E 6 GUT Models and FCNC Processes

EE66 GUT Models GUT Modelsandand

FCNC Processes FCNC Processes Kazuki SakuraiKazuki Sakurai

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

(Nagoya Univ.)(Nagoya Univ.)

2007/8/4 SI07@Fujiyoshida

PlanPlanI. Introduction I. Introduction

II. EII. E66 GUT and Horizontal Symmetry GUT and Horizontal Symmetry

III. Search for EIII. Search for E66×Horizontal GUT ×Horizontal GUT

-- Lepton Flavor Violation -- Lepton Flavor Violation

-- CPA in rare B meson decay -- CPA in rare B meson decay

IV. Summary IV. Summary

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

Problems in MSSMProblems in MSSM

Universal sfermion massesUniversal sfermion masses

Large SUSY breaking scaleLarge SUSY breaking scale

Not large stop massesNot large stop masses

SUSY Flavor ProblemSUSY Flavor ProblemGenerally, SUSY breaking terms brake flavor symmetry. They generate too large FCNCs.

Little Hierarchy ProblemLittle Hierarchy Problem

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

Suppressed SUSY CP phasesSuppressed SUSY CP phases


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

Horizontal SymmetryHorizontal SymmetryFlavor symmetry is natural idea, in order to realize the universal sfermion mauniversal sfermion masses.sses.

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!!

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

in SO(10), E6

SU(2)H

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

Horizontal sym. can explain smallness of Yukawa couplings!!

Horizontal Symmetry Horizontal Symmetry However,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.

EE66 Unification UnificationE6 GUT models are interesting, because…

-- all one generation quarks leptons are unified into 2727.

decouple

-- realistic Yukawa hierarchies are obtained.

Low energy three 55(Dc L) of SU(5) come from

only first two generation of 2727 not 272733.

Guisey-Ramond-Sikivie,Aichiman-Stech, Shafi,Barbieri-Nanopoulos,Bando-Kugo,…



decouple



only first two generation of 2727 not 272733.

up sector:


Cabibbo angle



decouple



only first two generation of 27 27 not 272733.

up sector:

down &charged lepton:


Cabibbo angle



decouple



only first two generation of 27 27 not 272733.

up sector:

down &charged lepton:

neutrino sector:


Cabibbo angle

Horizontal Symmetry on EHorizontal Symmetry on E66N.Maekawa. 02, N.Maekawa, T.Yamashita 04

Horizontal Symmetry on EHorizontal Symmetry on E66

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

No LFV problem due to full universality in !!

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

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

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

Problems in MSSMProblems in MSSM

Universal sfermion massesUniversal sfermion masses


Not large stop massesNot large stop masses

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

Little Hierarchy ProblemLittle Hierarchy Problem

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

Suppressed SUSY CP phasesSuppressed SUSY CP phases


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

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

Search for ESearch for E66×Horizontal GUT×Horizontal GUTNext question is,how can we confirm this model experimentally?

[ 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

Lepton Flavor ViolationLepton Flavor Violation

Lepton Flavor Violation 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-hright-handed chiralityanded chirality.. We can check this by measuring angular distribution of final state lepton.

Left-handed

Right-handed

spin

spin

e

e+

++

+

Can we discover the LFVs Can we discover the LFVs at future experim at future experim

ents?ents?

(exp. bound)

8105.4

super-KEKB

11100.1 (exp. bound)

MEG experiment

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

may be discovered in MEG, If 　　 < 300GeV.

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

CP asymmetries CP asymmetries in rare B meson decayin rare B meson decay

CP asym. of BCP asym. of BφKφKss, B, Bη’Kη’KssTime dependent CP asymmetry of BφK, Bη’K are composed of two part, B-Bbar mixing part and direct decay part.

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

gluino:

chargino:

0.68 (SM prediction)

SM predictions may deviate from experiments.

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

Gluino and Charginoare always interfere with same sign!

in this model.

Numerical ResultsNumerical Results (preliminary)

tota

l

tota

l

chargino chargino

gluino(C8)

gluino(C8)gluino(C3-6)gluino(C3-6)

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


Scanning in SUSY CP phase

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

SummarySummaryE6×Horizontal GUT models can solve some problems in MSSM.

Final state lepton have right-handed chirality.

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

KEKB or super-KEKB < 250 GeV

MEG experiment < 300 GeV

We analyze the Lepton Flavor Violations.

Parameter independent predictions

We analyze the CP asymmetry in rare B decays.

Deviations from SM of Time Dependent CP Asymmetry of Bdφ,η’ Ks:

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


tota

l

tota

l

chargino chargino

gluino(C8)

gluino(C8)gluino(C3-6)gluino(C3-6)

decoupling

gluino(C8):

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

chargino:

non decoupling

finite

NeutrinosNeutrinosRight-handed neutrino masses:Right-handed neutrino masses:

Seasaw mechanism:Seasaw mechanism:

decoupleMass scale:Mass scale:

Lepton Flavor Violation 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 right-handed chiralitychirality.. We can check this by measuring angular distribution of final state lepton.

Left-handed

Right-handed

spin

spin

e

e+

++

+

Non Decoupling FeaturesNon Decoupling Features

If we raise overall SUSY scale m …

Propagator suppression increase, but also mass difference increase.

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

Characteristic Feature of Characteristic Feature of Decay Decay

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

Chirality flip is required from operator form.

ie jep

ppq

p

Right-handed

Left-handed

spin

spin

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

e

e

Numerical ResultsNumerical Results

Non decoupling features

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

Time Dependent CP Time Dependent CP AsymmetryAsymmetry

BBdd φK φKss, η’K, η’Kss

SM (>>SUSY 31 transition.) Loop = SM + NP

(SUSY)

OPEOPE

…

Gluino-Chargino InterferenceGluino-Chargino InterferenceGluino: Chargino:

=

Chargino contribution have a same CP phase as gluino’s one. Strong interference (additive or negative)

Numerical ResultsNumerical Results(preliminary)

bbsγ constrantsγ constrant

Charged Higgs

Chargino with CKM

Chargino with θSUSY

b sγ constraint requires large SUSY phase.

EE66 GUT GUTSymmetry Breaking:

Fields and Rep.:


generation

MSSM: E6 GUT:

at low energy:

decoupledecouple

E6 × R parity invariant interactions :

SM interactions

assumption

EE66 GUT GUT M.Bando, N.Maekawa. 01N.Maekawa, T. Yamashita 02

assumption

up sector

downcharged lepton

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 ?

eigenvalues

Experiments:Models:

Disagreement !?

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

FCNC induced EDMFCNC induced EDM

finite

Non decoupling !Non decoupling !

Im

Exp. Bounds require < 10-2 .

1 0 1 2 3

1.5

1

0.5

0

0.5

1

1.5

2

Gauge invariant InteractionsGauge invariant Interactions

SU(5) invariant Yukawa interactions :

SU(5) GUT relations :

at GUT scale (1016GeV)

Not BadNot Bad

SO(10) GUTSO(10) GUT

: SO(10) spinor : SO(10) vector

SU(5) representations:

SO(10) invariant interaction :

SO(10) GUT relation :

: at GUT scale

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

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E 6 GUT Models and FCNC Processes