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Quest for the Dynamical Origin of Mass K. Yamawaki (KMI, Nagoya) Feb.10, 2011@ MISC, Kyoto Sangyo Dynamical Symmetry Breaking with Large Anomalous Dimension

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Page 1: Dynamical Symmetry Breaking Dynamical Origin of … · Dynamical Symmetry Breaking with Large Anomalous Dimension. To be open in March, 2011. ORIGIN of ... Haba-Matsuzaki-KY, in preparation

Quest for the

Dynamical Origin of Mass

K. Yamawaki (KMI, Nagoya)

Feb.10, 2011@ MISC, Kyoto Sangyo

Dynamical Symmetry Breaking

with Large Anomalous Dimension

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To be open in March, 2011

Page 3: Dynamical Symmetry Breaking Dynamical Origin of … · Dynamical Symmetry Breaking with Large Anomalous Dimension. To be open in March, 2011. ORIGIN of ... Haba-Matsuzaki-KY, in preparation

ORIGIN

of

MASS ?

LHC

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Page 5: Dynamical Symmetry Breaking Dynamical Origin of … · Dynamical Symmetry Breaking with Large Anomalous Dimension. To be open in March, 2011. ORIGIN of ... Haba-Matsuzaki-KY, in preparation

mZ,Wmq,l

gYg1,2

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h

Tachyon!?

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Tachyon !

Gell-Mann-Levy (1960)

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Spontaneous Symmetry Breaking

was born as

Dynamical Symmetry Breaking

BCS Analogue Nambu-Jona-Lasinio (1960)

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(1948)

(``Higgs’’)

p

n

p

n

Λ

(1956)

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Miransky,Tanabashi and K.Y. (Dec. 1988)

Nambu (Feb. 1989)

Bardeen, Hill and Lindner (July, 1989)

Composite Higgs I

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Z0W± (QCD effects)

(+ other effects)

Refinements:

• Top seesaw

• Technicolor-assisted Topcolor (TC2)

• Top condensate in SM with extra

dimensions

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Essentially the samein QCD

Nucleon Quark

4-fermion int. Gauge int.

~~ ~ ~~

gluon

~ ~ ~

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Origin of Mass (Nucleon)

Linear Sigma Model

(Gell-Mann-Levy)QCD

tachyonAttractive force

(BCS instability)

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: Scale-invariant (Classical)

Scale-anomaly (Quantum)

Origin of Mass (QCD)

BCS-Nambu

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X 2600

Technicolor: a Scale-Up of QCD

Composite Higgs II

S. Weinberg (1976)

L. Susskind (1979)

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FCNC

qR,lR

qL,lL

FL

FR

X

FL

qL,lL

qR,lR

FR

Problems:

Mass of Quarks/Leptons

ETC

Needs 103 enhancement

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Anomalous Scaling Holdom (1981)

QCD

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Explicit Dynamics ?

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Walking/Conformal Technicolor

・ K.Y., Bando, Matumoto (Dec. 1985)

・ Appelquist, Karabali, Wijewardhane (June 1986)

・ Akiba, Yanagida (Jan. 1986)

(Holdom (Jan. 1985))

Ladder Schwinger-Dyson Equation

Maskawa-Nakajima Solution (1974)

Scale-invariant

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Schwinger-Dyson Gap Equation

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Scale-inv. form

Maskawa-Nakajima (1974)

(Ladder)

SSB solution

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0

Miransky scaling

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Walking/Conformal Technicolor

Large separation

Naturalness Conformal sym.

UVFP

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Realistic Dynamics for

?

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α

β(α)

IRFP

(Q)α ≈ Const. α≈ *

Walking/Conformal

Coupling

Large Nf QCD

0Nf

Banks, Zaks (1989)

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Caswell(1974)

Banks, Zaks(1982)

IR Fixed Point

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``Conformal Window’’ Nfcr < Nf < 11Nc/2

Nf Nf

Chiral Symmetry Restoration at

SD equation

Appelquist,Terning,Wijewardhana

(1996)

Walking

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UV

IR

Conformal sym

IRFT UVFT

IRFP

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QCD Walking/Conformal TC

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Conformal Phase Transition

Essential singularity

Miransky ScalingMiransky-K.Y. (1997)

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・usual QCD

・Gross-Neveu Model

: Repulsive four-fermion int.

(no bound states)

conformal

: scalar bound state (``Dilaton’’)

would-be NG boson

No bound states (unphysical)

Conformal sym. breaking

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D (2<D<4) –dimensional Gross-Neveu Model

Y. Kikukawa - K.Y. (1990)

UV=IRrepulsive

repulsive

No bound states

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・Gross-Neveu Model Conformal sym.

