Walking on the Weak Scale with/without

Extra Dimensions

K. Yamawaki

Oct. 10-11, 　２００５ @KIAS-KAIST WORKSHOP

α α

β(α)β(α)

UVFP IRFP

(Q)α ≈ Const. α≈*

Walking/Conformal Coupling

Large Anomalous Dimensions

α α

β(α)β(α)

UVFP IRFP

(Q)α ≈ Const. α≈*

Walking/Conformal Coupling

)

PART I WALKING

WITH

MANY FLAVORS

PART II

Walkingwith

Extra Dimensions

References:

• Walking with Many Flavors (Large Nf QCD) M. Harada, M. Kurachi & K.Y., 　 hep-ph/0509193 　　　　 　　　　 PR D70 (2004) 033009-(1-11) PR D68 (2003) 076001-(1-16) V.A. Miransky & K.Y., PR D55 (1997) 5051

• Walking with Extra Dimensions H. Fukano & K.Y. , hep-ph/0508065 M. Hashimoto, M. Tanabashi & K. Y., PR D69 (2004) 076004-(1-23) PR D64 (2001) 056003-(1-19) V.P. Gusynin, M. Hashimoto, M. Tanabashi & K. Y. , PR D70 (2004) 096005-(1-32) 　 　　　　　　　　　　　　　 PR D65 (2002) 116008-(1-25)

　

• Walking/Conformal DSB (before 1996) K. Y., “Dynamical Symmetry Breaking with Large Anomalous Dimension”,

(Cheju Symposium, July 1995) hep-ph/9603293

)

PART I WALKING

WITH

MANY FLAVORS

ORIGIN of

MASS ?

mZ,Wmq,l

gYg1,2

• Fundamental Parameter ?

• Dynamically Generated ?

What is Higgs ?Origin of

Weak Scale

In the Past …

Macroscopic Microscopic

Superconductor

Ginzburg-Landau Bardeen-Cooper-Schriefer

φ (ψ↑ψ↓)

Cooper PairOrder parameter

Spontaneous Symmetry Breaking

Hadron Physics

Linear Sigma Model

σ

π

<σ> 　 = 　 fπ ＝　 93 　 MeV

QCD

Compositeness/UnderlyingTheory

h

Underlying QCD

2. Technicolor S. Weinberg (1976)L. Susskind (1979)

X 2600

Technicolor: a Scale-Up of QCD

FCNC

qR,lR

qL,lL

FL

FR

X

FL

qL,lL

qR,lR

FR

dd

Mass of Quarks/Leptons

ETC

Needs 103 enhancement

FCNC Problem :

Light Pseudo NG Bosons

Typical Model:

Qiα

Li

qiα

li

SU(8)L x SU(8)R

Farhi, Susskind (1979)

82 – 1 = 63 NG Bosons: 3 MW,Z

60 psuedo NGs Qbar L m2 ~ αc ΛTC2

Qbar Q - 3 Lbar L

τα m2 ~ α1,2 ΛTC2

P0,P0’ m2 ~ (1/ΛETC2 ) 　・ΛTC

６

10-6 ~ GeV2

techniaxion

~ αemΛQCD

2

- - - - - - - -++

Anomalous Scaling B. Holdom (1981)

QCD

3. Walking/Conformal Technicolor

・ K.Y., Bando, Matumoto (1986)

・ Appelquist, Karabali, Wijewardhane (1986)

・ Akiba, Yanagida (1986)

(Holdom (1985))

Schwinger-Dyson Gap Equation

+ UVBC & IRBC

Oscillating Sol= SSB Solution

α ~ const ( ＞ αcr)

OPE

DSB solution

≈ Fixed point

Quasi-conformal

Electroweak Constraints

S(exp)=L10= 0.32 ±0.04 (QCD)S(pert)=NDNc /(6π) 0.16 (QCD)

S(exp) < 0.1?

