Transcript Seesaw Realization of Bi－Large Mixing and Leptogenesis

Quark and Lepton Mixing
in S4 Flavor Model
September 28, 2010
Max-Planck-Institut für Kernphysik
Heidelberg, Germany
Morimitsu Tanimoto (Niigata University)
with H. Ishimori and Y. Shimizu
1
Niigata
↓
2
Niigata City
Population: 811,996
Niigata City is an urban center developed by its port.
Even though it is located on a substantial expansion
of agricultural landscapes, it has also easy accesses
to major cities by airplanes, express omnibuses, and
bullet trains. Also from its international airport, there
are regular flights to Harbin, Shanghai, Seoul,
Vladivostok , Khabarovsk, Guam. Niigata aspires to
be a gateway to the East Asia.
NiigataUniversity
University
Niigata
Plan
of my talk
1 Tri-bi maximal mixing and Flavor Symmetry
2 S4 Flavor Model in Quarks and Leptons
3 S4 Flavor Model in Sleptons
4 Summary
4
1 Tri-bimaximal mixing and Flavor symmetry
Recent experiments of the neutrino oscillations go into a new phase
of precise determination of mixing angles and mass squared differences.
Three Flavor analysis strongly suggests
Tri-bimaximal Mixing of Neutrinos
Harrison, Perkins, Scott (2002)
indicates Non-Abelian Flavor Symmetry ? 5
Consider the structure of Neutrino Mass Matrix,
which gives Tri-bi maximal mixing
Mixing angles are independent of mass eigenvalues
Different from quark mixing angles
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Quark Sector
7
Let us consider Flavor Symmetry.
8
×
Need some ideas to realize Tri-bi maximal mixing by S3
flavor symmetry
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A4 Symmetry may be hidden.
triplet (νe ,νμ,ντ)L
○
3L×3L×3H
3L×3L
A4 should be broken !
T’ , S4 , Δ(54) flavor models also give Tri-bi maximal mixing !
Δ（27）, Δ（54）, Σ（81）
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Origin of the non-Abelian Flavor symmetry ?
Tri-bimaximal neutrino mixing from orbifolding,
G.Altarelli, F.Feruglio, Y.Lin, NPB775, 31 (2007) hep-ph/0610165
Stringy origin of non-Abelian discrete flavor symmetries
T. Kobayashi, H. Niles, F. Ploeger, S. Raby, M. Ratz, NPB768,135(2007) hep-ph/0611020
Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting
Brane Models
H. Abe, K-S. Choi, T. Kobayashi, H. Ohki, NPB820, 317 (2009) , 0904.2631
Non-Abelian Discrete Flavor Symmetry from T2/ZN Orbifolds
A.Adulpravitchai, A. Blum, M. Lindner, JHEP0907, 053 (2009), 0906.0468
Non-Abelian Discrete Groups from the Breaking of Continuous
Flavor Symmetries
A.Adulpravitchai, A. Blum, M. Lindner, JHEP0909, 018 (2009), 0907.2332
Reference
Non-Abelian Discrete Symmetries in Particle Physics
Hajime Ishimori, Tatsuo Kobayashi, Hiroshi Ohki,
Hiroshi Okada, Yusuke Shimizu, Morimitsu Tanimoto,
e-Print: arXiv:1003.3552 [hep-th]
Prog.Theor.Phys.Suppl.183:1-163,2010
We review pedagogically non-Abelian discrete groups and
show some applications for physical aspects.
This article includes a brief view on general aspects of
group theory, i.e. something basic and useful theorems.
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Flavor Symmetry of Neutrinos
is related with Physical Phenomena.
●Ue3=0 in Tri-bimaximal mixing!
There are hints Non-zero Ue3 in experiments.
How can one predict Ue3 ?
●CKM mixing in Quarks ? Cabibbo angle?
We need Quark-lepton unification in a GUT.
●SUSY Flavor Sector, SUSY FCNC , EDM
We discuss the case of S4 symmetry.
Before discussing S4 model, let us understand
how to get the tri-bimaximal mixing
in the example of A4 flavor model.
E. Ma and G. Rajasekaran, PRD64(2001)113012
Four irreducible representations in A 4 symmetry
1
1’
1”
3
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3L × 3flavon → 1
3L × 3flavon → 1”
3L × 3flavon → 1’
3L × 3L → 1
3L × 3L × 3flavon → 1
1’ × 1” → 1
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These mass matrices do not yet predict tri-bimaximal mixing !
Can one get Desired Vacuum
in Spontaneous Symmetry Breaking ?
Scalar Potential Analysis
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----------- -------------
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As seen in this A4 model,
in order to reproduce the tri-bi maximal mixing, we need
Non-Abelian Discrete Symmetry
(A4, T’, S4 … )
and
Symmetry Breaking
Vacuum Alignment of flavons.
Spontaneous Breaking ? ( Scalar potential )
Explicit Breaking ? (Boundary condition in extra-dim.)