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Infrared free

conformal

Asymptotic free

Broken conformal

Conformal sym breaking

PCDC massive dilaton

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Gauged NJL Model as a W/C TC

Resembles Large Nf QCD with

TC-induced

ETC-originBardeen-Leung-Love (1986)

Induced

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(induced four-fermi)

Phase Diagram

Kondo-Mino-K.Y. (1988)

Appelquist-Soldate-Takeuchi-Wijewardhana (1988)

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Kondo-Shuto-K.Y. (1991)

Kodo-Tanabashi-K.Y.(1993)

Aoki-Morilawa-Sumi-Terao-Tomoyose(1999)

(continuous parameter)

(discrete parameter)

repulsive attractive

No bound states

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Broken phase

Conformal sym. Broken

Massive dilaton =Techni-dilaton

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Conformal Phase Transition

IR=UV

Conformal Sym

Naturalness

Techni-dilaton

(composite Higgs)

Miransky-KY (1997)

KY-Bando-Matumoto (1986)

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Conformal Higgs, or Technidilaton

Mass estimate (SD via gauged NJL)

Mass estimate (SD + BS in Large Nf QCD)incl. Ps, V, A spectra

Mass estimate (Holographic Method)

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Shuto-Tanabashi-KY (1990)

Shuto-Tanabashi-KY (1990)Carena-Wagner (1992)

M. Hashimoto (1998)

(PCDC)

1

Gauged NJL Model Calculations

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(Improved) Ladder SD & BS Equations

Straightforward Calculation

SD + IBS

SD + BS

S parameter

Light Spectrano induced/ETC four-fermi

no mixing with glueball, multi-body bound states

no KM-’t Hooft determinant

Harada-Kurachi-K.Y.

(2003-2006)

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Light Spectra (SD+HBS)Harada-Kurachi-KY (2003)

Nf=11.92 Nf=11.42

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Light Spectra (SD+HBS)Harada-Kurachi-KY (2003)

Kurachi-Shrock (2006)

S

A

V

Ladder

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Holographic Techni-DilatonHaba-Matsuzaki-KY (2010) , PRD

for

for

Erlich-Katz-Son-Stephanov; Da Rold-Pomarol (2005)

Hong-Yee; Piai (2006); Haba-Matsuzaki-KY(2008)

Improves OPE:

vz

(solution)

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Γ=0 Γ=5 Γ=10

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Ladder result

(one-family model)

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Techni-Dilaton at Conformal Edge

M. Hashimoto & KY (2010)

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PCDC

Pagels-Stokar formula

Massless TD = Decoupled TD

Dark Matter? -> Hong-Matsuzaki(2011)

for

Holographic estimate of In progress

Hashimoto-Matsuzaki-KY

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: Scale-invariant (Classical)

Scale-anomaly (Quantum)

Origin of Mass (W/C TC)

BCS-Nambu

``Conformal Symmetry’’

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Folklore:

Technicolor = Higgsless

(No light scalar)

Walking/Conformal Technicolor

Techni-dilaton

Approx. Conformal Symmetry

LHC

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•Yukawa coupling

•Gauge coupling (no tree vertex)

LHC Signature

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Various Issues

2. Determination of

3. Light spectrum

1. Existence of IR fixed point

techni-dilaton

4. S Parameter・・・・

Lattice !

(Phenomenological issues: mt, explicit ETC, )

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KMI理論計算機 2011.3月〜

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Light spectra(one family TC Fπ ~125GeV)

Techni-dilaton ~ 500 GeV

Techni-rho/a1 ~ 1.3 - 1.5 TeV

Holography (S<0.1)

w. technigluon condensate

・Techni-dilaton ~ 500-600 GeV

・Techni-rho/a1 ~ 3.5-4.0 TeV

Haba-Matsuzaki-KY, in preparation

Haba, poster session

Ladder

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Probing Composite Higgs in LHC

Walking/Conformal TC : Techni-dilaton

Top Quark Condensate : Top-sigma

Topcolor-Assisted TC (TC2):

Top-pion/Top-sigma

Top Seesaw: Top-sigma

Top-mode SM with Extra Dim. (D=6,8)

Bulk Composite Scalar Zero Mode

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Search for Higgs

Present Lower Limit (LEP)

mH > 114 GeV/c2

LHC (2009~ ):

Could be searched for mH < 1 TeV/c2

130 180

SM ( No New Physics) Composite SUSY

114 GeV/c2

500

Techni-dilaton ?

