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Transcript of KITPC Program on Neutrino Physics 2008.9.1-9.21 Nearly Tri-bimaximal Mixing & Small Masses of...
![Page 1: KITPC Program on Neutrino Physics 2008.9.1-9.21 Nearly Tri-bimaximal Mixing & Small Masses of Neutrinos Yue-Liang Wu Kavli Institute for Theoretical Physics.](https://reader036.fdocuments.in/reader036/viewer/2022062301/56649ebb5503460f94bc2df7/html5/thumbnails/1.jpg)
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
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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
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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
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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?
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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 ?
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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
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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
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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
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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 :
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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
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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
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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
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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:
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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
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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:
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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
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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).
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SO(3) Gauge Model
Exact Discrete symmetry
Tri-bimaximal with 13 = 0
Experimental Data (99%)
Gauge Symmetry has been well tested
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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
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Uniqueness of Lagrangian & New Particles
Symmetry
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SO(3) Expression of Tri-triplet Higgs Bosons
In terms of SO(3) representation:
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Symmetry as Subgroup of SO(3) Discrete symmetric group:
Cyclic permutation group: Coset space :
Cyclic permuted form:
with i+j-1 mod. 3
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Why Local SO(3) Symmetry Fixing Gauge: invariant Lagrangian
In terms of SO(3) Representation
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Vacuum StructureWith the given fixing gauge:
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Type-II like (generalized) see-saw mechanism
For neutrinos: For charged leptons:
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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 ???
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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 !!!
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Nearly Tri-bimaximal neutrino mixings Neutrino and charged lepton mixings:
≈
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Lepton Mixing Matrix and Neutrino Masses
CKM-like Lepton mixing:
Neutrino Masses
Heavy Majorana Masses
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Numerical Results 4 Parameters: / / Two inputs:
Neutrino masses with given parameter
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Considering the hierarchy: One parameter in Vacuum:
Interesting case:
Two cases for charged lepton mixing:
13
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Numerical results for given parameter
13
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Taking
Optimistic Predictions
Which can be detected by the future neutrino Experiments, like Daya Bay
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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
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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
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THANKSTHANKS