Abstract
We have performed a comprehensive analysis of the type D group D (1)9n, 3n as flavor symmetry and the generalized CP symmetry. All possible residual symmetries and their consequences for the prediction of the mixing parameters are studied. We find that only one type of mixing pattern is able to accommodate the measured values of the mixing angles in both “direct” and “variant of semidirect” approaches, and four types of mixing patterns are phenomenologically viable in the “semidirect” approach. The admissible values of the mixing angles as well as CP violating phases are studied in detail for each case. It is remarkable that the first two smallest D (1)9n, 3n groups with n = 1, 2 can fit the experimental data very well. The phenomenological predictions for neutrinoless double beta decay are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
MINOS collaboration, P. Adamson et al., Improved search for muon-neutrino to electron-neutrino oscillations in MINOS, Phys. Rev. Lett. 107 (2011) 181802 [arXiv:1108.0015] [INSPIRE].
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].
Double CHOOZ collaboration, Y. Abe et al., Reactor electron antineutrino disappearance in the Double CHOOZ experiment, Phys. Rev. D 86 (2012) 052008 [arXiv:1207.6632] [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].
Daya Bay collaboration, F.P. An et al., Improved measurement of electron antineutrino disappearance at Daya Bay, Chin. Phys. C 37 (2013) 011001 [arXiv:1210.6327] [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].
T2K collaboration, K. Abe et al., Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with 6.6 × 1020 protons on target, Phys. Rev. D 91 (2015) 072010 [arXiv:1502.01550] [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].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
H. Ishimori, T. Kobayashi, H. Ohki, Y. Shimizu, H. Okada and M. Tanimoto, Non-abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [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].
S.F. King, Models of neutrino mass, mixing and CP-violation, J. Phys. G 42 (2015) 123001 [arXiv:1510.02091] [INSPIRE].
R.M. Fonseca and W. Grimus, Classification of lepton mixing matrices from finite residual symmetries, JHEP 09 (2014) 033 [arXiv:1405.3678] [INSPIRE].
C.-Y. Yao and G.-J. Ding, Lepton and quark mixing patterns from finite flavor symmetries, Phys. Rev. D 92 (2015) 096010 [arXiv:1505.03798] [INSPIRE].
P. Chen, C.-C. Li and G.-J. Ding, Lepton flavor mixing and CP symmetry, Phys. Rev. D 91 (2015) 033003 [arXiv:1412.8352] [INSPIRE].
P. Chen, C.-Y. Yao and G.-J. Ding, Neutrino mixing from CP symmetry, Phys. Rev. D 92 (2015) 073002 [arXiv:1507.03419] [INSPIRE].
L.L. Everett, T. Garon and A.J. Stuart, A bottom-up approach to lepton flavor and CP symmetries, JHEP 04 (2015) 069 [arXiv:1501.04336] [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, μ-τ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett. B 547 (2002) 219 [hep-ph/0210197] [INSPIRE].
P.F. Harrison and W.G. Scott, The simplest neutrino mass matrix, Phys. Lett. B 594 (2004) 324 [hep-ph/0403278] [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].
W. Grimus and L. Lavoura, μ-τ interchange symmetry and lepton mixing, Fortsch. Phys. 61 (2013) 535 [arXiv:1207.1678] [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].
P. Chen, G.-J. Ding, F. Gonzalez-Canales and J.W.F. Valle, Generalized μ-τ reflection symmetry and leptonic CP-violation, Phys. Lett. B 753 (2016) 644 [arXiv:1512.01551] [INSPIRE].
F. Feruglio, C. Hagedorn and R. Ziegler, Lepton mixing parameters from discrete and CP symmetries, JHEP 07 (2013) 027 [arXiv:1211.5560] [INSPIRE].
M. Holthausen, M. Lindner and M.A. Schmidt, CP and discrete flavour symmetries, JHEP 04 (2013) 122 [arXiv:1211.6953] [INSPIRE].
G. Ecker, W. Grimus and W. Konetschny, Quark mass matrices in left-right symmetric gauge theories, Nucl. Phys. B 191 (1981) 465 [INSPIRE].
G. Ecker, W. Grimus and H. Neufeld, Spontaneous CP violation in left-right symmetric gauge theories, Nucl. Phys. B 247 (1984) 70 [INSPIRE].
J. Bernabeu, G.C. Branco and M. Gronau, CP restrictions on quark mass matrices, Phys. Lett. B 169 (1986) 243 [INSPIRE].
G. Ecker, W. Grimus and H. Neufeld, A standard form for generalized CP transformations, J. Phys. A 20 (1987) L807 [INSPIRE].
H. Neufeld, W. Grimus and G. Ecker, Generalized CP invariance, neutral flavor conservation and the structure of the mixing matrix, Int. J. Mod. Phys. A 3 (1988) 603 [INSPIRE].
W. Grimus and M.N. Rebelo, Automorphisms in gauge theories and the definition of CP and P, Phys. Rept. 281 (1997) 239 [hep-ph/9506272] [INSPIRE].