Walking

Solves S,T,U

?FCNC

4 ． Large Nf QCD

Realistic Field Theoretical Model of

Walking/Conformal Technicolor

IR Fixed Point

Banks, Zaks 　（１９８２）

IR Fixed Point

``Conformal Window’’

8.05 < Nf < 16.5

Nf Nf

Chiral Symmetry Restoration at

SD equation

Banks, Zaks 　（１９８２）

Appelquist,Terning,Wijewardhana (1996)

Miransky scaling

Conformal Phase TransitionMiransky & K.Y. (1997) Ginzburg-Landau

５ . , S M. Harada, M. Kurachi & KY, M. Harada, M. Kurachi & KY, 　　

hep-ph/0509193 hep-ph/0509193 　　　　 　　　　 　　　 　　　 PRD68 (2003) PRD68 (2003)

076001-(1-16)076001-(1-16) 　　　　 　　　　 　　　 　　　 PRD70 (200PRD70 (200

4) 033009-(1-11)4) 033009-(1-11)

(Improved) Ladder SD & BS Equations

Harada, Kurachi, KY (2004)

Works in Real-life QCD

Artificial cutWalking/Conformal

Harada, Kurachi, KY (2004)

Miransky scaling

Nf crit= 11.9

αcr= π/4=0.785

０

０

Walking

S parameter ?

０．１４

By 　 simply adjusting Nc, Nf

Nf Nf cr

S < 0.1

6. Walking/Conformal Technicolor with Many Flavors

Straightforward Calculation based on DS & IBS Equations (improved ladder)

near Conformal Window

By adjusting NTC, ND

●

●

●

●

●

• Need data for

α ｃｒ ＜ α ＊ ＜０．８９

NTC≠3 (future work)

Example:

NTC=3, ND=Nf/2=6 α*= 6π/25 < αcr= π/4=6π/24

Higher order corrections to SD Eq. αcr - (1- 20%)

Appelquist, Lane & Mahanta (1988)

αcr= π/4=6π/24 　　 - (4% - 4.65%)

（ Nfcr =11.9)

Nf crit= 12.06

αcr= 0.733 < π/4

Miransky scaling

Non-running case

Nf crit= 11.9

αcr= π/4=0.785 >0.733

Non-running case

Walking on the Weak Scale with/without

Extra Dimensions

K. Yamawaki

Oct. 10-11, 　２００５ @KAIST-KIAS Workshop

PART II

Walkingwith

Extra Dimensions

α

β(α)

UVFP

(Q)α ≈ Const. α≈*

Walking/Conformal Coupling

Top Mode Standard Modelwith

Extra Dimensions

H. Fukano and K.Y. hep-ph/0508065 M. Hashimoto, M. Tanabashi and K. Y. PR D69 (2004) 076004-(1-23) D64 (2001) 056003-(1-19) V.P. Gusynin, M. Hashimoto, M. Tanabashi and K. Y. PRD70 (2004) 096005-(1-32) 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 D65 (2002) 116008-(1-25) 　

ORIGIN of

MASS ?

mZ,Wmq,l

gYg1,2

≪

Top Quark Condensate (Top Mode Standard Model)

Miransky,Tanabashi 　 & K.Y. (1989) Nambu (1989)Bardeen, Hill & Lindner (1990)

Miransky,Tanabashi & K.Y. (1989)Bardeen, Hill & Lindner (1990)

Explicit Model　Explicit Model　(gauged NJL model)

Gtb: t b mbU(1)A

Σ(p)=gt

+t t

t t

+(b)

+

tt tt t

(gb) (b)

(b)(b)

(b) (b) (b)(b)(b)

g, BΣ

Σ

(Improved) Ladder SD Equation

κ

g

β(g)

UVFP

(Q)g ≈ Const. ≈ g*

NJL Model

m =Σ(p)=g

+

Σ = m

g

g

1

1

1

1 1

Λ↑

+ IRBC, UVBC

SSB Sol. Even for

Gauged NJL Model

OPE

NJL

Gauge

Kondo, Mino & K.Y. (1989)

Appelquist, Soldate, Takeuchi & Wijewardhana (1989)

+ gtgb

gt

+

+ +

gb

U(1)Y

Decay const. of composite NG boson

given

(Pagels-Stokar formula)

Miransky,Tanabashi & K.Y. (1989) Bardeen, Hill & Lindner (1990)

Compositeness Conditions

RG EquationsSD Equations

Pagels-Stokar Formula

equivalent

SM form

Boundary cond. of SM RGE

(SD Equation)

Incl. 1/Nc subleading

Problems:

・ Origin of Four-fermion Interactions?

