Abstract
We study the linking between the CP violating phase of the lepton sectors and the unitarity triangle of the B0 meson system. Antusch, King, Malinsky and Spinrath have shown that the quark mass matrices with the negligible 1-3 mixing give an interesting relation between the phase of the quark mixing matrices and CP violating measure ϕ2(α). This approach is extended by considering the SO(10) GUT including the Pati-Salam symmetry, which links the Yukawa matrices of the quark sector to the one of the lepton sector. We discuss the relation of the CP violating phases between both quark and lepton sectors as well as the mixing angles. Then, the leptonic CP violating phase is predicted in terms of the angle of the unitarity triangle of the B0 meson system. The leptonic CP violating phase δPMNS is predicted in the region −74 ~ −89°, which is the consistent with the recent T2K results. Our predicted phase is sensitive to ϕ2(α) and ϕ3(γ). These predictions will be clearly tested in the future neutrino experiments as well as the Belle-II experiment.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T2K collaboration, K. Abe et al., Observation of electron neutrino appearance in a muon neutrino beam, Phys. Rev. Lett. 112 (2014) 061802 [arXiv:1311.4750] [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].
MINOS collaboration, P. Adamson et al., Measurement of neutrino and antineutrino oscillations using beam and atmospheric data in MINOS, Phys. Rev. Lett. 110 (2013) 251801 [arXiv:1304.6335] [INSPIRE].
Double CHOOZ collaboration, Y. Abe et al., Background-independent measurement of θ 13 in Double CHOOZ, Phys. Lett. B 735 (2014) 51 [arXiv:1401.5981] [INSPIRE].
S.K. Kang, C.S. Kim and J.D. Kim, Neutrino masses and leptonic CP-violation, Phys. Rev. D 62 (2000) 073011 [hep-ph/0004020] [INSPIRE].
M. Fukugita and M. Tanimoto, Lepton flavor mixing matrix and CP-violation from neutrino oscillation experiments, Phys. Lett. B 515 (2001) 30 [hep-ph/0107082] [INSPIRE].
C. Giunti and M. Tanimoto, CP violation in bilarge lepton mixing, Phys. Rev. D 66 (2002) 113006 [hep-ph/0209169] [INSPIRE].
Z.-z. Xing, Nearly tri bimaximal neutrino mixing and CP-violation, Phys. Lett. B 533 (2002) 85 [hep-ph/0204049] [INSPIRE].
B. Adhikary and A. Ghosal, Constraining it CP-violation in a softly broken A 4 symmetric Model, Phys. Rev. D 75 (2007) 073020 [hep-ph/0609193] [INSPIRE].
B. Adhikary and A. Ghosal, Nonzero U e3 , CP-violation and leptogenesis in a see-saw type softly broken A 4 symmetric model, Phys. Rev. D 78 (2008) 073007 [arXiv:0803.3582] [INSPIRE].
G.C. Branco, R.G. Felipe and F.R. Joaquim, Leptonic CP-violation, Rev. Mod. Phys. 84 (2012) 515 [arXiv:1111.5332] [INSPIRE].
G.C. Branco, R. Gonzalez Felipe, F.R. Joaquim and H. Serodio, Spontaneous leptonic CP-violation and nonzero θ 13, Phys. Rev. D 86 (2012) 076008 [arXiv:1203.2646] [INSPIRE].
Y.H. Ahn and S.K. Kang, Non-zero θ 13 and CP-violation in a model with A 4 flavor symmetry, Phys. Rev. D 86 (2012) 093003 [arXiv:1203.4185] [INSPIRE].
H. Ishimori, S. Khalil and E. Ma, CP phases of neutrino mixing in a supersymmetric B-L Gauge Model with T 7 lepton flavor symmetry, Phys. Rev. D 86 (2012) 013008 [arXiv:1204.2705] [INSPIRE].
H. Ishimori and E. Ma, New simple A 4 neutrino model for nonzero θ 13 and large δ CP , Phys. Rev. D 86 (2012) 045030 [arXiv:1205.0075] [INSPIRE].
W. Rodejohann and H. Zhang, Simple two parameter description of lepton mixing, Phys. Rev. D 86 (2012) 093008 [arXiv:1207.1225] [INSPIRE].
D. Marzocca, S.T. Petcov, A. Romanino and M.C. Sevilla, Nonzero |U e3| from charged lepton corrections and the atmospheric neutrino mixing angle, JHEP 05 (2013) 073 [arXiv:1302.0423] [INSPIRE].
P. Ballett, S.F. King, C. Luhn, S. Pascoli and M.A. Schmidt, Testing atmospheric mixing sum rules at precision neutrino facilities, Phys. Rev. D 89 (2014) 016016 [arXiv:1308.4314] [INSPIRE].
