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					Neutrino mixing angle θ13
In a SUSY SO(10) GUT

         Xiangdong Ji
        Peking University
      University of Maryland
   Outline
1. Neutrino (lepton) mixing
2. Why SUSY SO(10)?
3. A new SUSY SO(10) model
4. Looking ahead


X. Ji, Y. Li, R. Mohapatra, Phys. Lett. B633, 755 (2006) hep-ph/0510353
Neutrino (lepton) mixing
 Neutrinos, like quarks, have both masses and
  weak charges (flavor), and the mass
  eigenstates are not the same as the flavor
  eigenstates. One can write the neutrino of a
  definite flavor as



  Where U is the neutrino (or lepton) mixing matrix.
     Three flavors
      From the standard model, we know there are
       at least 3 neutrino flavor (e,μ,τ), therefore,
       there are at least three mass eigenstates.
      In the minimal case, we have 3-mixing angle
       (θ12 θ23 θ13) and 1(Dirac)+2(Majorana) CP-
       violating phases PNMS matrix
     e1 U e 2 U e 3 
     U
                    
U   1 U  2 U  3 
     U
                    
     U
      1 U 2 U 3 
  
   1    0           0   cos13         0 ei CP sin 13   cos12     sin 12   0 1     0            0        
                                                                                                            
  cos 23
   0             sin  23        0    1        0         sin 12   cos12    0 0 e i / 2        0        
                          i CP                                                                               
   sin  23
   0             cos 23  e sin 13   0    cos13   0
                                                                              0       1 0     0       e i / 2i   
What do we know?
 From past experiments, we know θ12 & θ23
  quite well
      Solar-ν mixing angle θ12
        Super-K, SNO, KamLand
        sin2 θ12 = 0.30 ±0.07
      Atmosphetic-ν mixing angle θ23
        Super-K, K2K,
        sin2 θ23 = 0.52 ±0.20
 There is an upper bound on θ13
     sin2 θ23 < 0.054 or sin2 2θ23 < 0.1 from Chooz exp.
Solar mixing angle
Current limit on θ13




                       Chooz
Why do we care about precision on θ13

 Three important questions in neutrino physics
    What is the neutrino mass hierarchy?
    Are neutrinos Dirac or Majorana particles?
    What is the CP violation in lepton sector?

 CP violation
   Important for understanding baryon genesis in the
    universe
   One of the major goals for neutrino superbeam
    expts.
   Is related to the size of θ13 (Jarlskog invariant)
Upcoming experiments
 Reactor neutrinos
     Double Chooz, <0.03     approved
     Daya Bay      <0.01?    US-China collaboration?
     Braidwood     <0.01      $100M




                                Pee e
                                Pe
                                           detector 1

                                                     detector 2
                                        nuclear reactor



 Neutrino superbeams
     Much more expensives                                 Distance (km)

      hundreds of Million $
Theories on neutrino mixing angles
 Top-down approach
  Assume a fundamental theory which
  accommodates the neutrino mixing and
  derive the mixing parameters from the
  constraints of the model.
 Bottom-up approach
  From experimental data, look for symmetry
  patterns and derive neutrino texture.
Why a GUT theory?
 Unifies the quarks and leptons, and treat the
  neutrinos in the same way as for the other
  elementary particles.
 A SO(10) GUT naturally contains a GUT
  scale mass for right-handed neutrinos and
  allows the sea-saw mechanism
               m  ~ mD 2 / m R
  Which explains why neutrino mass is so
   much smaller than other fermions!
SUSY SO(10) GUT
 There are two popular ways to break SUSY
  SO(10) to SU(5) to SM
   Low-dimensional Higgs
     16, 16-bar, 45, 10
    16s (break B-L symmetry) can be easily obtained
    from string theory
   High-dimensional Higgs
     126, 126-bar, 120, 10
      does not break R-parity (Z2), hence allows SUSY
    dark matter candidates.
      R = (-1)3(B-L)+2S
What can SUSY SO(10) GUTs achieve?

 SUSY GUT
   Stabilize weak scale & dark matter
   Coupling constant unification
   Delay proton decay

 Mass pattern for quarks and leptons
   Flavor mixing & CP violation
   Neutrino masses and mixing
   Mixing θ13
         126H large θ13   sin2 2θ13 ~ 0.16    (Mohapatra etal)
         16H small θ13     sin2 2θ13 < 0.01    (Albright, Barr)
Albright-Barr Model
 Fermions in 16-spinor rep.
  16 = 3 (up) + 3 (up-bar) + 3 (down) + 3 (down-bar) +
  1 (e) + 1 (e-bar) + 1(nu-L)
  + 1(nu-R)
  Assume 3-generations 16i (i=1,2,3)
 Mass term
    L  16 116110H 16216310H 45H
     16116216H16H '   '16116316H16H '   16216 H16316 H '
      For example, eta contribute the mass to the first family, up
       quark, down quark, electrons and electron neutrino
Mass matrices
 Dirac masses




 Majorana Masses   Lopsidedness
Diagonalization
 An arbitrary complex matrix can be
   diagonalized by two unitary matrices
        MD = L (m1, m2 m3)R+

 Majorana neutrino mass matrix is complex
   and symmetric, and can be diagonalized by
   a unitary matrix
         MM = U (m1, m2 m3)U*
CKM & lepton mixing
 The quark-mixing CKM matrix is almost
  diagonal
                 VCKM  L†U LD




 The lepton mixing matrix (large mixing)
      VPMNS  L† L L
Large solar mixing angle
 It can either be generated from lepton or
  neutrino or a combination of both.
    From lepton matrix,
    Babu and Barr, PLB525, 289 (2002)
     again very small sin2 2θ13 < 0.01
 If it is generated from neutrino mass matrix, it
  can come from either Dirac or Majorana mass
  or a mixture of both.
      In the Albright-Barr model, the large solar mixing
       comes from the Majorana mass.
            Fine tuning….
Lopsided mass matrix
 Generate the large atmospheric mixing angle
  from lepton mass matrix.
 Georgi-Jarlskog relation



 Why
A model (Ji,Li,Mohapatra)
 Assume the large solar mixing is generated
  from the neutrino Dirac mass and the
  Majorana mass term is simple




      The above mass terms can be generated from
      16, 16-bar & 45
What can the model predict ?
 In the non-neutrino sector, there are 10
  parameters, which can be determined by 3
  up-type, and 3-lepton masses, and 4 CKM
  parameters.
     3 down quark masses come out as predictions


 In the neutrino sector, we use solar mixing
  angle and mass ratios as input
     Prediction: right-handed neutrino spectrum
     Atmospheric mixing and θ13
Predictions
Looking ahead
 Leptogenesis
    Baryon number asymmetry cannot be generated
     at just the EW scale (CP violation too small)
    CP-violating decay of heavy majorana neutrino
     generates net lepton number L.
    The lepton number can be converted into B-
     number through sphaleron effects (B-L
     conserved.)
    Does model generates enough lepton number
     asymmetry?
Looking ahead
 Proton Decay
   Is the proton decay too fast?
     Dimension-5 operator from the exchange of
  charged Higgsino.

				
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posted:10/3/2012
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