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Conformal Higgs, or Technidilaton
- Composite Higgs at Conformal Phase Transition
K. Yamawaki
@Lorentz Center Aug. 26, 2009
SM Higgs is Nice
○ simplicity (technically)○ renormalizability○ unitarity
SM Higgs is Bad
× boring× m2<0 (tachyon)× triviality × many parameters (Yukawa)× naturalness
Dynamical Symmetry Breaking (Technicolor, top quark condensation, composite W/Z, etc)
Extra dimension
Nambu (1960)
mN
N
N N
N
Attractive forces(BCS instability)(Tachyon)
Gauge theories:
Dim. transmutation
Log separation
Walking/Conformal Technicolor
a la Banks-Zaks IRFP
UV
IRindependent
Conformal sym
IRFT UVFT
β(α)
IRFP
1. Introduction
2.Walking/Conformal Technicolor
3.Conformal Phase Transition: Gross-Neveu Model Gauged NJL Model as W/C TC Phase Diagram of Large Nf QCD
4. Conformal Higgs, or Technidilaton
5. Various Issues 6. Conclusion
Miransky-K.Y. (1997)
FCNC
qR,lR
qL,lL
FL
FR
X
FL
qL,lL
qR,lR
FR
dd
Problems:
Mass of Quarks/Leptons
ETC
Needs 103 enhancement
Walking/Conformal Technicolor
・ K.Y., Bando, Matumoto (1986)
・ Appelquist, Karabali, Wijewardhane (1986)
・ Akiba, Yanagida (1986)
(Holdom (1985))
Ladder Schwinger-Dyson Equation: Scale-invariant
Scale Invariant Technicolor Model and a Technidilaton.Koichi Yamawaki (Nagoya U.) , Masako Bando (Kyoto U.) , Ken-iti Matumoto (Toyama U.) . DPNU-85-47, Dec 1985. 13pp. Published in Phys.Rev.Lett.56:1335,1986. (*Title changed in journal*)
at
Maskawa-Nakajima Solution (1974)
``Conformal Window’’
Nfcr < Nf < 11Nc/2
Nf Nf
Chiral Symmetry Restoration at
SD equation
Appelquist,Terning,Wijewardhana (1996)
Walking
essential singularity at
Order parameter
1. No light spectrum for
2. No parameter s.t.
Ginzburg-Landau
・ 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
D (2<D<4) –dimensional Gross-Neveu Model
Y. Kikukawa - K.Y. (1990)
UV=IRrepulsive
repulsive
No bound states
Gauged NJL Model as a W/C TC
Resembles Large Nf QCD with
TC-inducedETC-origin
Bardeen-Leung-Love (1986)
Induced
(induced four-fermi)
Phase Diagram
Kondo-Mino-K.Y. (1988)Appelquist-Soldate-Takeuchi-Wijewardhana (1988)
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
Phases in Large Nf QCD
First order p.t.
Banks-Zaks (1982)
Kogut-Susskind fermion
bulk p.t. (first order)
Coulomb phase
?
Conformal Higgs, or Techni-dilaton
• Mass estimate (SD via gauged NJL)
• Mass estimate (SD + BS in Large Nf QCD)
incl. Ps, V, A spectra
(Improved) Ladder SD & BS Equations
Straightforward Calculation
SD + IBS
SD + BS
S parameter
Light Spectrano induced/ETC four-fermino mixing with glueball, multi-body bound statesno KM-’t Hooft determinant
Harada-Kurachi-K.Y. (2003-2006)
Search for Higgs• Present Lower Limit ( LEP)
m H > 114 GeV/c2
• LHC ( 2009~ ) :
Could be searched for m H < 1 T eV/c2
130 180
SM ( No New Physics) Composite SUSY
114 GeV/c2
500
Techni-dilaton ?
Various Issues
2. Determination of
3. Light spectrum
1. Existence of IR fixed point
techni-dilaton
4. S Parameter
・・・・
Lattice Appelquist et al, Sannino et al, Lombardo et al, Onogi et al (Hayakawa et al), ……
(Phenomenological issues: mt, explicit ETC, )