Transcript 1．Motivation

Democratic (s)fermions
and lepton flavor violation
Mitsuru Kakizaki (ICRR, University of Tokyo)
June 18, 2004
Ref.: K. Hamaguchi, M. K. and Masahiro Yamaguchi, PRD68 (2003) 056007
We propose a new alignment mechanism
to solve SUSY flavor problem
Construction of a new alignment mechanism
Comparison between the alignment mechanism
and mSUGRA (degenerate sfermions)

June 18, 2004
Mitsuru Kakizaki
1
１．Motivation
Two 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
June 18, 2004
Mitsuru Kakizaki
2
Attempts to solve
SUSY flavor problem
1. Degeneracy:
2. Alignment:
without degeneracy
This talk
Idea： High energy theory which controls flavor
SUSY FCNC suppression Fermion masses and mixing
Interesting points of alignment:


Fermion and sfermion mass puzzles are simultaneously solved
Measurement of FCNC processes and sfermion mass spectra
Fermion mass generation mechanism may be revealed
June 18, 2004
Mitsuru Kakizaki
3
Purpose
 Proposal of a new alignment mechanism
based on the democratic mass matrix model,
which explains neutrino bi-large mixing
 Comparison between the alignment
mechanism and conventional mSUGRA：
 Mass spectra of sfermions
 Charged lepton flavor violation (LFV)
June 18, 2004
Mitsuru Kakizaki
4
2. Democratic mass matrix model
[Harari—Haut--Weyers (1978); Koide (1983, 1989);
Fritzsch--Xing (1995); Fukugita—Tanimoto--Yanagida(1998)]
Idea: Equality of three generations
 Charged lepton mass matrix
sym.
Democratic mass matrix:
Unique invariant
Small breaking
Hierarchical mass spectra:
Bi-large unitary matrix:
June 18, 2004
Mitsuru Kakizaki
5
Neutrino mass matrix

Consider Majorana neutrinos:
sym.
Universal

Democratic
Here we take universal mass term:
Degenerate neutrinos；Bi-large mixing, small
 Small angles in the quark sector:
June 18, 2004
Mitsuru Kakizaki
6
3. Democratic sfermions
[Hamaguchi--M. K.--Yamaguchi (2002)]
Idea： Interactions between SUSY SM fields
and hidden fields are also democratic

Kahler potential （Bilinear part of

Soft sfermion mass matrix:
）：
Hidden fields
3rd generation sfermion mass differs from
first two generation masses
June 18, 2004
Mitsuru Kakizaki
7
Sfermion mixing

Sfermion mass matrix in the superCKM basis:
SUSY contributions to FCNCs are suppressed

Small generation mixing without universality
Alignment is realized
Democratic model solves SUSY flavor problem
June 18, 2004
Mitsuru Kakizaki
8
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
June 18, 2004
Mitsuru Kakizaki
9


Experimental bound:
Foreseeable future:
Prediction of democratic model：
small
）
June 18, 2004
Mitsuru Kakizaki
[MEGA (1999)]
[MEG@PSI]
（For
10
CP violating squark mixing
When breaking parameters have CP phases of
,
, 199Hg EDM are dangerous
 Experimental bounds
Democratic model

199Hg
EDM
[Hisano--Shimizu(2003)]
199Hg
EDM
[Endo--M.K.--Yamaguchi(2003)]
June 18, 2004
Mitsuru Kakizaki
11
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
June 18, 2004
Mitsuru Kakizaki
12
4. Comparison between
mSUGRA and democratic model


SUSY SM
+ right-handed neutrinos
(mSUGRA + RG effects)
Collider experiments:
Democratic model
（Generation mixing
without RG effects）

[Moroi(1994)]

LFV searches:
LHC, polarized muon may distinguish models of SUSY
[Kuno—Okada(1996)]
June 18, 2004
Mitsuru Kakizaki
13
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
those of mSUGRA


Observable
June 18, 2004
Mitsuru Kakizaki
14
Backup slides
June 18, 2004
Mitsuru Kakizaki
15

For large
June 18, 2004
Mitsuru Kakizaki
16
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
June 18, 2004
Mitsuru Kakizaki
17
Comparison between U(2) and democratic
（1,2 generations～Doublets, ３rd generations～
Singlets）
Differences in neutrino mass matrix
（In the basis of diagonal charged lepton mass matrix）

U(2)
No symmetric singlet
Small mixing ×
June 18, 2004

Democratic
Universal masses are allowed:
Large mixing arises
from breaking terms
Mitsuru Kakizaki
18
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 ×
June 18, 2004
Mitsuru Kakizaki
19
Soft sfermion mass matrix
Masses of 3rd generation sfermions
differ from those of 1,2 generations
June 18, 2004
Mitsuru Kakizaki
20
2. Democratic mass matrix model
[Harari—Haut--Weyers (1978); Koide (1983, 1989);
Fritzsch--Xing (1995); Fukugita—Tanimoto--Yanagida(1998)]

Idea: Equality of three generations
Permutation group on 3 objects:
: 3-dim. reducible rep.
3rd generations:
3=1+2
June 18, 2004
Mitsuru Kakizaki
21
Constraint on
CP violating
mixing
[Endo--M.K.--Yamaguchi(2003)]

Experimental constraint on 199Hg EDM
induced by chargino—up-type squark loop
×
×
June 18, 2004
Mitsuru Kakizaki
×
22
199Hg
EDM

CP violating interaction:
T violating nuclear force:
Interaction between nuclear and ：
Spin of nuclear
EDM of 199Hg atom
June 18, 2004
Mitsuru Kakizaki
23
Group theoretical interpretation

Charged lepton mass matrix
sym. broken by vevs:
Hierarchical mass spectrum:
Same result as the case of
democratic + diagonal breaking
June 18, 2004
Mitsuru Kakizaki
24
Neutrino masses generated
by seesaw mechanism
[Fujii--Hamaguchi--Yanagida(2002)]


Dirac, heavy neutrino mass matrix:
Light neutrino mass matrix:
Assume that right-handed neutrinos transform as
triplet under
and take universal matrix
Degenerate light neutrino masses
June 18, 2004
Mitsuru Kakizaki
25
Slepton mixing in mSUGRA
MSSM + 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:
June 18, 2004
Mitsuru Kakizaki
26
breaking in sfermion mass terms

Here we introduce new parity symmetry:
Doublets: -- Singlets: +

Yukawa structure is NOT modified

Sfermion mass matrix:
Magnitude of sfermion mixing is same as
the case without breaking
June 18, 2004
Mitsuru Kakizaki
27
Scalar trilinear coupling
（A-term）
Source of Left-Right mixing

In superCKM basis
Small generation mixing
June 18, 2004
Mitsuru Kakizaki
Alignment is realized
28
LFV decay of

Prediction of democratic model

Present upper bound:
June 18, 2004
Mitsuru Kakizaki
29
transition
SUSY GUT +
（mSUGRA + RG effects）

Democratic model
Squark mixing
(real)

Sizable contribution to
 199

Hg EDM is dangerous
June 18, 2004
Due to
CP asym. in
mixing
Hg EDM can be avoided
 199
Mitsuru Kakizaki
30
Problems of democratic model
Absence of physical motivations
 What is the origin of the democratic mass matrix?
 Symmetry
[Watari—Yanagida(2002)]
 Geometry

What is the origin of the small

Why is the democratic part absent for
June 18, 2004
Mitsuru Kakizaki
breaking?
?
31
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].
June 18, 2004
Mitsuru Kakizaki
32