Abstract
In this paper, we derive in a novel approach the possible textures of neutrino mass matrix that can lead us to maximal atmospheric mixing angle and Dirac CP phase which are consistent with the current neutrino oscillation data. A total of eleven textures are thus found. Interestingly, the specific texture given by the μ-τ reflection symmetry can be reproduced from one of the obtained textures. For these textures, some neutrino mass sum rules which relate the neutrino masses and Majorana CP phases will emerge.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
B. Pontecorvo, Neutrino Experiments and the Problem of Conservation of Leptonic Charge, Sov. Phys. JETP 26 (1968) 984 [INSPIRE].
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].
I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler and T. Schwetz, Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, JHEP 01 (2017) 087 [arXiv:1611.01514] [INSPIRE].
P.F. Harrison and W.G. Scott, μ-τ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett. B 547 (2002) 219 [hep-ph/0210197] [INSPIRE].
P.M. Ferreira, W. Grimus, L. Lavoura and P.O. Ludl, Maximal CP-violation in Lepton Mixing from a Model with Δ(27) flavour Symmetry, JHEP 09 (2012) 128 [arXiv:1206.7072] [INSPIRE].
R.N. Mohapatra and C.C. Nishi, S 4 Flavored CP Symmetry for Neutrinos, Phys. Rev. D 86 (2012) 073007 [arXiv:1208.2875] [INSPIRE].
R.N. Mohapatra and C.C. Nishi, Implications of μ-τ flavored CP symmetry of leptons, JHEP 08 (2015) 092 [arXiv:1506.06788] [INSPIRE].
Y.-L. Zhou, μ-τ reflection symmetry and radiative corrections, arXiv:1409.8600 [INSPIRE].
E. Ma, A. Natale and O. Popov, Neutrino Mixing and CP Phase Correlations, Phys. Lett. B 746 (2015) 114 [arXiv:1502.08023] [INSPIRE].
E. Ma, Transformative A 4 mixing of neutrinos with CP-violation, Phys. Rev. D 92 (2015) 051301 [arXiv:1504.02086] [INSPIRE].
E. Ma, Neutrino mixing: A 4 variations, Phys. Lett. B 752 (2016) 198 [arXiv:1510.02501] [INSPIRE].
G.-N. Li and X.-G. He, CP violation in neutrino mixing with δ = −π/2 in A 4 Type-II seesaw model, Phys. Lett. B 750 (2015) 620 [arXiv:1505.01932] [INSPIRE].
A.S. Joshipura and K.M. Patel, Generalized μ-τ symmetry and discrete subgroups of O(3), Phys. Lett. B 749 (2015) 159 [arXiv:1507.01235] [INSPIRE].
H.-J. He, W. Rodejohann and X.-J. Xu, Origin of Constrained Maximal CP-violation in Flavor Symmetry, Phys. Lett. B 751 (2015) 586 [arXiv:1507.03541] [INSPIRE].
C.C. Nishi, New and trivial CP symmetry for extended A 4 flavor, Phys. Rev. D 93 (2016) 093009 [arXiv:1601.00977] [INSPIRE].
P.M. Ferreira, W. Grimus, D. Jurciukonis and L. Lavoura, Scotogenic model for co-bimaximal mixing, JHEP 07 (2016) 010 [arXiv:1604.07777] [INSPIRE].
A.S. Joshipura and N. Nath, Neutrino masses and mixing in A 5 with flavor antisymmetry, Phys. Rev. D 94 (2016) 036008 [arXiv:1606.01697] [INSPIRE].
C.-C. Li, J.-N. Lu and G.-J. Ding, A 4 and CP symmetry and a model with maximal CP-violation, Nucl. Phys. B 913 (2016) 110 [arXiv:1608.01860] [INSPIRE].
C.C. Nishi and B.L. Sánchez-Vega, Mu-tau reflection symmetry with a texture-zero, JHEP 01 (2017) 068 [arXiv:1611.08282] [INSPIRE].
Z.-h. Zhao, Breakings of the neutrino μ-τ reflection symmetry, JHEP 09 (2017) 023 [arXiv:1703.04984] [INSPIRE].
Z.-h. Zhao, Modifications to the neutrino mixing from the μ-τ reflection symmetry, Nucl. Phys. B 935 (2018) 129 [arXiv:1803.04603] [INSPIRE].
Z.-z. Xing and J.-y. Zhu, Neutrino mass ordering and μ-τ reflection symmetry breaking, Chin. Phys. C 41 (2017) 123103 [arXiv:1707.03676] [INSPIRE].
Z.-C. Liu, C.-X. Yue and Z.-h. Zhao, Neutrino μ-τ reflection symmetry and its breaking in the minimal seesaw, JHEP 10 (2017) 102 [arXiv:1707.05535] [INSPIRE].
Z.-z. Xing, D. Zhang and J.-y. Zhu, The μ-τ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections, JHEP 11 (2017) 135 [arXiv:1708.09144] [INSPIRE].
R. Samanta, P. Roy and A. Ghosal, Consequences of minimal seesaw with complex μτ antisymmetry of neutrinos, JHEP 06 (2018) 085 [arXiv:1712.06555] [INSPIRE].
N. Nath, Z.-z. Xing and J. Zhang, μ-τ Reflection Symmetry Embedded in Minimal Seesaw, Eur. Phys. J. C 78 (2018) 289 [arXiv:1801.09931] [INSPIRE].
K. Chakraborty, K.N. Deepthi, S. Goswami, A.S. Joshipura and N. Nath, Partial μ-τ Reflection Symmetry and Its Verification at DUNE and Hyper-Kamiokande, arXiv:1804.02022 [INSPIRE].
