Nonzero and Neutrino Masses from Modified Tribimaximal Neutrino

Mixing Matrix

Asan DamanikFaculty of Science and Technology

Sanata Dharma UniversityYogyakarta, Indonesia

e-mail: d.asan@lycos.com

13

Presented at 24th Rencontres de Blois, Chateaux, France, 27 May – 1 June 2012

Introduction Nonzero from the modified TBM Neutrino masses from the modified TBM Conclusion Acknowledgment References

Content:

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We have three well-known neutrino mixing matrices:

Tribimaximal (TBM) Bimaximal (BM) Democratic (DC)

Recently, from experimental results: MINOS [2] Double Chooz [3] T2K [4] Daya Bay [5]

Introduction

013

013

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

Due to the fact that , Ishimori and Ma have a conclusion that the TBM may be dead or ruled out [1].

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

013

013

Neutrino 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:

Nonzero from modified TBM13

3

2

1

Ve

13232312231223122312

13232312231223122312

*13121312

cczcssczccss

cszsscczsccs

zcscc

V

where . There are three kinds of neutrino mixing matrix, one of them is the tribimaximal mixing read [8 -13]:

(11)

21

31

61

21

31

61

31

32 0

TBMV

iesz 13

which lead to . The can be derived from discrete symmetry such as A4.

013 TBMV

(10)

Mixing angle from experimental results:T2K:

NH : IH : Daya Bay:

RENO:

13

(syst.) 005.0 (stat.) 016.0092.02sin 132

oo 0.160.5 13 oo 8.178.5 13

(syst.) 014.0 (stat.) 013.0113.02sin 132

There are 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:

yTBMTBM VVV '

yV

yy

yyy

cs

scV

0

0

001

ysyc yy sin,cos

yyyy

yyyy

yy

TBM

cssc

cssc

sc

V

22

33

22

33

66

22

33

22

33

66

33

33

36

' (14)

By comparing (14) to (10) we have:

(15)

If experimental data is used to fix the value of , that is [14-15]: (16)

then we have: (17)

ycs

cs

y scyy

yy

33

132322

12 sin,tan,tan22

33

22

33

and/or yy sc

023

012 8.42,5.34

, use when we031676300.0 23yc

and (18)

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

12 use when we9713265692.0 yc

013 137265.0sin

013 89.7

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:

Neutrino Masses from the Modified Tribimaximal Mixing Matrix

TTBMTBMMVVM ''

FEC

EDB

CBA

M

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

,01311 MM

321 mmm

221m

232m

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.

Conclusion

130

13 89.7

[1] H. Ishimori and E. Ma, arXiv:1205.0075v1 [hep-ph]. [2] MINOS Collab. (P. Adamson et. al., Phys. Rev. Lett.

107, 181802 (2011),[arXiv:1108.0015]. [3] CHOOZ Collab. (M. Apollonio al.),Phys. Lett. B466,

415 (1999). [4] T2K Collab. (K. Abe et al.), arXiv:1106.2822 [hep-ph]. [5] F. P. An et al., arXiv:1203.1669v2 [hep-ex]. [6] RENO Collab. (J. K. Ahn et al.), arXiv: 1204.0626v2

[hep-ex]. [7] X-G. He and A. Zee, arXiv:1106.4359v4 [hep-ph]. [8] A. Damanik, arXiv:1201.2747v4 [hep-ph]. [9] P. F. Harrison, D. H. Perkins, and W. G. Scott, Phys.

Lett. B458, 79 (1999). [10] P. F. Harrison, D. H. Perkins, and W. G. Scott, Phys.

Lett. B530, 167 (2002).

References

[11] Z-z. Xing, Phys. Lett. B533, 85 (2002). [12] P. F. Harrison and W. G. Scott, Phys. Lett. B535, 163

(2002). [13] P. F. Harrison and W. G. Scott, Phys. Lett. B557, 76

(2003). [14] X.-G. He and A. Zee, Phys. Lett. B560, 87 (2003). [15] M. Gonzales-Carcia, M. Maltoni and J. Salvado,

arXiv: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,

arXiv:0705.3290v4 [hep-ph]. [18] H. fritzsch, Z-z. Xing, and S. Zhou, JHEP 1109, 083

(2011), arXiv:1108.4534 [hep-ph].

I thank you for your attention!!!