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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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