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June 18, 2004 Mitsuru Kakizaki 1
Democratic (s)fermions and lepton flavor violation
Mitsuru Kakizaki (ICRR, University of Tokyo)June 18, 2004
We propose a new alignment mechanismto solve SUSY flavor problem
We propose a new alignment mechanismto solve SUSY flavor problem
Construction of a new alignment mechanismComparison between the alignment mechanism and mSUGRA (degenerate sfermions)
Ref.: K. Hamaguchi, M. K. and Masahiro Yamaguchi, PRD68 (2003) 056007
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1. Motivation
Two severe flavor puzzles in SUSY modelsTwo severe flavor puzzles in SUSY models
1. Fermion masses and mixing Large mass hierarchy among charged fermions Small quark mixing Large lepton mixing
2. SUSY flavor problem Generic sfermion masses and mixing Unacceptably large FCNC processes Experimental constraints: for
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Attempts to solve SUSY flavor problem
1. Degeneracy:2. Alignment: without degeneracy
Idea : High energy theory which controls flavor
SUSY FCNC suppression Fermion masses and mixing
Idea : High energy theory which controls flavor
SUSY FCNC suppression Fermion masses and mixing
Fermion and sfermion mass puzzles are simultaneously solved Measurement of FCNC processes and sfermion mass spectra
Fermion mass generation mechanism may be revealed
Interesting points of alignment:
This talk
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Purpose
Proposal of a new alignment mechanism based on the democratic mass matrix model, which explains neutrino bi-large mixing Comparison between the alignment mechanis
m and conventional mSUGRA : Mass spectra of sfermions Charged lepton flavor violation (LFV)
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Unique invariant Small breaking
Democratic mass matrix:
Bi-large unitary matrix:
sym.
Charged lepton mass matrix
Hierarchical mass spectra:
Idea: Equality of three generationsIdea: Equality of three generations
2. Democratic mass matrix model
[Harari—Haut--Weyers (1978); Koide (1983, 1989); Fritzsch--Xing (1995); Fukugita—Tanimoto--Yanagida(1998)]
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Neutrino mass matrix
Consider Majorana neutrinos:
Here we take universal mass term:Universal Democratic
sym.
Degenerate neutrinos ; Bi-large mixing, small
Small angles in the quark sector:
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Idea : Interactions between SUSY SM fields and hidden fields are also democratic
Idea : Interactions between SUSY SM fields and hidden fields are also democratic
3. Democratic sfermions[Hamaguchi--M. K.--Yamaguchi (2002)]
Kahler potential ( Bilinear part of ):
3rd generation sfermion mass differs from first two generation masses
Hidden fields
Soft sfermion mass matrix:
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Sfermion mass matrix in the superCKM basis:
Small generation mixing without universality
Alignment is realized
SUSY contributions to FCNCs are suppressed
Democratic model solves SUSY flavor problemDemocratic model solves SUSY flavor problem
Sfermion mixing
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Slepton masses Left-handed slepton mass spectrum
Presence of democratic part in Kahler potential for Democratic part in neutrino mass matrix in canonical basis × Bi-large neutrino mixing requires universal form for Kahler potential for :
Left-Left mixing vanishes Right-handed slepton mass spectrum Small Right-Right mixing
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Experimental bound: Foreseeable future: Prediction of democratic model : ( For small
)
[MEGA (1999)]
[MEG@PSI]
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CP violating squark mixing
[Endo--M.K.--Yamaguchi(2003)]
[Hisano--Shimizu(2003)]
Experimental bounds Democratic model
When breaking parameters have CP phases of , , 199Hg EDM are dangerous
199Hg EDM
199Hg EDM
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Solution to CP violating FCNC problem
In the absence of Left-Left or Right-Right mixing CP violating squark generation mixing are suppressed
Democratic model embedded in SU(5) GUT SU(5):Universal masses of right-handed sdowns and left-handed sleptons is required by bi-large neutrino mixing
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4. Comparison between mSUGRA and democratic model
SUSY SM + right-handed neutrinos (mSUGRA + RG effects) Collider experiments:
LFV searches:
Democratic model( Generation mixing
without RG effects )
LHC, polarized muon may distinguish models of SUSY [Kuno—Okada(1996)]
[Moroi(1994)]
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5. Summary One interesting solution to SUSY flavor problem:
