KITPC Program on Neutrino Physics 2008.9.1-9.21

Nearly Tri-bimaximal Mixing

& Small Masses of Neutrinos

Yue-Liang WuKavli Institute for Theoretical Physics China

(KITPC)

Institute of Theoretical Physics

Chinese Academy of Sciences

78 Years Old Neutrino1930 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- 1957 T.D.Lee & C.N.Yang: Parity Non-conservation (NP) C.S. Wu ： Experimental Test1957 Landau, Lee & Yang, Salam Two Component Theory of Massless Neutrino m_ =0,

Maximal Parity Violation1958 Feynman-Gell-Mann, Marshak-Sudarshan V-A Theory1967 GWS Standard Model ： SU(2)_L x U(1) (NP) Based on Massless Neutrinos

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 Pontecorvo

_e _

Solar Neutrino Puzzle: ½

1967 R. Davis Solar Neutrino Experiment (NP) 1969 Gribov & Pontecorvo Majorana-type Neutrino Mixing 1976 Bilenky & Pontecorvo Dirac-type Neutrino Mixing 1978 L. Wolfenstein; 1986 S.P. Mikheyev and A. Yu.

Smirnov Matter Effects of Neutrino Oscillations (MSW) 1979 See-Saw Mechanism & GUTs 1994 ： ‘ 1 ， 3 ， 5 ’ － Massive ， ‘ 2 ， 4 ， 6 ’ － Massless ， 7 － No think 1998.6 Super-Kamiokande Experiment Evidence of Massive Neutrinos & Neutrino Oscillations

Answer Question: Massive or Massless?

Unknown Questions:

Neutrinos are Dirac or Majorana？

Absolute Values of Neutrino Masses？ Hierarchy or Degeneracy？

CP Violation in Lepton-Neutrino Sector？

How Many Neutrinos， Sterile Neutrinos？

Leptogenesis and Matter-Antimatter Asymmetry？

Rules of Neutrino in Astrophysics and Cosmology ?

Theoretical Questions

Why neutrino masses are so small

Why neutrino mixings are so large in comparison with quark mixings

23 is exactly maximal ？

13 ? ， Ue3 0 ？

Mass hierarchy m312 > 0 ？ m31

2 < 0 ？

7 13~ 10 ~ 10e tm m m

1.01 6 2 1SSM 0.81

0.44 0.46 6 2 1SNO 0.43 0.43

Measured flux agrees with SSM

5.05 10 cm s

5.09 10 cm s

：

Flavor changing at 5.3

arXiv:nucl-ex/0610020

Electron neutrino generated from Sun

Solar Neutrino: SNOe

Oscillation parameters ：2 0.10 0.10

sun 0.07 0.06

2 0.14 0.15 5 2sun 0.13 0.15

tan 0.56 (stat) (syst)

7.58 (stat) (syst) 10 eVm

arXiv:0801.4589

A scaled reactor spectrum without distortions from neutrino oscillationis excluded at more than 5σ!

Reactor neutrino: KamLAND

Cosmic-rayshower

0+

+

e

e+

Underground e,e,,

detector

Atmospheric neutrino source

+ + + e+ + e +

– – + e– + e +

~30 kilometers

θz

232atm

23

atm2

eV 104.3eV 105.1

12sin92.0

m

Atmosphere Neutrino: Super-K

Oscillation parameters ：

iα ii

U

3

1

J. Valle et al. hep-ph/0405172, updated at Sep 2007

13 13 23 23

12 12 23 23

12 12 13 13

1 0 0 0 0 0 0

0 . 0 1 0 . 0 . 0 0

0 0 0 0 1 0 0 1

i i

iMNS

i

c s e c s e

U c s s c e

s c s e c

Solar ： Super-K, SNOAtmosphere ： Super-KReactor:KamLAND, CHOOZAccelerator:K2K ， MINOS

2

:

Mixing Angel

Mass Difference m

：Osci l l at i on parameters：

General Formalism ：Neutrino Oscillation

1. Dirac / Majorana Neutrinoless Double Beta Decay

2. Mass scale: m1

Neutrinoless Double Beta Decay, Single Beta Decay, Cosmology

3. Sterile neutrinos, LSND?

Excludes at 98% CL two-neutrino appearance oscillations as an explanation of the LSND anomaly. arXiv:0704.1500

MiniBooNE

(3+1): inconsistency at the level of 4σ. (3+2) ,(3+3): severe tension at the level of more than 3σ. arXiv:0705.0107

Issues in Neutrino Physics

2. Single Beta Decay

3. Neutrinoless Double Beta Decay

1. Cosmology (CMB+LSS):

0.61 eV (95% C.L.) WMAP 5 yearsim

i

ieiemUm )( 22

Troitsk eV2.2

Mainz eV3.2

e

e

m

m

|| 233

222

211 eeeee

UmUmUmm (0.35 1.24) eV (HM)

(0.33 1.35) eV (IGEX)ee

ee

m

m

Planck: 0.025-0.1 eV

KATRIN: 0.2 eV

CUORE: 0.02-0.1 eV

Strumia-Vissani arXiv:hep-ph/0503246

Neutrino Masses

3σ

arXiv:hep-ex/0509019

13

213

Daya Bay (90%CL)

Sin 2 0.01

Kam-Biu Luk, Jan 8 2007Int'l Symp on Neutrino Physics and Neutrino Cosmology

2 213 13Sin 0.050 Sin 2 0.19

Global fits:

N

h.c.nMM

Mn

h.c.NMNNML

LR

TD

DcL

RRcRRDLY

0

2

1

2

1

R

cL

LN

n

TD

1RD MMMM v

Fukugita & Yanagida (1986):Leptogenesis Mechanism

Type II? Type III?

