1. SU(3) Gauge Family Model for Neutrino Mixing and Masses
Yue-Liang Wu
Kavli Institute for Theoretical Physics China (KITPC)
State Key Laboratory of Theoretical Physics (SKLTP)
ITP-CAS
University of Chinese Academy of Sciences (UCAS)

2. 82 Years Old Neutrino
1930 Pauli (30 years old)：
Neutrino with s=1/2、NWIP、m < m_e
To solve energy conservation problem and spin- statistical problem involved in  decay
1933 Fermi: H_3  He_3 + e + anti-  (Tritium decay)
1957 T.D.Lee & C.N.Yang: Parity Non-conservation (NP)
C.S. Wu： Experimental Test
1957 Landau, Lee & Yang, Salam
Two Component Theory of Massless Neutrino m_ =0, Maximal Parity Violation
1958 Feynman-Gell-Mann, Marshak-Sudarshan
V-A Theory
1967 GWS Standard Model： SU(2)_L x U(1) (NP)
Based on Massless Neutrinos

3. 1957 Pontecorvo
Massive neutrinos、Neutrino Mixing & Oscillations
_e  anti-_e
1957 R.Davis: Reactor Experiment
anti-  + Cl_37  e + Ar_37
1962 Lederman, Schwartz & Steinberge
Observed _ at Brookhaven (NP)
1962 MNS – Maki-Nakagawa-Sakata
Lepton Mixing Angle: 
1967 R. Davis
Solar Neutrino Experiment (NP)
Solar Neutrino missing puzzle

4. Solar Neutrino Puzzle: ½ 1969 Gribov & Pontecorvo
1967 Pontecorvo _e  _
Solar Neutrino Puzzle: ½
1969 Gribov & Pontecorvo
Majorana-type Neutrino Mixing
1976 Bilenky & Pontecorvo
Dirac-type Neutrino Mixing
1978 L. Wolfenstein; S.P. Mikheyev and A. Yu. Smirnov
Matter Effects of Neutrino Oscillations (MSW)
See-Saw Mechanism & GUTs
1994： ‘1，3，5 ’ － Massive，
‘ 2，4，6 ’ －Massless， 7 － No think
Super-Kamiokande Experiment
Evidence of Massive Neutrinos &
Neutrino Oscillations
Answer Question: Massive or Massless?

5. 1998-2011 more experiments for mixing angles & mass-square differences
Solar Neutrino: SNO，Super-K
Atmosphere Neutrino: Super-K
Reactor Neutrino: KamLAND， CHOOZ
Accelerator: K2K，MINOS，T2K
2012 more precise measurement for
Reactor Neutrino: Daya Bay
RENO

6. Neutrino Oscillation General Formalism：
Experimental Data （Global Fitting)
G. L. Fogli, E. Lisi, A. Marrone, A. Palazzo and A. M. Rotunno, arXiv:
Schwetz, M. Tortola, J. W. F. Valle, New J. Phys., 13, (2011),

7. Progresses 2012 Daya Bay Experiment: RENO Experimental
F. P. An et al. [DAYA-BAY Collaboration], PRL 108, (2012), arXiv:
RENO Experimental
PRL 108, (2012) , arXiv:
Double Chooz Experimental
Y. Abe et al. [Double Chooz Collaboration], PRL 108, (2012) , arXiv:

8. Theoretical Prediction Based on:
SU(3) gauge symmetry and Z_2 symmetry + ~ U(1)
Theoretical Prediction:
SU(3) gauge symmetry and Z_2 symmetry, ~ U(1)
YLWu, Physics Letters B 714 (2012) 286–294, arXiv:
Maximal CP violation:
Nearly Maximal 2-3 mixing

9. Unknown Questions:  Neutrinos are Dirac or Majorana？
 Absolute Values of Neutrino Masses？
Hierarchy or largely Degeneracy？
 CP Violation in Lepton-Neutrino Sector？
 How Many Neutrinos，Sterile Neutrinos？
 Leptogenesis and Matter-Antimatter Asymmetry？
 Rules of Neutrino in Astrophysics and Cosmology ?

10. Other Theoretical Questions
 Why neutrino masses are so small
 Mass hierarchy m312 > 0 ？ m312 < 0 ？
 Why neutrino mixings are so large in comparison with quark mixings
 Possible relation between CKM & MNSP
 Family Symmetry?