N. Nath, Consequences of μ-τ Reflection Symmetry at DUNE, arXiv:1805.05823 [INSPIRE].
N. Nath, μ-τ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model, arXiv:1808.05062 [INSPIRE].
J.-N. Lu and G.-J. Ding, Quark and lepton mixing patterns from a common discrete flavor symmetry with a generalized CP symmetry, Phys. Rev. D 98 (2018) 055011 [arXiv:1806.02301] [INSPIRE].
G.-y. Huang, Z.-z. Xing and J.-y. Zhu, Correlation of normal neutrino mass ordering with upper octant of θ 23 and third quadrant of δ via spontaneous μ-τ symmetry breaking, arXiv:1806.06640 [INSPIRE].
C.C. Nishi, B.L. Sánchez-Vega and G. Souza Silva, μτ reflection symmetry with a high scale texture-zero, JHEP 09 (2018) 042 [arXiv:1806.07412] [INSPIRE].
S.F. King and C.C. Nishi, Mu-tau symmetry and the Littlest Seesaw, Phys. Lett. B 785 (2018) 391 [arXiv:1807.00023] [INSPIRE].
W. Grimus and L. Lavoura, μ-τ Interchange symmetry and lepton mixing, Fortsch. Phys. 61 (2013) 535 [arXiv:1207.1678] [INSPIRE].
W. Grimus and L. Lavoura, A Nonstandard CP transformation leading to maximal atmospheric neutrino mixing, Phys. Lett. B 579 (2004) 113 [hep-ph/0305309] [INSPIRE].
I. Aizawa, T. Kitabayashi and M. Yasue, Constraints on flavor neutrino masses and sin 22θ 12 ≫ sin 2 θ 13 in neutrino oscillations, Phys. Rev. D 71 (2005) 075011 [hep-ph/0502135] [INSPIRE].
I. Aizawa, T. Kitabayashi and M. Yasue, Determination of neutrino mass texture for maximal CP-violation, Nucl. Phys. B 728 (2005) 220 [hep-ph/0507332] [INSPIRE].
T. Kitabayashi and M. Yasue, mu-tau symmetry and maximal CP-violation, Phys. Lett. B 621 (2005) 133 [hep-ph/0504212] [INSPIRE].
T. Kitabayashi and M. Yasuè, Maximal CP-violation in Flavor Neutrino Masses, Int. J. Mod. Phys. A 31 (2016) 1650043 [arXiv:1509.06071] [INSPIRE].
Z.-z. Xing and Y.-L. Zhou, A Generic Diagonalization of the 3 × 3 Neutrino Mass Matrix and Its Implications on the μ-τ Flavor Symmetry and Maximal CP-violation, Phys. Lett. B 693 (2010) 584 [arXiv:1008.4906] [INSPIRE].
J. Barry and W. Rodejohann, Neutrino Mass Sum-rules in Flavor Symmetry Models, Nucl. Phys. B 842 (2011) 33 [arXiv:1007.5217] [INSPIRE].
S.F. King, A. Merle and A.J. Stuart, The Power of Neutrino Mass Sum Rules for Neutrinoless Double Beta Decay Experiments, JHEP 12 (2013) 005 [arXiv:1307.2901] [INSPIRE].
J. Gehrlein, A. Merle and M. Spinrath, Renormalisation Group Corrections to Neutrino Mass Sum Rules, JHEP 09 (2015) 066 [arXiv:1506.06139] [INSPIRE].
J. Gehrlein, A. Merle and M. Spinrath, Predictivity of Neutrino Mass Sum Rules, Phys. Rev. D 94 (2016) 093003 [arXiv:1606.04965] [INSPIRE].
M. Agostini, A. Merle and K. Zuber, Probing flavor models with 76 Ge-based experiments on neutrinoless double-β decay, Eur. Phys. J. C 76 (2016) 176 [arXiv:1506.06133] [INSPIRE].
J. Gehrlein and M. Spinrath, Neutrino Mass Sum Rules and Symmetries of the Mass Matrix, Eur. Phys. J. C 77 (2017) 281 [arXiv:1704.02371] [INSPIRE].
T. Fukuyama and H. Nishiura, Mass matrix of Majorana neutrinos, hep-ph/9702253 [INSPIRE].
E. Ma and M. Raidal, Neutrino mass, muon anomalous magnetic moment and lepton flavor nonconservation, Phys. Rev. Lett. 87 (2001) 011802 [Erratum ibid. 87 (2001) 159901] [hep-ph/0102255] [INSPIRE].
C.S. Lam, A 2-3 symmetry in neutrino oscillations, Phys. Lett. B 507 (2001) 214 [hep-ph/0104116] [INSPIRE].
K.R.S. Balaji, W. Grimus and T. Schwetz, The Solar LMA neutrino oscillation solution in the Zee model, Phys. Lett. B 508 (2001) 301 [hep-ph/0104035] [INSPIRE].
Z.-z. Xing and Z.-h. Zhao, A review of μ-τ flavor symmetry in neutrino physics, Rept. Prog. Phys. 79 (2016) 076201 [arXiv:1512.04207] [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].
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].
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: 1807.10031
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
Liu, ZC., Yue, CX. & Zhao, Zh. On the textures of neutrino mass matrix for maximal atmospheric mixing angle and Dirac CP phase. J. High Energ. Phys. 2018, 106 (2018). https://doi.org/10.1007/JHEP10(2018)106
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2018)106