June 18, 2004Mitsuru Kakizaki1 Democratic (s)fermions and lepton flavor violation Mitsuru Kakizaki...

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


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


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


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)


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)]


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:


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:


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


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


Experimental bound:　 Foreseeable future: Prediction of democratic model ：　（ For small 　　　

）　

[MEGA (1999)]

[MEG@PSI]


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


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


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)]


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


Backup slides


For large 　


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


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:


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 ×


Soft sfermion mass matrix

Masses of 3rd generation sfermionsdiffer from those of 1,2 generations


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:


Experimental constraint on 199Hg EDM induced by chargino—up-type squark loop 　

Constraint on CP violating mixing

[Endo--M.K.--Yamaguchi(2003)]

×

××


199Hg EDM

CP violating interaction:　　 T violating nuclear force:

　　 Interaction between nuclear and ：　　　　　　　　　　　　　 Spin of nuclear　　 EDM of 199Hg atom


Group theoretical interpretation

Charged lepton mass matrix

sym. broken by vevs:

Hierarchical mass spectrum:Same result as the case of democratic + diagonal breaking


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


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:


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: +


Scalar trilinear coupling （ A-term ）

Source of Left-Right mixing

Alignment is realized

In superCKM basis

Small generation mixing


LFV decay of Prediction of democratic model

Present upper bound: 　　　　　　　　　　　　　


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


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)]


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, 2004Mitsuru Kakizaki1 Democratic (s)fermions and lepton flavor violation Mitsuru Kakizaki...

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