oct. 25, 2004mitsuru kakizaki1 flavor structure in supersymmetric models mitsuru kakizaki (icrr,...
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Oct. 25, 2004 Mitsuru Kakizaki 1
Flavor structure in supersymmetric models
Mitsuru Kakizaki (ICRR, University of Tokyo)Oct. 25, 2004 @ Ochanomizu University
We proposed a new alignment mechanism
to solve the SUSY flavor problem
We proposed a new alignment mechanism
to solve the SUSY flavor problem
Construction of a new alignment mechanism Comparison between the alignment mechanism and mSUGRA (degenerate sfermions)
Oct. 25, 2004 Mitsuru Kakizaki 2
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,’’ PLB594 (2004) 205.
Oct. 25, 2004 Mitsuru Kakizaki 3
1. Motivation
1. Fermion masses and mixing in the standard model (with neutrino mass term
s) Hierarchy in charged fermion masses : Small generation mixing in the quark sector : Large mixing in the lepton sector :
Two severe flavor puzzles in SUSY modelsTwo severe flavor puzzles in SUSY models
Oct. 25, 2004 Mitsuru Kakizaki 4
2. Flavor problem of (soft) sfermion masses
generation
(tilde: superpartner)Viable solution to the hierarchy problem
FermionBoson Supersymmetry (SUSY) :Quark Squark
GauginoGauge bosone.g.
Superparticles have not been discovered(Soft) SUSY breaking terms are required
e.g. Soft sfermion mass terms:
New flavor parameters are introducedNew flavor parameters are introduced
Oct. 25, 2004 Mitsuru Kakizaki 5
Generic sfermion masses and mixing Unacceptably large flavor changing neutral currents (FCNCs)
Generic sfermion masses and mixing Unacceptably large flavor changing neutral currents (FCNCs)
SUSY flavor problem
Constraint :
e.g. K meson mixing:
c.f. FCNCs are suppressed by GIM mechanism in SM
Oct. 25, 2004 Mitsuru Kakizaki 6
Attempts to solve SUSY flavor problem
1. Degeneracy: e.g. mSUGRA:
Sfermion masses arise in flavor blind manner at a high energy scale Generation mixing is induced only by RG effects
SUSY flavor problem is solved2. Alignment: Today’s talk
Oct. 25, 2004 Mitsuru Kakizaki 7
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
Alignment :
Interesting points : Fermion and sfermion mass puzzles are simultaneously solved Measurement of FCNC processes and sfermion mass spectra
Fermion mass generation mechanism may be revealed
[Nir--Seiberg(1993)]
Fermion and sfermion squared mass matrices arealigned in field space simultaneously diagonalized
Oct. 25, 2004 Mitsuru Kakizaki 8
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 ×
Oct. 25, 2004 Mitsuru Kakizaki 9
Purpose
Proposal of a new alignment mechanism based on the democratic mass matrix model, which explains neutrino bi-large mixing Comparison between this alignment mechanis
m and conventional mSUGRA : Mass spectra of sfermions Charged lepton flavor violation (LFV)
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Contents
1. Motivation2. Democratic mass matrix model3. Democratic sfermions4. Comparison between the mSUGRA and democratic model5. Summary
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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:
Oct. 25, 2004 Mitsuru Kakizaki 12
Charged lepton mass matrix
Unique invariant Small breaking
Democratic mass matrix:
Hierarchical mass spectra:Bi-large unitary matrix:
Small angles in the quark sector:
sym.
Oct. 25, 2004 Mitsuru Kakizaki 13
Neutrino mass matrix
Consider Majorana neutrinos:
Here we take universal mass term:Universal Democratic
sym.