11. Issues in Neutrino Physics
1. Dirac / Majorana
Neutrinoless Double Beta Decay
2. Mass scale: m
Neutrinoless Double Beta Decay,
Single Beta Decay, Cosmology
1. Cosmology (CMB+LSS):
Planck: eV
2. Single Beta Decay
KATRIN: 0.2 eV
CUORE: eV
3. Neutrinoless Double Beta Decay HD
Cuoricini
NEMO3
Bilenky, Giunti, arXiv: v3 [hep-ph]

12. Seesaw Mechanism  N  Leptogenesis Mechanism
Fukugita & Yanagida (1986):

13. Family Symmetry Exact Discrete symmetry 
Tri-Bimaximal Mixing:
(Harrison,Perkins and Scott)
Exact Discrete symmetry 
Tri-bimaximal mixing with 13 = 0
Based SO(3) gauge family symmetry :
( YLWu, 2008 PRD)

17. SU(3) Gauge Family Model
YLWu, Physics Letters B 714 (2012) 286–294, arXiv:
Gauge Symmetry has been well tested
Why lepton sector is so different from quark sector ?
Neutrinos are neutral fermions and can be Majorana!
Invariant Lagrangian for Yukawa Interactions

18. Why Local SU(3) Family Symmetry
In terms of SU(3) representation with Z_2 symmetry (2--3):
Fixing gauge :
Z_2 symmetry invariant Lagrangian

19. SU(3) Expression of Tri-triplet Higgs Bosons
In terms of SU(3) Representation
Vacuum Structure

20. Standard Sea-saw Mechanism
Neutrino Mass:
Charged-lepton Mass :

21. Global U(1) Family Symmetries
For Infinite Large Majorana neutrino masses
Majorana neutrinos decouple
Generating global U(1) family symmetries
U(1)_1 x U(1)_2 x U(1)_3
Large but Finite Majorana Neutrino Masses
M_N >> v

22. Small Mass and Large Mixing of Neutrinos
Approximate global U(1) family symmetries
Smallness of neutrino masses and charged lepton mixing
Neutrino mixings could be large !!!

23. Approximate Global U(1) Family Symmetries
~ U(1)_1 x U(1)_2 x U(1)_3 ~
Exact Tri-bimaximal
Neutrino Mixing

24. Lepton Mixing Matrix and CP Violation

25. Lepton Mixing Matrix and CP Violation

26. Lepton Mixing Matrix and CP Violation
Agree to the experimental
data within the errors
Maximal CP Violation and CP-invariant Quantity 最大CP破坏位相与CP 破坏不变量

27. Lepton Mixing Matrix and CP Violation
/ ~ 0
Fit to recent global analyses:
G. L. Fogli, E. Lisi, A. Marrone, D. Montanino, A. Palazzo, and A. M. Rotunno, Phys. Rev. D 86 (2012)
symmetry between 1 & (W.Z.Guo & M.Li )
It needs to consider the next-to-leading order and next-to-next-leading order corrections from charged lepton sector to fit the experimental data with a CP-violating phase δ ~ π

28. Neutrino Masses 中微子质量
Neutrino Masses
Heavy Majorana Masses

29. Neutrino Masses 中微子质量 Two inputs: with given parameter and
Normal spectrum 中微子质量的正常排序
Inverse Spectrum 中微子质量的反常排序
Total Mass
中微子总质量
Neutrino cosmology 中微子宇宙学

30. Summary
SU(3) gauge family symmetry is a natural motivation from three families of quarks/leptons
Smallness of neutrino masses and charged-lepton mixing is understandable from approximate global U(1) family symmetries with standard see-saw mechanism.
Tri-bimaximal mixing in the neutrino sector is a consequence of Z_2 symmetry of the vacuum structure of SU(3) gauge family symmetry
Nonzero 13 arises from the small mixing of charged-lepton and is related to the Cabibbo angle of CKM quark mixing with a prediction consistent with experiments

31. Summary
CP violation in lepton sector can be maximal and testable when 2-3 mixing is nearly maximal
CP violation in lepton sector could be minimal and untestable for a non-maximal 2-3 mixing
Necessary for a more precise measurement on
&
The neutrino masses are largely degenerate and testable from next generation experiments & cosmology

32. THANKS