The mechanism which dictates fermion mass structure also suppresses FCNCs Alignment
We proposed a new successful alignment mechanism based on
the democratic mass matrix model Predictions of the democratic model differ from thos
e of mSUGRA Observable
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Backup slides
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For large
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Properties of democratic model
Predictions of lepton sector Slepton mass spectra LFV decay
CP violating squark generation mixing Experimental bounds and estimation in democratic model Solution to CP violating squark generation mixing
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Comparison between U(2) and democratic ( 1,2 generations ~ Doublets, 3 rd generations ~ Singlets )
Differences in neutrino mass matrix
U(2)
No symmetric singlet
Small mixing ×
Democratic
Large mixing arises from breaking terms
( In the basis of diagonal charged lepton mass matrix )
Universal masses are allowed:
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Weak points of characteristic alignment mechanisms
U(1) flavor symmetry (Abelian) : [Nir—Seiberg (1993)]
Many U(1) flavor symmetries are necessary for adequate FCNC suppression × U(2) flavor symmetry (Non-Abelian) :
[Barbieri—Hall—Raby—Romanino (1997)]
1, 2 generations doublets FCNC suppression
Small mixing in the lepton sector ×
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Soft sfermion mass matrix
Masses of 3rd generation sfermionsdiffer from those of 1,2 generations
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Idea: Equality of three generations Idea: Equality of three generations
2. Democratic mass matrix model
[Harari—Haut--Weyers (1978); Koide (1983, 1989); Fritzsch--Xing (1995); Fukugita—Tanimoto--Yanagida(1998)]
3 = 1 + 2
Permutation group on 3 objects:: 3-dim. reducible rep.3rd generations:
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Experimental constraint on 199Hg EDM induced by chargino—up-type squark loop
Constraint on CP violating mixing
[Endo--M.K.--Yamaguchi(2003)]
×
××
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199Hg EDM
CP violating interaction: T violating nuclear force:
Interaction between nuclear and : Spin of nuclear EDM of 199Hg atom
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Group theoretical interpretation
Charged lepton mass matrix
sym. broken by vevs:
Hierarchical mass spectrum:Same result as the case of democratic + diagonal breaking
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Neutrino masses generated by seesaw mechanism
Dirac, heavy neutrino mass matrix:Light neutrino mass matrix:
Assume that right-handed neutrinos transform as triplet under and take universal matrix
[Fujii--Hamaguchi--Yanagida(2002)]
Degenerate light neutrino masses
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Slepton mixing in mSUGRAMSSM + Right-handed neutrinos + mSUGRA Slepton masses arise in flavor blind manner at a high energy scale: at
Heavy right-handed neutrinos have flavor changing Yukawa couplings
Left-handed slepton mixing is induced by RG effects:
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Magnitude of sfermion mixing is same as the case without breaking
breaking in sfermion mass terms
Yukawa structure is NOT modified Sfermion mass matrix:
Here we introduce new parity symmetry:Doublets: -- Singlets: +
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Scalar trilinear coupling ( A-term )
Source of Left-Right mixing
Alignment is realized
In superCKM basis
Small generation mixing
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LFV decay of Prediction of democratic model
Present upper bound:
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transition
199Hg EDM can be avoided 199Hg EDM is dangerous
SUSY GUT + ( mSUGRA + RG effects )
Democratic model
Squark mixing(real)
Sizable contribution to Due to mixingCP asym. in
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Problems of democratic model
Absence of physical motivations What is the origin of the democratic mass
matrix? Symmetry Geometry
What is the origin of the small breaking?
Why is the democratic part absent for ?
[Watari—Yanagida(2002)]
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Refs.: K. Hamaguchi, M. K. and M. Yamaguchi, “Democratic (s)fermions and lepton flavor violation,’’
PRD68 (2003) 056007; M. Endo, M.K. and M. Yamaguchi, “New constraint on squark flavor mixing from Hg-199
electric dipole moment,’’ PLB583 (2004) 186; M. Endo, M.K. and M. Yamaguchi, “Large supersymmetric contribution to CP asymmetry of from left-handed squark mixing,’’ To appear in PLB [hep-ph/0403260].