Oct. 25, 2004Mitsuru Kakizaki1 Flavor structure in supersymmetric models Mitsuru Kakizaki (ICRR, University of Tokyo) Oct. 25, 2004 @ Ochanomizu University.

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.

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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

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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

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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

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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

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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

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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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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:

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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.

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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

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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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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

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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

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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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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 　　　

）　

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

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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

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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[Kuno—Okada(1996)]

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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 form thos

e of mSUGRA Observable

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Backup slides

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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 the following vevs:

Hierarchical mass spectrum: Same results 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 massesDegenerate light neutrino masses

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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:

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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:

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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 of 　implies

c.f. Challenging for super B factories

[Belle(2003)]

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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

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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)]