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Exploring Non-degenerate Majorana Neutrinos

This paper discusses the Fukugita-Tanimoto-Yanagida ansatz with partially non-degenerate right-handed Majorana neutrinos and its impact on neutrino observables. The Fritzsch texture for lepton mass matrices is used, and a numerical analysis is performed to determine the allowed parameter ranges. The results show that the maximal atmospheric neutrino mixing angle can only be achieved in certain cases, while the small mixing angle has a lower bound. The study emphasizes the importance of considering the deviation from mass degeneracy in future experiments.

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Exploring Non-degenerate Majorana Neutrinos

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  1. On the Fukugita-Tanimoto-Yanagida Ansatzwith Partially Non-degenerateRight-handed Majorana Neutrinos 29October, 2006 High Energy Physics Meeting@Guilin IHEP Midori Obara (小原 绿) M. O. and Z.Z. Xing, hep-ph/0608280

  2. §1. Introduction Recent neutrino experimental results (at 99% C.L.) Mixing angles Mass-squared differences Neutrinos have two large mixing angles and one small mixing angle. Cosmological bound on neutrino masses Neutrinos have very small masses.

  3. Why are neutrino masses so small? Seesaw Mechanism Variousphenomenological ansatz for lepton mass matrices have been actively studied. “Texture zeros” An empirical relation S. Weinberg (1977), H. Fritzsch (1977), F. Wilczek and A. Zee (1977) R. Gatto, G. Sartori and M. Tonin (1968), N. Cabibbo and Maiani (1968), R.J. Oakes (1969) Fritzsch texture for lepton mass matrices Z.Z. Xing (2002)

  4. Within the seesaw framework ... M. Fukugita. M. Tanimoto and T. Yanagida (2003) Fukugita-Tanimoto-Yanagida (FTY) ansatz with In this work We generalize the FTY ansatz by allowing the masses of to be partially non-degenerate and examined how thedeviation from the mass degeneracy can affectthe neutrino observables. (A) (B) (C)

  5. Contents §1. Introduction §2. Model §3. Numerical Analysis §4. Summary

  6. §2. Model

  7. We take the Fritzsch texture for and . can be decomposed by diagonal phase matrix as where Similarly, where

  8. is given as follows: Here we assume

  9. Mass splitting parameter where (A) (B) (C)

  10. where where we have neglected the terms of and by assuming and .

  11. where and with Parametrization

  12. §3. Numerical Analysis

  13. We have seven parameters in our model: These parameters are constrained by the neutrino experimental results. Results In the case of (the FTY case) Predicted values

  14. In the case of In the case of The differences of parameter regions between and cases can be distinguishable in . We show the allowed range for the parameters at the typical value of in the three cases. (A) (B) (C)

  15. (A)

  16. (B)

  17. (C)

  18. Typical results at Experimental upper bounds:

  19. Remarks ・The maximal atmospheric neutrino mixing anglecan only be achieved in the cases B and C. + + ・In all cases, is not well restricted. ・The smallest mixing angle has an lower bound in each case. In future experiments ・In all cases, the allowed range for is roughly the same. could be measured in the future long-baseline neutrino experiments.

  20. §4. Summary We have generalized the FTY ansatz by allowing the masses of to be partially non-degenerate and examined how thedeviation from the mass degeneracy can affectthe neutrino observables. (A) (B) (C) The dependence of mixing angles on The case C is the most sensitive to the effect of the deviation from the mass degeneracy.

  21. Future work ・ Including the complex phases into and/or . Leptogenesis

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