Nonzero and Neutrino Masses from Modified Tribimaximal by pptfiles

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									    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 24th Rencontres de Blois, Chateaux, France, 27 May – 1
June 2012
Content:
ØIntroduction
ØNonzero      from the modified TBM
ØNeutrino masses from the modified TBM
ØConclusion
ØAcknowledgment
ØReferences
Introduction
ØWe have three well-known neutrino mixing
 matrices:
   § Tribimaximal (TBM)
   § Bimaximal (BM)
   § Democratic (DC)


ØRecently, from experimental results:
   §   MINOS [2]
   §   Double Chooz [3]
   §   T2K [4]
   §   Daya Bay [5]
ØIn 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
ØDue to the fact that       , Ishimori and Ma
 have a conclusion that the TBM may be dead
 or ruled out [1].
ØWe 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       from modified TBM

 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:
                                                                      (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             can be derived from discrete
symmetry such as A4.
 Mixing angle   from experimental results:
  T2K:
    NH :
    IH :
  Daya Bay:



    RENO:


 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:
                                                           (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)
 and
                                         (18
  )

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

								
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