Seesaw Mechanism

2(2) (1)L YSU U Z

0 ( ) / 2S iA

S or A may be Dark Matter!R. Barbieri, L. Hall and V.S. Rychkov, PRD 74, 015007, 2007

E. Ma, PRD 73, 077301, 2006

3 loop generation of neutrino masses: L.M. Krauss, S. Nasri and M. Trodden,

PRD 67, 085002, 2003

Right-handed neutrino as Dark Matter!

Other Mechanism for Neutrino MassesTwo Higgs doublets Model:

Tri-Bimaximal Mixing:

12 23 13

3 2Sin ;Sin ;Sin 0

3 2

6 30

3 3

6 3 2

6 3 2

6 3 2

6 3 2

MNSU

(Harrison,Perkins and Scott)

2 4, , (3)...Z A SO

Friedberg-Lee Symmetry:

Invariant under Friedberg-Lee symmetry: hep-ph/0606071

z a space-time independent constant element of the Grassmann algebra

Some papers：Xing, Zhang, Zhou, PLB641Luo, Xing, PLB 646C.S. Huang, T.J. Li, W. Liao and S.H. Zhu, arXiv:0803.4124

Family Symmetry

F. Harrison, D. H. Perkins and W. G. Scott, Phys. Lett. {\bf B 530}, 167 (2002) Z.-Z. Xing, Phys. Lett. {\bf B533}, 85(2002). P. F. Harrison and W.G. Scott, Phys. Lett. {\bf B535},163(2002). P.F. Harrison and W. G. Scott, Phys. Lett. {\bf B557},76(2003). X. G. He and A. Zee, Phys. Lett. {\bf B560}, 87(2003). C.I. Low and R. R. Volkas, Phys. Rev. {\bf D68}, 033007 (2003). E. Ma, Phys. Rev. {\bf D70}, 031901R(2004); E.Ma, hep-ph/0701016 G. Altarelli and F. Feruglio, Nucl. Phys. {\bf B720}, 64(2005); E. Ma, Phys. Rev. D72, 037301 (2005).; E. Ma, Mod.\ Phys.\ Lett.\ A 20, 2601 (2005) A. Zee, Phys. Lett. {\bf B630}, 58 (2005). E. Ma, Phys.\ Rev.\ D {\bf 73}, 057304 (2006). G. Altarelli and F. Feruglio, Nucl. Phys. {\bf B741}, 215(2006). W. Grimus and L. Lavoura, {\bf JHEP}, 0601:018(2006). J.E. Kim and J.-C. Park, {\bf JHEP} 0605:017(2006). N. Singh, M. Rajkhowa and A. Borach, hep-ph/0603189. R. Mohapatra, S. Naris and Y.-H. Yu, Phys.Lett. {\bf B639} 318 (2006). P. Kovtun and A. Zee, Phys.Lett. {\bf B640} (2006) 37. N. Haba, A. Watanabe and K. Yoshioka, Phys.Rev.Lett. 97 (2006) 041601. X.G. He, Y.Y. Keum and R. Volkas, {\bf JHEP}, 0604:039(2006). Varizelas, S.-F. King and G.G. Ross, Phys.Lett. B644 (2007) 153. R. Friedberg and T. D. Lee, arXiv:hep-ph/0606071; arXiv:hep-ph/0705.4156 B.Hu, F. Wu and Y.L. Wu, Phys.Rev. {\bf D75} 113003 (2007).

SO(3) Gauge Model

Exact Discrete symmetry

Tri-bimaximal with 13 = 0

Experimental Data (99%)

Gauge Symmetry has been well tested

Why SO(3) Gauge Model? YLW arXiv:0708.0867, PRD 2008

Why lepton sector is so different from quark sector ?

Neutrinos are neutral fermions and can be Majorana!

Majorana fermions only have real representations

They possess orthogonal symmetry Invariant Lagrangian for

Yukawa Interactions

Uniqueness of Lagrangian & New Particles

Symmetry

SO(3) Expression of Tri-triplet Higgs Bosons

In terms of SO(3) representation:

Symmetry as Subgroup of SO(3) Discrete symmetric group:

Cyclic permutation group: Coset space :

Cyclic permuted form:

with i+j-1 mod. 3

Why Local SO(3) Symmetry Fixing Gauge: invariant Lagrangian

In terms of SO(3) Representation

Vacuum StructureWith the given fixing gauge:

Type-II like (generalized) see-saw mechanism

For neutrinos: For charged leptons:

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 ???

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 !!!

Nearly Tri-bimaximal neutrino mixings Neutrino and charged lepton mixings:

≈

Lepton Mixing Matrix and Neutrino Masses

CKM-like Lepton mixing:

Neutrino Masses

Heavy Majorana Masses

Numerical Results 4 Parameters: / / Two inputs:

Neutrino masses with given parameter

Considering the hierarchy: One parameter in Vacuum:

Interesting case:

Two cases for charged lepton mixing:

13

Numerical results for given parameter

13

Taking

Optimistic Predictions

Which can be detected by the future neutrino Experiments, like Daya Bay

Vector-Like Heavy Neutrino and Charged Lepton Masses

Taking and

It leads to and

Taking

The lightest vector-like charged lepton mass

Which may be detected at LHC/ILC

Summary Smallness of neutrino masses and charged lepton

mixing could be understood from approximate global U(1) family symmetries

Tri-bimaxiaml neutrino mixing is obtainable from the vacuum structure of SO(3) gauge symmetry

13 is in general non-zero and testable at the

experimental sensitivity Some of the vector-like fermions could have

masses at electroweak scale and be probed at LHC The mechanism can simply be extended to quark

sector for smallness of quark mixing

THANKSTHANKS