Degenerate neutrinos ; Bi-large mixing, small
Oct. 25, 2004 Mitsuru Kakizaki 14
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:
Oct. 25, 2004 Mitsuru Kakizaki 15
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
Universal Democratic
[Hamaguchi--M. K.--Yamaguchi (2002)]
Kahler potential ( Bilinear part of ):
Functions of (hidden) fields
Oct. 25, 2004 Mitsuru Kakizaki 16
Soft sfermion mass matrix
Masses of 3rd generation sfermionsdiffer from those of 1,2 generations
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Democratic model solves SUSY flavor problem
Squark generation mixing:
Small generation mixing without universality
Alignment is realized Masses of 1,2 generation sfermions are degenerate 1-2 mixing is extremely suppressed
Suppression of SUSY contributions to FCNCs
Oct. 25, 2004 Mitsuru Kakizaki 18
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
Oct. 25, 2004 Mitsuru Kakizaki 19
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
Oct. 25, 2004 Mitsuru Kakizaki 20
Experimental bound: Foreseeable future: Prediction of democratic model : ( For small
)
Branching ratio ofLFV decay
[MEGA (1999)]
[MEG@PSI]
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Branching ratio ofLFV decay
For large
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CP violating squark mixing
[Hisano--Shimizu(2003,2004)]
Experimental bounds Democratic model
When breaking parameters have CP phases of , , hadronic EDMs are dangerous
hadronic EDMs: :
For
Oct. 25, 2004 Mitsuru Kakizaki 23
Democratic model embedded in SU(5) GUT is promising SU(5): Universal masses of right-handed sdowns and left-handed sleptons is required by bi-large neutrino mixing
Democratic model embedded in SU(5) GUT is promising SU(5): Universal masses of right-handed sdowns and left-handed sleptons is required by bi-large neutrino mixing
Solution to CP violating FCNC problem
In the absence of Left-Left or Right-Right mixing, CP violating squark generation mixing are suppressed
Oct. 25, 2004 Mitsuru Kakizaki 24
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[Kuno—Okada(1996)]
Oct. 25, 2004 Mitsuru Kakizaki 25
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 form thos
e of mSUGRA Observable
Oct. 25, 2004 Mitsuru Kakizaki 26
Backup slides
Oct. 25, 2004 Mitsuru Kakizaki 27
Experimental constraint on 199Hg EDM induced by chargino—up-type squark loop
Constraint on CP violating mixing
[Endo--M.K.--Yamaguchi(2003)]
×
××
Oct. 25, 2004 Mitsuru Kakizaki 28
199Hg EDM
CP violating interaction: T violating nuclear force:
Interaction between nuclear and : Spin of nuclear EDM of 199Hg atom
Oct. 25, 2004 Mitsuru Kakizaki 29
Group theoretical interpretation
Charged lepton mass matrix sym. broken by the following vevs:
Hierarchical mass spectrum: Same results as the case of democratic + diagonal breaking
Oct. 25, 2004 Mitsuru Kakizaki 30
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 massesDegenerate light neutrino masses
Oct. 25, 2004 Mitsuru Kakizaki 31
Slepton mixing in mSUGRA mSUGRA + Right-handed neutrinos + Seesaw 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:
Oct. 25, 2004 Mitsuru Kakizaki 32
Magnitude of sfermion mixing is same order as the case without breaking
breaking in sfermion mass terms
Yukawa structure is NOT modified Resultant sfermion mass matrix:
Here we introduce new parity symmetry:Doublets: -- Singlets: +Assignment:
Oct. 25, 2004 Mitsuru Kakizaki 33
Scalar trilinear coupling ( A-term )
Source of Left-Right mixing
Alignment is realized
In superCKM basis
Small generation mixing
Oct. 25, 2004 Mitsuru Kakizaki 34
LFV decay of Prediction of democratic model
Present upper bound of implies
c.f. Challenging for super B factories
[Belle(2003)]
Oct. 25, 2004 Mitsuru Kakizaki 35
transition
Large hadronic EDM can be avoided
Hadrnic EDM is dangerous
SUSY GUT + ( mSUGRA + RG effects )
Democratic model
Squark mixing(real)
mixing
CP asym. inCP asym. inmixing
Oct. 25, 2004 Mitsuru Kakizaki 36
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)]