・ Realistic Top Mass?

The origin of the four-fermion interactions.

KK-modes of gluon/B

KK-modes of top quark.

The realistic top quark mass .

A most attractive improved scenario is TMSM with extra dimensions.

Cheng, Dobrescu & Hill (2000)Arkani-Hamed, Cheng, Dobrescu & Hall (2000)

Gauge Theories with Extra Dimensions

Dimensionless coupling: -compactification

UVFPHashimoto, Tanabashi & K.Y. (2001)

Q

D→ 4

3-brane (4D)

2. TMSM in 6D 2. TMSM in 6D withoutwithout four-fermion four-fermion interactionsinteractions

3-rd generationgauge bosons

1-st and 2-nd generations are fixed on the 3-brane

3-brane (4D)

Nonlocal gauge

SSB Solution

Miransky Scaling

Conformal Invariance of SD Eq. at UVFP

The runnings of τ-condensation

No condensation

Gusynin, Hashimoto, Tanabashi and K.Y. (2002)

Improved Ladder-SDE &

Non-local gauge

Hashimoto, Tanabashi and K.Y (2003)In the real world

TMSM in 6D without four-fermion interactions

7D-gluon-model

8D-gluon-model

3. TMSM in 6D 3. TMSM in 6D withwith four-fermion four-fermion interactionsinteractions

We consider two models (6D is on )

7D 6D7D is comapctified on

Only the gluon can propagate in 7D.

8D 6DOnly the gluon can propagate in 8D.

8D are comapctified on

7D-gluon-model

KK-decomposition

Gluon = zero mode + Kaluza-Klein modes

7D 6D-massless gluon

6D-massivegluons (KK-gluons)

7D is compactified on

Four-fermion interaction in 6DKK-gluon exchange

KK-gluon

The gauged NJL-dynamics in 6D

Gusynin, Hashimoto, Tanabashi and K.Y. (2004)

In the broken-phase

Broken

Sym.

We expect is a free parameter.

: induced four-fermion coupling in 6D

Dimensionless four-fermion coupling in D-dim.:

UVFP

Up to coefficients

7D

-compactification has a free parameter.

-compactification doesn’t have a free parameter.

brane positionbrane position

-compactification

5-brane (6D-bulk)

0.636allowed region

Top quark can condense &

7D-gluon-modelno tau condensation

But, top quark cannot condensewithout tau condensate.

Sym.

In a manner similar to ,

8D-gluon-model

7D-gluon-model

KK-gluon four-fermion interactions in 6D

8D are compactified on

Numerically,

1.42

1.25lowest-KK effect

Therefore,

We need

In our model, brane position plays the role of a free parameter.

As long as , we can get

• top quark condensation.• top quark mass is by the free parameter.

no tau condensation

1.42 allowed region

Top quark can condense without tau condensation!!

8D-gluon-model

Sym.

In tMAC scale, top quark can condense without tau condensation.

scale is tMAC

τ-condensationtMACNo condensation

4. Mass of top quark and Higgs 4. Mass of top quark and Higgs We use the RGEs for and with

and are defined asBardeen, Hill & Lindner (1990)

Cf. experimental value

Higgs mass in our model

hep-ph/0412238 at LHC

Higgs will be discovered in

Immediately!!!

5.Summary5.Summary1. TMSM in 6D with four-fermion interactions.2. The four-fermion interactions are induced by gluons living in 8D bulk.3. Thanks to the four-fermion interactions & brane positions (free parameter), we can get scale : 4. Result

tMAC

5. How do other fermions obtain their masses ?

’t Hooft flavor determinant (8D color instanton) ?

Pati-Salam gauge ?

Horizontal gauge sym. ? ETC