Nonzero and Neutrino Masses from Modified Tribimaximal Neutrino

Nonzero and Neutrino Masses from Modified Tribimaximal Neutrino Mixing Matrix Asan Damanik Faculty of Science and Technology Sanata Dharma University Yogyakarta, Indonesia e-mail: d. asan@lycos. com Presented at 24 th Rencontres de Blois, Chateaux, France, 27 May – 1 June 2012

Content: Ø Introduction Ø Nonzero from the modified TBM Ø Neutrino masses from the modified TBM Ø Conclusion Ø Acknowledgment Ø References

Introduction Ø We have three well-known neutrino mixing matrices: § Tribimaximal (TBM) § Bimaximal (BM) § Democratic (DC) Ø Recently, § § from experimental results: MINOS [2] Double Chooz [3] T 2 K [4] Daya Bay [5]

Ø In this talk, only TBM to be considered because TBM have got much attention for long time due to its predictions on neutrino mass spectrum, some phenomenological consequences, and its underlying symmetries Ø Due to the fact that , Ishimori and Ma have a conclusion that the TBM may be dead or ruled out [1]. Ø We modified TBM by introducing a simple perturbation matrix, such that modified TBM can give nonzero and it also can correctly predict neutrino mass spectrum our motivations

Nonzero � Neutrino from modified TBM mixing matrix existence based on the experimental facts: mixing flavor in neutrino sector does exist like quark sector � Mixing matrix, flavor eigenstates basis, mass eigentates basis related by: where:

(10) where. There are three kinds of neutrino mixing matrix, one of them is the tribimaximal mixing read [8 -13]: (11) which lead to. The symmetry such as A 4. can be derived from discrete

� Mixing angle T 2 K: NH : IH : Daya Bay: RENO: � from experimental results:

� There also some modification performed to TBM, in this talk I use simple modification to TBM by introducing a simple perturbation matrix into TBM: (12) where the perturbation matrix is given by: (13) where . Using Eqs. (11), (12), (13) we then have the modified TBM as follow:

(14) By comparing (14) to (10) we have: (15) If experimental data is used to fix the value of -15]: then we have: , that is [14 (16) (17)

� and (18) � � this value give: � � which implies that: � � which data. in agreement with the experimental (19) (20)

Neutrino Masses from the Modified Tribimaximal Mixing Matrix � We construct a neutrino mass matrix as follow: (21) � � After perform some calculations, we then have the neutrino mass matrix pattern as follow: (22) � � To simplify the problem we impose texture zero into (22) as follow:

� This is the only texture zero can gives correctly the neutrino mass spectrum that is normal hierarchy: � (23) � If we use the solar neutrino squared-mass difference to fit the values of neutrino mass, then we have the neutrino mass that cannot give correctly the atmospheric neutrino squared-mass difference or conversely �

Conclusion � By introducing a simple perturbation neutrino mass matrix into TBM we can have a modified neutrino mixing matrix that can gives nonzero mixing angle � The predicted value of which is in agreement with the present experimental values. � Imposing texture zero into neutrino mass matrix and if we use the squared-mass difference of solar neutrino, then we cannot have the correct value of squared-mass difference for atmospheric neutrino, or conversely. � The hierarchy of neutrino mass is normal hierarchy in this scenario.

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� [11] Z-z. Xing, Phys. Lett. B 533, 85 (2002). � [12] P. F. Harrison and W. G. Scott, Phys. Lett. B 535, 163 (2002). � [13] P. F. Harrison and W. G. Scott, Phys. Lett. B 557, 76 (2003). � [14] X. -G. He and A. Zee, Phys. Lett. B 560, 87 (2003). � [15] M. Gonzales-Carcia, M. Maltoni and J. Salvado, ar. Xiv: 1001. 4524 [hep-ph]. � [16] G. Fogli et al. , J. Phys. Con. Ser. 203, 012103 (2010). � [17] A. Damanik, M. Satriawan, Muslim, and P. Anggraita, ar. Xiv: 0705. 3290 v 4 [hep-ph]. � [18] H. fritzsch, Z-z. Xing, and S. Zhou, JHEP 1109, 083 (2011), ar. Xiv: 1108. 4534 [hep-ph].

�I thank you for your attention!!!