E 6 gut models and fcnc processes
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E 6 GUT Models and FCNC Processes. with S-G.Kim, N.Maekawa, A.Matsuzaki, T.Yoshikawa. (Nagoya Univ.). Kazuki Sakurai. Plan. I. Introduction. II. E 6 GUT and Horizontal Symmetry. III. Search for E 6 ×Horizontal GUT. -- Lepton Flavor Violation. -- CPA in rare B meson decay. IV. Summary.

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E 6 gut models and fcnc processes

E6 GUT ModelsandFCNC Processes

with S-G.Kim, N.Maekawa, A.Matsuzaki, T.Yoshikawa

(Nagoya Univ.)

Kazuki Sakurai

Plan

I. Introduction

II. E6 GUT and Horizontal Symmetry

III. Search for E6×Horizontal GUT

-- Lepton Flavor Violation

-- CPA in rare B meson decay

IV. Summary

2007/8/4 [email protected]


E 6 gut models and fcnc processes

Problems in MSSM

Supersymmetry is promising candidates of New Physics.However they have some phenomenological problems.

Universal sfermion masses

SUSY Flavor Problem

Generally, SUSY breaking terms brake flavor symmetry. They generate too large FCNCs.

Large SUSY breaking scale

SUSY CP Problem

Suppressed SUSY CP phases

Generally, couplings in SUSY breaking terms are complex. Such couplings violate CP and induce too large EDMs.

Large SUSY breaking scale

Little Hierarchy Problem

Up-type Higgs mass get a large quantum correction which proportional to stop mass.

Not large stop masses


Horizontal symmetry

SU(2)H invariance forbid Yukawa interactions in tree level except for top Yukawa.

in SO(10), E6

SU(2)H breaking effect generate first two generation Yukawa couplings through higher dimensional terms.

SU(2)H

Horizontal sym. can explain smallness of Yukawa couplings!!

Horizontal Symmetry

Flavor symmetry is natural idea, in order to realize the universal sfermion masses.

First two generations are identified as SU(2)H (or U(2)H) doublet. Third generation is singlet.

:singlet

:doublet

If SUSY breaking mediation scale is higher than SU(2)H breaking scale, SUSY breaking terms should respect the SU(2)H symmetry.

Universality in first two generations is realized due to SU(2)H!!


Horizontal symmetry1

Horizontal Symmetry

However, if is lepton doublet…

In mass eigenstate basis of fermion,

Neutrino oscillation suggest is large mixing. Therefore large off-diagonal entries arise after this unitary transformation.

Such large off-diagonal entries induce too large Lepton Flavor Violation.


E 6 unification

decouple

Low energy three5(Dc L) of SU(5) comefrom only first two generation of27not273.

Guisey-Ramond-Sikivie,

Aichiman-Stech, Shafi,

Barbieri-Nanopoulos,

Bando-Kugo,…

E6 Unification

E6 GUT models are interesting, because…

-- all one generation quarks leptons are unified into 27.

-- realistic Yukawa hierarchies are obtained.


E 6 unification1

up sector:

decouple

Low energy three5(Dc L) of SU(5) comefrom only first two generation of27not273.

Guisey-Ramond-Sikivie,

Aichiman-Stech, Shafi,

Barbieri-Nanopoulos,

Bando-Kugo,…

E6 Unification

E6 GUT models are interesting, because…

-- all one generation quarks leptons are unified into 27.

-- realistic Yukawa hierarchies are obtained.

Cabibbo angle


E 6 unification2

decouple

Guisey-Ramond-Sikivie,

Aichiman-Stech, Shafi,

Barbieri-Nanopoulos,

Bando-Kugo,…

E6 Unification

E6 GUT models are interesting, because…

-- all one generation quarks leptons are unified into 27.

-- realistic Yukawa hierarchies are obtained.

up sector:

down &

charged lepton:

Cabibbo angle

Low energy three5(Dc L) of SU(5) comefrom only first two generation of27 not273.