M.-C. Chen, M. Fallbacher, K.T. Mahanthappa, M. Ratz and A. Trautner, CP violation from finite groups, Nucl. Phys. B 883 (2014) 267 [arXiv:1402.0507] [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].
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].
C. Luhn, Trimaximal TM 1 neutrino mixing in S 4 with spontaneous CP-violation, Nucl. Phys. B 875 (2013) 80 [arXiv:1306.2358] [INSPIRE].
C.-C. Li and G.-J. Ding, Generalised CP and trimaximal T M 1 lepton mixing in S 4 family symmetry, Nucl. Phys. B 881 (2014) 206 [arXiv:1312.4401] [INSPIRE].
C.-C. Li and G.-J. Ding, Deviation from bimaximal mixing and leptonic CP phases in S 4 family symmetry and generalized CP, JHEP 08 (2015) 017 [arXiv:1408.0785] [INSPIRE].
G.C. Branco, I. de Medeiros Varzielas and S.F. King, Invariant approach to CP in unbroken Δ(27), Nucl. Phys. B 899 (2015) 14 [arXiv:1505.06165] [INSPIRE].
G.C. Branco, I. de Medeiros Varzielas and S.F. King, Invariant approach to CP in family symmetry models, Phys. Rev. D 92 (2015) 036007 [arXiv:1502.03105] [INSPIRE].
G.-J. Ding and Y.-L. Zhou, Predicting lepton flavor mixing from Δ(48) and generalized CP symmetries, Chin. Phys. C 39 (2015) 021001 [arXiv:1312.5222] [INSPIRE].
G.-J. Ding and Y.-L. Zhou, Lepton mixing parameters from Δ(48) family symmetry and generalised CP, JHEP 06 (2014) 023 [arXiv:1404.0592] [INSPIRE].
C.-C. Li and G.-J. Ding, Lepton mixing in A 5 family symmetry and generalized CP, JHEP 05 (2015) 100 [arXiv:1503.03711] [INSPIRE].
A. Di Iura, C. Hagedorn and D. Meloni, Lepton mixing from the interplay of the alternating group A 5 and CP, JHEP 08 (2015) 037 [arXiv:1503.04140] [INSPIRE].
P. Ballett, S. Pascoli and J. Turner, Mixing angle and phase correlations from A 5 with generalized CP and their prospects for discovery, Phys. Rev. D 92 (2015) 093008 [arXiv:1503.07543] [INSPIRE].
G.-J. Ding and S.F. King, Generalized CP and Δ(96) family symmetry, Phys. Rev. D 89 (2014) 093020 [arXiv:1403.5846] [INSPIRE].
C. Hagedorn, A. Meroni and E. Molinaro, Lepton mixing from Δ(3n 2) and Δ(6n 2) and CP, Nucl. Phys. B 891 (2015) 499 [arXiv:1408.7118] [INSPIRE].
G.-J. Ding and S.F. King, Generalized CP and Δ(3n 2) family symmetry for semi-direct predictions of the PMNS matrix, Phys. Rev. D 93 (2016) 025013 [arXiv:1510.03188] [INSPIRE].
G.-J. Ding, S.F. King and T. Neder, Generalised CP and Δ(6n 2) family symmetry in semi-direct models of leptons, JHEP 12 (2014) 007 [arXiv:1409.8005] [INSPIRE].
S.F. King and T. Neder, Lepton mixing predictions including Majorana phases from Δ(6n 2) flavour symmetry and generalised CP, Phys. Lett. B 736 (2014) 308 [arXiv:1403.1758] [INSPIRE].
G.A. Miller, H.F. Blichfeldt and L.E. Dickson, Theory and applications of finite groups, John Wiley & Sons, New York U.S.A. (1916).
W. Grimus and P.O. Ludl, Principal series of finite subgroups of SU(3), J. Phys. A 43 (2010) 445209 [arXiv:1006.0098] [INSPIRE].
W. Grimus and P.O. Ludl, On the characterization of the SU(3)-subgroups of type C and D, J. Phys. A 47 (2014) 075202 [arXiv:1310.3746] [INSPIRE].
W. Grimus and P.O. Ludl, Finite flavour groups of fermions, J. Phys. A 45 (2012) 233001 [arXiv:1110.6376] [INSPIRE].
S.F. King, T. Neder and A.J. Stuart, Lepton mixing predictions from Δ(6n 2) family symmetry, Phys. Lett. B 726 (2013) 312 [arXiv:1305.3200] [INSPIRE].
J.A. Escobar and C. Luhn, The flavor group Δ(6n 2), J. Math. Phys. 50 (2009) 013524 [arXiv:0809.0639] [INSPIRE].
GAP group, GAP — Groups, algorithms, and programming, version 4.4.12, http://www.gap-system.org (2008).
C.S. Lam, Symmetry of lepton mixing, Phys. Lett. B 656 (2007) 193 [arXiv:0708.3665] [INSPIRE].
