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
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