E 6 unification3

decouple

Guisey-Ramond-Sikivie,

Aichiman-Stech, Shafi,

Barbieri-Nanopoulos,

Bando-Kugo,…

E6 Unification

E6 GUT models are interesting, because…

-- all one generation quarks leptons are unified into 27.

-- realistic Yukawa hierarchies are obtained.

up sector:

down &

charged lepton:

neutrino sector:

Cabibbo angle

Low energy three5(Dc L) of SU(5) comefrom only first two generation of27 not273.


Horizontal symmetry on e 6

N.Maekawa. 02, N.Maekawa, T.Yamashita 04

Horizontal Symmetry on E6


Horizontal symmetry on e 61

Since contain lepton doublet, Neutrino oscillation suggest is large mixing.

No LFV problem due to full universality in !!

In above sfermion masses, we can take large SUSY breaking scale with keeping stop masses around weak scale, because correspond to stop masses.

N.Maekawa. 02, N.Maekawa, T.Yamashita 04

Horizontal Symmetry on E6


E 6 gut models and fcnc processes

Problems in MSSM

Some problems in MSSM can be solved in E6×Horizontal GUT models!!

SUSY and GUT are promising candidate of New Physics.However they have some phenomenological problems.

Universal sfermion masses

SUSY Flavor Problem

SUSY breaking terms brake flavor symmetry generally. They generate too large FCNCs.

Large SUSY breaking scale

SUSY CP Problem

Suppressed SUSY CP phases

SUSY breaking terms have complex coupling. Such couplings violate CP and induce too large CPV observables (EDMs,...).

Large SUSY breaking scale

Little Hierarchy Problem

Up-type Higgs mass get a large quantum correction which proportional to stop mass.

Not large stop masses


Search for e 6 horizontal gut

[ Strategy ]

It is expected that FCNC processes become large through the sfermions in 10 of SU(5).

Lepton Flavor Violation,

CP asymmetries in B meson decay

Search for E6×Horizontal GUT

Next question is,

how can we confirm this model experimentally?


Lepton flavor violation

Lepton Flavor Violation


Lepton flavor violation1

e

Left-handed

Right-handed

e

Lepton Flavor Violation

Lepton Flavor Violations (LFVs) are good process for search the New Physics, because LFV processes are forbidden in Standard Model.

In E6 models, LFV processes take place with picking up the off-diagonal entries respectively.

We can get parameter independent prediction,

Since 10 of SU(5) contain not , final state lepton have right-handed chirality. We can check this by measuring angular distribution of final state lepton.

spin

+

+

spin

+

+


Can we discover the lfvs at future experiments

MEG experiment

S.-G.Kim, N.Maekawa, A.Matsuzaki, K.S, T,Yoshikawa ‘06

Can we discover the LFVs at future experiments?

(exp. bound)

(exp. bound)

super-KEKB

may be discovered in KEKB or super-KEKB, If < 250GeV.

may be discovered in MEG, If < 300GeV.


Cp asymmetries in rare b meson decay

CP asymmetries in rare B meson decay


Cp asym of b k s b k s

In SM, CP violation is contained in only B-Bbar mixing part through a KM phase.

gluino:

SM predictions may deviate from experiments.

chargino:

SUSY CP phase can contribute in direct decay parts. So, current deviations may be explained.

in this model.

0.68 (SM prediction)

Gluino and Chargino

are always interfere with same sign!

CP asym. of BφKs, Bη’Ks

Time dependent CP asymmetry of BφK, Bη’K are composed of two part, B-Bbar mixing part and direct decay part.


Numerical results

(preliminary)

Numerical Results

total

total

chargino

chargino

gluino(C8)

gluino(C8)

gluino(C3-6)

gluino(C3-6)

Deviations from SM can be large(~±0.15)!!


Numerical results1

E6×Horizontal GUT models suggest that current deviations can be true!

(preliminary)

Numerical Results

Scanning in

SUSY CP phase


Summary

Summary

E6×Horizontal GUT models can solve some problems in MSSM.

We analyze the Lepton Flavor Violations.

Parameter independent predictions

Final state lepton have right-handed chirality.

There are large parameter region in which LFV decays can be discovered in near future experiments.