P. Ballett, S.F. King, C. Luhn, S. Pascoli and M.A. Schmidt, Testing solar lepton mixing sum rules in neutrino oscillation experiments, JHEP 12 (2014) 122 [arXiv:1410.7573] [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].
Z.-z. Xing and S. Zhou, A partial μ-τ symmetry and its prediction for leptonic CP-violation, Phys. Lett. B 737 (2014) 196 [arXiv:1404.7021] [INSPIRE].
G.C. Branco, M.N. Rebelo, J.I. Silva-Marcos and D. Wegman, Quasidegeneracy of Majorana neutrinos and the origin of large leptonic mixing, Phys. Rev. D 91 (2015) 013001 [arXiv:1405.5120] [INSPIRE].
S.T. Petcov, Predicting the values of the leptonic CP-violation phases in theories with discrete flavour symmetries, Nucl. Phys. B 892 (2015) 400 [arXiv:1405.6006] [INSPIRE].
S.K. Kang and C.S. Kim, Prediction of leptonic CP phase from perturbatively modified tribimaximal (or bimaximal) mixing, Phys. Rev. D 90 (2014) 077301 [arXiv:1406.5014] [INSPIRE].
Y. Shimizu, M. Tanimoto and K. Yamamoto, Predicting CP-violation in deviation from tri-bimaximal mixing of neutrinos, Mod. Phys. Lett. A 30 (2015) 1550002 [arXiv:1405.1521] [INSPIRE].
I. Girardi, S.T. Petcov and A.V. Titov, Determining the Dirac CP-violation phase in the neutrino mixing matrix from sum rules, arXiv:1410.8056 [INSPIRE].
S.K. Kang and M. Tanimoto, Prediction of leptonic CP phase in A 4 symmetric model, arXiv:1501.07428 [INSPIRE].
S. Antusch, S.F. King, M. Malinsky and M. Spinrath, Quark mixing sum rules and the right unitarity triangle, Phys. Rev. D 81 (2010) 033008 [arXiv:0910.5127] [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, \( {\theta}_{13}^{PMNS} = {\theta}_C/\sqrt{2} \) 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 \( {\theta}_{13}^{PMNS} \simeq {\theta}_C/\sqrt{2} \), Nucl. Phys. B 877 (2013) 772 [arXiv:1305.6612] [INSPIRE].
S. Antusch and V. Maurer, Large neutrino mixing angle θ MNS13 and quark-lepton mass ratios in unified flavour models, Phys. Rev. D 84 (2011) 117301 [arXiv:1107.3728] [INSPIRE].
D. Marzocca, S.T. Petcov, A. Romanino and M. Spinrath, Sizeable θ 13 from the charged lepton sector in SU(5), (tri-)bimaximal neutrino mixing and Dirac CP-violation, JHEP 11 (2011) 009 [arXiv:1108.0614] [INSPIRE].
P.S. Bhupal Dev, R.N. Mohapatra and M. Severson, Neutrino mixings in SO(10) with type II seesaw and θ 13, Phys. Rev. D 84 (2011) 053005 [arXiv:1107.2378] [INSPIRE].
P.S. Bhupal Dev, B. Dutta, R.N. Mohapatra and M. Severson, θ 13 and proton decay in a minimal SO(10) × S 4 model of flavor, Phys. Rev. D 86 (2012) 035002 [arXiv:1202.4012] [INSPIRE].
M. Bando, S. Kaneko, M. Obara and M. Tanimoto, Can symmetric texture reproduce neutrino bilarge mixing?, Phys. Lett. B 580 (2004) 229 [hep-ph/0309310] [INSPIRE].
M. Bando, S. Kaneko, M. Obara and M. Tanimoto, Symmetric mass matrix with two zeros in SUSY SO(10) GUT, lepton flavor violations and leptogenesis, Prog. Theor. Phys. 112 (2004) 533 [hep-ph/0405071] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].
C. Jarlskog, Commutator of the quark mass matrices in the standard electroweak model and a measure of maximal CP-violation, Phys. Rev. Lett. 55 (1985) 1039 [INSPIRE].
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].
B. Pontecorvo, Neutrino experiments and the problem of conservation of leptonic charge, Sov. Phys. JETP 26 (1968) 984 [Zh. Eksp. Teor. Fiz. 53 (1967) 1717] [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].
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].
D.V. Forero, M. Tortola and J.W.F. Valle, Global status of neutrino oscillation parameters after Neutrino-2012, Phys. Rev. D 86 (2012) 073012 [arXiv:1205.4018] [INSPIRE].
G.L. 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].
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: 1501.07717
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
Tanimoto, M., Yamamoto, K. Linking leptonic CP violation to quark unitarity triangle. J. High Energ. Phys. 2015, 37 (2015). https://doi.org/10.1007/JHEP04(2015)037
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)037