# Linking leptonic CP violation to quark unitarity triangle

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## Abstract

We study the linking between the CP violating phase of the lepton sectors and the unitarity triangle of the *B*^{0} 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 *ϕ*_{2}(*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 *B*^{0} meson system. The leptonic CP violating phase *δ*_{PMNS} is predicted in the region −74 ~ −89°, which is the consistent with the recent T2K results. Our predicted phase is sensitive to *ϕ*_{2}(*α*) and *ϕ*_{3}(*γ*). These predictions will be clearly tested in the future neutrino experiments as well as the Belle-II experiment.

### Keywords

Neutrino Physics CP violation B-Physics## Notes

**Open Access**

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### References

- [1]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].ADSCrossRefGoogle Scholar - [2]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].CrossRefGoogle Scholar - [3]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].CrossRefGoogle Scholar - [4]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].CrossRefGoogle Scholar - [5]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].Google Scholar - [6]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].ADSGoogle Scholar - [7]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].ADSCrossRefGoogle Scholar - [8]C. Giunti and M. Tanimoto,
*CP violation in bilarge lepton mixing*,*Phys. Rev.***D 66**(2002) 113006 [hep-ph/0209169] [INSPIRE].ADSGoogle Scholar - [9]Z.-z. Xing,
*Nearly tri bimaximal neutrino mixing and CP-violation*,*Phys. Lett.***B 533**(2002) 85 [hep-ph/0204049] [INSPIRE].ADSGoogle Scholar - [10]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].ADSGoogle Scholar - [11]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].ADSGoogle Scholar - [12]G.C. Branco, R.G. Felipe and F.R. Joaquim,
*Leptonic CP-violation*,*Rev. Mod. Phys.***84**(2012) 515 [arXiv:1111.5332] [INSPIRE].ADSCrossRefGoogle Scholar - [13]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].ADSGoogle Scholar - [14]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].ADSGoogle Scholar - [15]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].ADSGoogle Scholar - [16]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].ADSGoogle Scholar - [17]W. Rodejohann and H. Zhang,
*Simple two parameter description of lepton mixing*,*Phys. Rev.***D 86**(2012) 093008 [arXiv:1207.1225] [INSPIRE].ADSGoogle Scholar - [18]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].ADSCrossRefGoogle Scholar - [19]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].ADSGoogle Scholar - [20]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].ADSCrossRefGoogle Scholar - [21]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].ADSCrossRefGoogle Scholar - [22]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].ADSCrossRefGoogle Scholar - [23]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].ADSGoogle Scholar - [24]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].ADSMathSciNetCrossRefMATHGoogle Scholar - [25]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].ADSGoogle Scholar - [26]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].ADSCrossRefGoogle Scholar - [27]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]. - [28]S.K. Kang and M. Tanimoto,
*Prediction of leptonic CP phase in A*_{4}*symmetric model*, arXiv:1501.07428 [INSPIRE]. - [29]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].ADSGoogle Scholar - [30]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].ADSCrossRefGoogle Scholar - [31]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].ADSCrossRefMATHGoogle Scholar - [32]S. Antusch and V. Maurer,
*Large neutrino mixing angle θ*_{13}^{MNS}*and quark-lepton mass ratios in unified flavour models*,*Phys. Rev.***D 84**(2011) 117301 [arXiv:1107.3728] [INSPIRE].ADSGoogle Scholar - [33]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].ADSCrossRefMATHGoogle Scholar - [34]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].ADSGoogle Scholar - [35]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].ADSGoogle Scholar - [36]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].ADSCrossRefGoogle Scholar - [37]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].ADSCrossRefGoogle Scholar - [38]Particle Data Group collaboration, J. Beringer et al.,
*Review of particle physics*,*Phys. Rev.***D 86**(2012) 010001 [INSPIRE].Google Scholar - [39]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].ADSCrossRefGoogle Scholar - [40]Z. Maki, M. Nakagawa and S. Sakata,
*Remarks on the unified model of elementary particles*,*Prog. Theor. Phys.***28**(1962) 870 [INSPIRE].ADSCrossRefMATHGoogle Scholar - [41]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]. - [42]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].ADSCrossRefGoogle Scholar - [43]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].ADSCrossRefGoogle Scholar - [44]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].ADSCrossRefGoogle Scholar - [45]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].ADSGoogle Scholar - [46]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].ADSGoogle Scholar