< 250 GeV

KEKB or super-KEKB

< 300 GeV

MEG experiment

We analyze the CP asymmetry in rare B decays.

Gluino and chargino always interfere with same sign, which makes CPA large enough to be able to detect in future experiments.

Deviations from SM of Time Dependent CP Asymmetry of Bdφ,η’ Ks:


Numerical results2

finite

decoupling

non decoupling

(preliminary)

Numerical Results

total

total

chargino

chargino

gluino(C8)

gluino(C8)

gluino(C3-6)

gluino(C3-6)

chargino:

gluino(C8):

Deviations from SM can be large(~±0.15) and non decoupling for m !!


Neutrinos

Neutrinos

Right-handed neutrino masses:

Seasaw mechanism:

Mass scale:

decouple


Lepton flavor violation2

e

Left-handed

Right-handed

e

Lepton Flavor Violation

Lepton Flavor Violations (LFVs) are good process for search the New Physics, because LFV processes are forbidden in Standard Model.

In E6 models, LFV processes take place through the off-diagonal entries respectively.

We can get parameter independent prediction,

Since 10 of SU(5) contain not , final state lepton have right-handed chirality. We can check this by measuring angular distribution of final state lepton.

spin

+

+

spin

+

+


E 6 gut models and fcnc processes

Propagator suppression increase, but also mass difference increase.

As a result, both transition rate remain finite, and don’t decouple!

Non Decoupling Features

If we raise overall SUSY scale m …


Characteristic feature of decay

e

Right-handed

Left-handed

e

Characteristic Feature of Decay

Chirality flip is required from operator form.

Chirality flip take place at first vertex and intermediate state is right-handed.initial lepton=left-handed,final lepton=right-handed

spin

spin

We can check this feature experimentally by measuring the angular distribution of final state lepton for spin direction of initial lepton.


Numerical results3

Numerical Results

Non decoupling features

In > 800 GeV region, the Branching ratios are independent of .


Time dependent cp asymmetry

Time Dependent CP Asymmetry


B d k s k s

(SUSY)

Bd φKs, η’Ks

Loop = SM +NP

SM (>>SUSY 31 transition.)


E 6 gut models and fcnc processes

OPE


Gluino chargino interference

Gluino-Chargino Interference

Gluino:

Chargino:

=

  • Chargino contribution have a same CP phase as gluino’s one.

  • Strong interference (additive or negative)


Numerical results4

(preliminary)

Numerical Results


B s constrant

bsγ constrant

Chargino

with θSUSY

Chargino

with CKM

Charged Higgs

b  sγ constraint requires large SUSY phase.


E 6 gut

decouple

decouple

at low energy:

Guisey-Ramond-Sikivie,

Aichiman-Stech, Shafi,

Barbieri-Nanopoulos,

Bando-Kugo,…

E6 GUT

Symmetry Breaking:

Fields and Rep.:

E6 GUT:

MSSM:

generation


E 6 gut models and fcnc processes

E6 × R parity invariant interactions :

SM interactions

assumption


E 6 gut1

down

charged lepton

M.Bando, N.Maekawa. 01

N.Maekawa, T. Yamashita 02

E6 GUT

assumption

up sector

Good :for up sector due to the assumption

Bad :for down and charged lepton sectors

Desired Yukawa structures are obtained in E6 GUT model !!


Up quark mass

Up quark mass ?

Models:

Experiments:

eigenvalues

Disagreement !?

Naïve order of up quark mass is larger than the experimental value about 10.


Fcnc induced edm

Im

Exp. Bounds require

< 10-2 .

FCNC induced EDM

finite

Non decoupling !


Gauge invariant interactions

Gauge invariant Interactions

SU(5) invariant Yukawa interactions :

SU(5) GUT relations :

Not Bad

at GUT scale (1016GeV)


So 10 gut

: SO(10) spinor

: SO(10) vector

SO(10) invariant interaction :

SO(10) GUT relation :

: at GUT scale

SO(10) GUT

SU(5) representations:

Grand Unified Theories unify not only the forces but also matters and interactions !!


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