Anomalous U(1) GUT

Toshifumi YAMASHITA

(Kyoto University)

2004/12/72004/12/7@UC Irvine@UC Irvine

IntroductionIntroductionAnomalous U(1) GUTAnomalous U(1) GUTHorizontal symmetryHorizontal symmetrySummary and Summary and DiscussionDiscussion

SUSY-GUT fascinating extension of SM

gauge coupling unification (GCU)

Introduction

Higgs? hierarchal Yukawa?

Proton decay?

SUSY?

•unifications of forces and of matter•charge quantization•stabilization of the weak scale

Introduction

The Hierarchy problem is solved. Gauge Coupling Unification

But ・・・ DT Splitting problem Proton decay (vs GCU) Fermion Yukawa SUSY flavor problem

U(1)A

Flavor Symm.

SUSY-GUT

Almost all the problem can be solved!!

: order of magnitude

• no fine-tuning• number of parameters

•all the possible interactions•order 1 coefficients

“generic interaction”

Anomalous U(1) GUT

Assumptions

a few ( # of fields) order of magnitude

( # in SM) : precise analysis

• : GUT singlet operator, : charge• : VEV of the Froggatte-Nielsen field•in a mass unit, the cutoff scale

vacuum structure

Anomalous U(1) GUT

Assumptions

mass term for and : factorization

<Z> may break GUT symmetry

•FN mechanism

•SUSY-zero mechanism

•“Natural Gauge Coupling UnificationDT SplittingDW VEV

“Generic interaction”

hierarchal Fermion Yukawa

proton decay

Anomalous U(1) GUT M.Bando N.Maekawa and T.Y.

Overview

Anomalous U(1) GUT

Example of E6 model PTP 107, 1201 (2002)N.Maekawa and T.Y.

•Gauge Coupling Unification•Doublet-Triplet Splitting

Anomalous U(1) GUT

Example of E6 model PTP 107, 1201 (2002)N.Maekawa and T.Y.

Horizontal Symmetry

How to break SUSY?

S.Martin Hep-ph/9709356

(1,2)-components of sfermion mass, , should be suppressed.

“SUSY flavor

problem”

PL B561, 273(2003)N.Maekawa

•degenerate•alignment•decoupling

given from in flavor basis by

non-Abelian horizontal symmetry

is in mass basis

If 1st and 2nd generations belong to a single multiplet, they can be degenerate.

Solutions to SUSY flavor problem

Horizontal Symmetry

degenerate

3rd should also be degenerate.

E-twisting

Even if , becomes large.

horizontal symmetry breaking

Horizontal Symmetry

Because fermion Yukawa is not symmetric.

The degeneracy is lifted by

Large mixing Large (1,2) element

SU(2)E

model

SU(2)E :

Horizontal Symmetry

PLB561, 273(2003)N.Maekawa

SU(2)H :

constraints

Horizontal Symmetry

RG factor :

(in MSSM)

model

Horizontal symmetry in Higgs sector

Horizontal Symmetry JHEP 0407 (2004) 009N.Maekawa and T.Y.

Inspired by the decomposition :

Summary and Discussion

“Anomalous U(1) GUT”

Non-abelian horizontal symmetry

A road toward realistic E8 Unification (?)

•DT Splitting through DW VEV•Realistic Fermion Yukawa•“Natural Gauge Coupling Unification”

•SUSY flavor problem can be solved.•Horizontal symmetry in Higgs sector.

•Low energy theory of string theory•Anomaly Green-Schwartz mechanism•Froggatte-Nielsen mechanism

Introduction

Anomalous U(1) Symmetry

Introduction

Anomalous U(1) Symmetry

Ex)

•Low energy theory of string theory•Anomaly Green-Schwartz mechanism•Froggatte-Nielsen mechanism

all come from and .

Anomalous U(1) GUT

sector in E6 model

massless :

large mixing

E-twisting

mild hierarchy in sector !!

mass

M.Bando and T.Kugo

Anomalous U(1) GUT

SUSY-zero mechanism

: analytic does not appear in .

Only positively charged operators can appear.

In the effective theory below ,

Anomalous U(1) GUT

SUSY-zero mechanism

Only positively charged operators can appear.

In the effective theory below ,

Ex) Adjoints of SO(10) :

Dimopoulos-Wilczek VEV DTS

Anomalous U(1) GUT

Gauge Coupling UnificationPRL 90, 121801 (2003)N.Maekawa and T.Y.

•We can calculate the Flows.

•When we recalculate the Flows by MSSM from the low energy values, three couplings meet at the cut-off scale if .•When , Proton Decay via Dim.5 operators are suppressed.

GCU in the minimal SU(5) SUSY-GUT!!

Gauge Coupling Unification

Anomalous U(1) GUT

PRL 90, 121801 (2003)N.Maekawa and T.Y.