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Prof. Nambu’s reply to my congraturations

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Hidden Local Symmetries (HLS)

Composite Gauge Bosons

Bando-Kugo-Uehara-KY-Yanagida (1985)

M. Bando, T.Kugo, K.Y., Phys. Rep.

164(’88) 217

M. Harada, K.Y., Phys. Rep. 381(’03) 1

5-dimensional gauge theory as Hidden Local Symmeties

HLS

~ KK tower

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Hidden Local SymmetryReviews: M. Bando, T.Kugo, K.Y., Phys. Rep. 164(’88) 217 (tree)

M. Harada, K.Y., Phys. Rep. 381(’03) 1 (loop)

G/H ≈ Gglobal x Hlocal

≈ Gglobal x Glocal

≈ Gglobal x Glocal x Hlocal

≈ Gglobal x Glocal x Glocal x・・・

HglobalHglobal+local

ρ

ρ, a1

ρ, a1 , ρ’

π

mρ ∞

Bando – Kugo –KY (1986)

Bando – Kugo –KY (1988)

Heavy HLS Bosons Integrated out

Bando – Fujiwara –KY (1988)

Bando-Kugo-Uehara-KY-Yanagida (1985)

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arbitrariness=gauge symmetry

VL R

L RL R

L RL RV

L R

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Moose (Georgi 1986)

VL R

L RL R

Gglobal x Hlocal

Gglobal x Glocal

“3-site model”

“5-site model”

Deconstructed/Latticized

5-dimensional Gauge Field

・・

AdS/QCD, Holographic QCD

Higgsless Model, Little Higgs

HLS

Condensed Moose (Arkani-Hamed-Cohen-Georgi 2001)

G Gs G

G G

Cheng-Hill-Pokorski-Wang (2001)

Arkani-Hamed-Cohen-Georgi(2001)

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VL R

L RL R

Gglobal x Hlocal

Gglobal x Glocal

“3-site model”

“4-site model”

Deconstructed/Latticized

5-dimensional Flavor Gauge Field

AdS/QCD, Holographic QCD

ρ

ρ, a1 , ρ’

ρ, a1

Infinite Sequence of Linear Moose

Gglobal x Glocal x HlocalL RL R

Son-Stephanov(2004)

V “5-site model”

Bottom-up Approach

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Integrating out via Eq. Mot.5D Gauge Theory for Flavor Symmetry

Harada-Matsuzaki-KY (2006)

Infinite Sequence of Linear MooseSon-Stephanov(2004)

Sakai-Sugimoto(2005)

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ホログラフィック レシピ

4DSCT large Nc 極限 5DWCT ツリーレベル

演算子 : O

O の次元(p-form) :

生成汎関数:

Oのソース: J

5次元場 :

5次元質量:

5次元有効作用:

の紫外境界での値 : :

1). ϕの運動方程式を解く。2). ϕの古典解を作用S5[ϕ]に代入。3). ϕ0で作用S5[ϕ0]を汎関数微分する。

グリーン関数の計算方法

Witten, (1998),

Gubser, et al (1998)

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AdS 計量 :

赤外(IR)カットオフ zm (質量ギャップ) :

4次元演算子 & 5次元場

作用: SU(Nf) L× SU(Nf)Rゲージ理論 + bifundamental ϕ

演算子 O Oの次元 p 5次元場 5次元質量

3 1 LaM 0

3 1 RaM 0

3 − γm 0 ϕ (3-γm)(1+γm)/L2

Erlich et al (2005), Da Rold and Pomarol, (2005) Hong and Yee (2007),

Piail, (2007), KH etal (2008)

ハードウォール QCD と W/C TC 模型

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中性・質量0の実スカラー場

中性・質量0の実スカラー場 を手で導入 (Ref.

のように)

指数関数型の相互作用 :

作用:ハードウォール模型+ +相互作用

Operator O dim of O p Bulk field Bulk mass

4 0 0

Forkel (2007), Katz and Schwertz (2007)

IRBCUVBC = ソース

KH et al in preparation

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Walking

Conformal

Solves S,T,U

?FCNC

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http://pdg.lbl.gov/2009/reviews/rpp2009-rev-standard-model.pdf

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Electroweak Constraints

S(exp)=-16πL10= 0.32 ±0.04

(QCD)

S(pert)=NDNc /(6π)

0.16 (QCD)

S(exp) < 0.1?

3 Y ’

L R

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x

x

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Harada, Kurachi, K.Y. (2004)

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Page 81: Dynamical Symmetry Breaking Dynamical Origin of … · Dynamical Symmetry Breaking with Large Anomalous Dimension. To be open in March, 2011. ORIGIN of ... Haba-Matsuzaki-KY, in preparation

SD & IBS Eqs.

Ladder QCD