. Babu and S. Gabriel, Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing, Phys. Rev. D 82 (2010) 073014 [arXiv:1006.0203] [INSPIRE].
M. Holthausen and M.A. Schmidt, Natural Vacuum Alignment from Group Theory: The Minimal Case, JHEP 01 (2012) 126 [arXiv:1111.1730] [INSPIRE].
M. Holthausen, M. Lindner and M.A. Schmidt, Lepton flavor at the electroweak scale: A complete A 4 model, Phys. Rev. D 87 (2013) 033006 [arXiv:1211.5143] [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].
R. de Adelhart Toorop, F. Bazzocchi, L. Merlo and A. Paris, Constraining Flavour Symmetries At The EW Scale I: The A4 Higgs Potential, JHEP 03 (2011) 035 [Erratum ibid. 1301 (2013) 098] [arXiv:1012.1791] [INSPIRE].
R. de Adelhart Toorop, F. Bazzocchi, L. Merlo and A. Paris, Constraining Flavour Symmetries At The EW Scale II: The Fermion Processes, JHEP 03 (2011) 040 [arXiv:1012.2091] [INSPIRE].
A. Degee, I.P. Ivanov and V. Keus, Geometric minimization of highly symmetric potentials, JHEP 02 (2013) 125 [arXiv:1211.4989] [INSPIRE].
V. Keus, S.F. King and S. Moretti, Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses, JHEP 01 (2014) 052 [arXiv:1310.8253] [INSPIRE].
L. Lavoura and H. Kuhbock, A 4 model for the quark mass matrices, Eur. Phys. J. C 55 (2008) 303 [arXiv:0711.0670] [INSPIRE].
S. Morisi and E. Peinado, An A 4 model for lepton masses and mixings, Phys. Rev. D 80 (2009) 113011 [arXiv:0910.4389] [INSPIRE].
A.E. Carcamo Hernandez, I. de Medeiros Varzielas, S.G. Kovalenko, H. Päs and I. Schmidt, Lepton masses and mixings in an A 4 multi-Higgs model with a radiative seesaw mechanism, Phys. Rev. D 88 (2013) 076014 [arXiv:1307.6499] [INSPIRE].
R. González Felipe, I.P. Ivanov, C.C. Nishi, H. Serôdio and J.P. Silva, Constraining multi-Higgs flavour models, Eur. Phys. J. C 74 (2014) 2953 [arXiv:1401.5807] [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: 1604.00925
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
Pascoli, S., Zhou, YL. The role of flavon cross couplings in leptonic flavour mixing. J. High Energ. Phys. 2016, 73 (2016). https://doi.org/10.1007/JHEP06(2016)073
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2016)073