Dynamical Symmetry Breaking Dynamical Origin of … · Dynamical Symmetry Breaking with Large...
Transcript of Dynamical Symmetry Breaking Dynamical Origin of … · Dynamical Symmetry Breaking with Large...
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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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To be open in March, 2011
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ORIGIN
of
MASS ?
LHC
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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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SD & IBS Eqs.
Ladder QCD