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2 S4 Flavor Model in Quarks and Leptons
H. Ishimori, K. Saga, Y. Shimizu, M. Tanimoto, arXiv:1004.5004
S4×Z4 with SUSY SU(5) GUT⇒Tri-bimaximal, Cabibbo angle
C.Hagedorn, M.Lindner, R.N.Mohapatra, JHEP 0606, 042 (2006) SO(10)
B.Dutta, Y. Mimura, R.N. Mohapatra, arXiv:0911.2242 SO(10)
C.Hagedorn, S. F. King, C. Luhn, arXiv:1003.4249 SU(5)
R.d.A. Toorop, F. Bazzocchi, L. Merlo, arXiv: 1003.4502 Pati-Salam
S4×Z4×U(1)FN with SUSY SU(5) GUT
Up
quarks
MR
Dirac
Neutrinos
Charged leptons
Down quarks
We take l=m=1, n=2.
S4 invariant superpotential for leptons
3L×2R×3flavon
3L×1R×3flavon
2R×2R
1R×1R
2R×2R×2flavon
3L×2R×3flavon
3L×1R×3flavon
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We take VEV’s
We get
Lepton Mass Matrices
○
○
○
○
Due to
m-n<0
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Vacuum alignment
No mixing in the left-hand !
Θ12=60°in the right-hand !
After seesaw, we get the tri-bimaximal mixing
26
Deviation from the Tri-bimaximal mixing
due to Higher dimensional mass operators
Superpotential of next-to-leading order
27
The charged lepton mass matrix including
the next-to-leading terms
Since the lepton mixing is given as
we have non-zero Ue3
0.003
Next-to-leading in Neutrino sector
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Determination of magnitudes
Desired Vacuum Alignments
FN charges l=m=1, n=2
Putting observed masses and M=1012 GeV, we get
We can predict mixing angles.
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Quark Sector is predicted.
Down Quarks
Left-handed mixing is given as
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Including next-to-leading order, we get
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Up Quark Sector
Direct Yukawa
coupling
We add the next-to-leading mass matrix
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Up Quarks
We take alignment
, we get
After rotating it by the orthogonal matrix,
We obtain
We obtain CKM matrix elements
In the leading order, we predict
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Including next-to-leading order corrections, we get
The parameter set
reproduces observed values very well.
Values of parameters are consistent with our mass matrices.
CP violation can be discussed !
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3. S4 Flavor Symmetry in Sleptons
Flavor symmetry constrains not only quark/lepton mass matrices,
but also mass matrices of their superpartner, i.e. squark/slepton
Specific patterns of squark/slepton mass matrices could be tested in future
experiments.
In this talk, we concentrate on lepton FCNC.
Consider Soft SUSY Breaking Term in Supergravity.
Second order
Slepton mass matrices are derived from
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For the left-handed sector, higher dimensional terms are given as
Left-handed Slepton mass matriｘ is
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Right-handed Slepton mass matrix is
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Move to Super-CKM basis (Diagonal Basis of Charged Lepton)
in order to estimate magnitudes of FCNC.
Dominant term
○
where
Mass Insertion Parameters
Experimental Constraint from
μ→eγ
F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, Nucl. Phys. B477(1996) 321
Numerical analyses are required.
A terms are obtained as
Experimental Constraint
Dangerous !
We need numerical analyses of μ→eγ .
μ→eγ Decay
○
○
○
○
EDM of Electron
○○
J.Hisano, M. Nagai, P. Paradisi, Phys.Rev.D80:095014,2009.
Preliminary
Assume the maximal phase
Assume the maximal phase
Assume the maximal phase
4 Summary
☆ S4 Flavor Symmetry in SU(5) can give
realistic quark and lepton mixing matrices.
Tri-bimaximal mixing, Cabibbo angle
☆ S4 discrete symmetries work to
suppress FCNC in the framework of
gravity mediation in SUSY breaking.
★ Squark sectors
in S4 Symmetry ?
★ Origin of S4 Symmetry ?
★ Mass Spectrum ?
50
One of Future Problems
Can we predict Neutrino Masses?
Symmetry cannot predict mass spectrum.
Symmetry breaking gives mass spectrum.
Normal mass hierarchy
Inverted mass hierarchy
T2K and NOνＡ !
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We know Koide formula !
Accuracy
10-5
for neutrinos
Can we predict neutrino spectrum consistent with Tribimaximal Mixing？
We need more studies of Symmetry Breakings !
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Thank you !
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What is interesting in Neutrino Physics ?
★Tiny Neutrino Masses ? Seesaw, Extra-Dimensions
Mass Spectrum?
★Large Flavor Mixings ? However Θ13 ? CP?
★Majorana Neutrinos？ L number violation?
★Right-handed Neutrinos？ LHC, Leptogenesis
★Sterile Neutrinos？
★New Interaction of Neutrinos？
★Neutrino Soft Mass？ ★Cosmic Neutrinos?
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K.Ichikawa, M. Fukugita, M. kawasaki, PRD71(2005)043001
M. Fukugita, K. Ichikawa, M. Kawasaki, O. Lahav, PRD74(2006)027302
mν< 0.63 eV
95% c.l
A.D. Dolgov, arXiv: 0803.3887
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Our Multiplication Rule of S4
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S4 invariant superpotential
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Realization of Vacuum Alignment
Introduce driving fields with R charge 2
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Scalar potential
We obtain Desired Vacuum Alignment
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The first neutrino was detected on 24thFeb 2010.
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A4 symmetry
(Tetrahedral Symmetry)
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EDM of Electron
○ ○
J.Hisano, M. Nagai, P. Paradisi, Phys.Rev.D80:095014,2009.
Anomalous Magnetic Moment of Muon
Neutrino Parameters
Global fit for 3 flavors
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