G. Altarelli, F. Feruglio and L. Merlo, Revisiting bimaximal neutrino mixing in a model with S 4 discrete symmetry, JHEP 05 (2009) 020 [arXiv:0903.1940] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
JUNO collaboration, F. An et al., Neutrino physics with JUNO, J. Phys. G 43 (2016) 030401 [arXiv:1507.05613] [INSPIRE].
S.-B. Kim, New results from RENO and prospects with RENO-50, Nucl. Part. Phys. Proc. 265-266 (2015) 93 [arXiv:1412.2199] [INSPIRE].
LBNE collaboration, C. Adams et al., The long-baseline neutrino experiment: exploring fundamental symmetries of the universe, arXiv:1307.7335 [INSPIRE].
M. Bass et al., Baseline optimization for the measurement of CP-violation, mass hierarchy and θ 23 octant in a long-baseline neutrino oscillation experiment, Phys. Rev. D 91 (2015) 052015 [arXiv:1311.0212] [INSPIRE].
LAGUNA-LBNO collaboration, S.K. Agarwalla et al., The mass-hierarchy and CP-violation discovery reach of the LBNO long-baseline neutrino experiment, JHEP 05 (2014) 094 [arXiv:1312.6520] [INSPIRE].
L. Agostino et al., LBNO-DEMO: Large-scale neutrino detector demonstrators for phased performance assessment in view of a long-baseline oscillation experiment, arXiv:1409.4405 [INSPIRE].
LAGUNA-LBNO collaboration, S.K. Agarwalla et al., Optimised sensitivity to leptonic CP-violation from spectral information: the LBNO case at 2300 km baseline, arXiv:1412.0593 [INSPIRE].
LAGUNA-LBNO collaboration, S.K. Agarwalla et al., The LBNO long-baseline oscillation sensitivities with two conventional neutrino beams at different baselines, arXiv:1412.0804 [INSPIRE].
Hyper-Kamiokande Working Group collaboration, E. Kearns et al., Hyper-Kamiokande physics opportunities, arXiv:1309.0184 [INSPIRE].
E. Baussan et al., The use the a high intensity neutrino beam from the ESS proton linac for measurement of neutrino CP-violation and mass hierarchy, arXiv:1212.5048 [INSPIRE].
ESSnuSB collaboration, E. Baussan et al., A very intense neutrino super beam experiment for leptonic CP-violation discovery based on the European spallation source linac, Nucl. Phys. B 885 (2014) 127 [arXiv:1309.7022] [INSPIRE].
S. Geer, Neutrino beams from muon storage rings: characteristics and physics potential, Phys. Rev. D 57 (1998) 6989 [Erratum ibid. D 59 (1999) 039903] [hep-ph/9712290] [INSPIRE].
A. De Rujula, M.B. Gavela and P. Hernández, Neutrino oscillation physics with a neutrino factory, Nucl. Phys. B 547 (1999) 21 [hep-ph/9811390] [INSPIRE].
ISS Physics Working Group collaboration, A. Bandyopadhyay, Physics at a future Neutrino Factory and super-beam facility, Rept. Prog. Phys. 72 (2009) 106201 [arXiv:0710.4947] [INSPIRE].
GERDA collaboration, M. Agostini et al., Results on neutrinoless double-β decay of 76 Ge from Phase I of the GERDA experiment, Phys. Rev. Lett. 111 (2013) 122503 [arXiv:1307.4720] [INSPIRE].
EXO-200 collaboration, M. Auger et al., Search for neutrinoless double-beta decay in 136 Xe with EXO-200, Phys. Rev. Lett. 109 (2012) 032505 [arXiv:1205.5608] [INSPIRE].
EXO-200 collaboration, J.B. Albert et al., Search for Majorana neutrinos with the first two years of EXO-200 data, Nature 510 (2014) 229 [arXiv:1402.6956] [INSPIRE].
KamLAND-Zen collaboration, A. Gando et al., Limit on neutrinoless ββ decay of 136 Xe from the first phase of KamLAND-Zen and comparison with the positive claim in 76 Ge, Phys. Rev. Lett. 110 (2013) 062502 [arXiv:1211.3863] [INSPIRE].
F. Piquemal, Future double beta decay experiments, Nucl. Phys. Proc. Suppl. 235-236 (2013) 273 [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE].
M. Yoshimura, Neutrino pair emission from excited atoms, Phys. Rev. D 75 (2007) 113007 [hep-ph/0611362] [INSPIRE].
G.W. Mackey, On induced representations of groups, Amer. J. Math. 73 (1951) 576.
G.W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958) 265.
L. Corwing, Induced representations of discrete groups, Proc. Amer. Math. Soc. 47 (1975) 279.
B. Simon, Representations of finite and compact groups, American Mathematical Society, U.S.A. (1996).
J.P. Serre, Linear representations of finite groups, Graduate Texts in Mathematicsvolume 42, Springer (2012).
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: 1601.06393
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
Li, CC., Yao, CY. & Ding, GJ. Lepton mixing predictions from infinite group series D (1)9n, 3n with generalized CP . J. High Energ. Phys. 2016, 7 (2016). https://doi.org/10.1007/JHEP05(2016)007
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2016)007