Journal of High Energy Physics

, 2012:92 | Cite as

A simple grand unified relation between neutrino mixing and quark mixing

  • S. M. Barr
  • Heng-Yu Chen


It is proposed that all flavor mixing is caused by the mixing of the three quark and lepton families with vectorlike fermions in \( 5+\bar{5} \) multiplets of SU(5). This simple assumption implies that both V CKM and U M N S are generated by a single matrix. The entire 3 × 3 complex mass matrix of the neutrinos M v is then found to have a simple expression in terms of two complex parameters and an overall scale. Thus, all the presently unknown neutrino parameters are predicted. The best fits are for θ atm ≲ 40°. The leptonic Dirac CP phase is found to be somewhat greater than π.


Neutrino Physics GUT CP violation Beyond Standard Model 


  1. [1]
    Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].ADSMATHCrossRefGoogle Scholar
  2. [2]
    N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    K. Babu and S.M. Barr, Large neutrino mixing angles in unified theories, Phys. Lett. B 381 (1996) 202 [hep-ph/9511446] [INSPIRE].ADSGoogle Scholar
  5. [5]
    C.H. Albright and S.M. Barr, Fermion masses in SO(10) with a single adjoint Higgs field, Phys. Rev. D 58 (1998) 013002 [hep-ph/9712488] [INSPIRE].ADSGoogle Scholar
  6. [6]
    J. Sato and T. Yanagida, Large lepton mixing in a coset space family unification on E 7 /SU(5) × U(1)3, Phys. Lett. B 430 (1998) 127 [hep-ph/9710516] [INSPIRE].ADSGoogle Scholar
  7. [7]
    C.H. Albright, K. Babu and S.M. Barr, A minimality condition and atmospheric neutrino oscillations, Phys. Rev. Lett. 81 (1998) 1167 [hep-ph/9802314] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    N. Irges, S. Lavignac and P. Ramond, Predictions from an anomalous U(1) model of Yukawa hierarchies, Phys. Rev. D 58 (1998) 035003 [hep-ph/9802334] [INSPIRE].ADSGoogle Scholar
  9. [9]
    K.S. Babu, J.C. Pati and F. Wilczek, Fermion masses, neutrino oscillations, and proton decay in the light of Super-Kamiokande, Nucl. Phys. B 566 (2000) 33 [hep-ph/9812538] [INSPIRE].CrossRefGoogle Scholar
  10. [10]
    J. Sato and T. Yanagida, Low-energy predictions of lopsided family charges, Phys. Lett. B 493 (2000) 356 [hep-ph/0009205] [INSPIRE].ADSGoogle Scholar
  11. [11]
    T. Asaka, Lopsided mass matrices and leptogenesis in SO(10) GUT, Phys. Lett. B 562 (2003) 291 [hep-ph/0304124] [INSPIRE].ADSGoogle Scholar
  12. [12]
    X.-d. Ji, Y.-c. Li and R. Mohapatra, An SO(10) GUT model with lopsided mass matrix and neutrino mixing angle θ13, Phys. Lett. B 633 (2006) 755 [hep-ph/0510353] [INSPIRE].ADSGoogle Scholar
  13. [13]
    H. Georgi, Towards a grand unified theory of flavor, Nucl. Phys. B 156 (1979) 126 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    S.M. Barr, Light fermion mass hierarchy and grand unification, Phys. Rev. D 21 (1980) 1424 [INSPIRE].ADSGoogle Scholar
  15. [15]
    A.E. Nelson, Naturally weak CP-violation, Phys. Lett. B 136 (1984) 387 [INSPIRE].ADSGoogle Scholar
  16. [16]
    S.M. Barr, A natural class of non-Peccei-Quinn models, Phys. Rev. D 30 (1984) 1805 [INSPIRE].MathSciNetADSGoogle Scholar
  17. [17]
    S.M. Barr, Solving the strong CP problem without the Peccei-Quinn symmetry, Phys. Rev. Lett. 53 (1984) 329 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    K. Babu, J.C. Pati and H. Stremnitzer, Fermion masses and CP-violation in a model with scale unification, Phys. Rev. Lett. 67 (1991) 1688 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    K. Babu and J.C. Pati, The problems of unification mismatch and low α3 : a solution with light vector-like matter, Phys. Lett. B 384 (1996) 140 [hep-ph/9606215] [INSPIRE].ADSGoogle Scholar
  20. [20]
    K. Kannike, M. Raidal, D.M. Straub and A. Strumia, Anthropic solution to the magnetic muon anomaly: the charged see-saw, JHEP 02 (2012) 106 [Erratum ibid. 1210 (2012) 136] [arXiv:1111.2551] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    R. Dermisek, Insensitive unification of gauge couplings, Phys. Lett. B 713 (2012) 469 [arXiv:1204.6533] [INSPIRE].ADSGoogle Scholar
  22. [22]
    H. Georgi and S. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    S. Weinberg, Baryon- and lepton-nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566.ADSCrossRefGoogle Scholar
  24. [24]
    Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].ADSGoogle Scholar
  25. [25]
    G. 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
  26. [26]
    Z.-z. Xing, H. Zhang and S. Zhou, Updated values of running quark and lepton masses, Phys. Rev. D 77 (2008) 113016 [arXiv:0712.1419] [INSPIRE].ADSGoogle Scholar
  27. [27]
    C. Froggatt and H.B. Nielsen, Hierarchy of quark masses, Cabibbo angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Department of Physics and Astronomy and The Bartol Research InstituteUniversity of DelawareNewarkU.S.A

Personalised recommendations