Conformal Higgs, or Technidilaton

- Composite Higgs at Conformal Phase Transition

K. Yamawaki

@Lorentz Center Aug. 26, 2009

ORIGIN

of

MASS ?

LHC

mZ,Wmq,l

gYg1,2

SM Higgs is Nice

○ 　 simplicity (technically)○ renormalizability○ unitarity

SM Higgs is Bad

×　 boring× m2<0 (tachyon)× triviality ×　many parameters (Yukawa)×　 naturalness

Naturalness

= =

SUSY

+

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

Large separation

Naturalness Conformal inv.

UVFP

Techni-dilaton

Walking/Conformal Technicolor

a la Banks-Zaks IRFP

UV

IRindependent

Conformal sym

IRFT UVFT

β(α)

IRFP

Conformal Phase Transition

IR=UV

Conformal Sym

Naturalness

Techni-dilaton (composite Higgs)

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)

X 2600

Technicolor: a Scale-Up of QCD

FCNC

qR,lR

qL,lL

FL

FR

X

FL

qL,lL

qR,lR

FR

dd

Problems:

Mass of Quarks/Leptons

ETC

Needs 103 enhancement

Anomalous Scaling Holdom (1981)

QCD

Explicit Dynamics ?

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)

Schwinger-Dyson Gap Equation

Scale-inv. form

Maskawa-Nakajima (1974)

（Ｌａｄｄｅｒ）

SSB solution

< 0

0

Miransky scaling

α ~ const ( ＞ αcr)

OPE

DSB solution

≈ Fixed point

Quasi-conformal

Realistic Dynamics for

?

α

β(α)

IRFP

(Q)α ≈ Const. α≈*

Walking/Conformal Coupling

Large Nf QCD

0Nf

Banks, Zaks 　 (1989)

Banks, Zaks 　（１９８２）

IR Fixed Point

``Conformal Window’’

Nfcr < Nf < 11Nc/2

Nf Nf

Chiral Symmetry Restoration at

SD equation

Appelquist,Terning,Wijewardhana (1996)

Walking

Conformal sym. broken

α

β(α)

IRFP

(Q)α ≈ Const. α≈*

Walking/Conformal Technicolor

Conformal Phase Transition

Essential singularity

Miransky Scaling

Miransky-K.Y. (1997)

essential singularity at

Order parameter

1. No light spectrum for

2. No parameter s.t.

Ginzburg-Landau

Ex: Chiral symmetry breaking (SD & BS eqs.)

: Order parameter

BS

SD

・ 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

・ Gross-Neveu Model

Conformal sym.

Infrared freeconformal

Asymptotic freeBroken conformal

Conformal sym breaking

PCDC massive dilaton

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

A=8/7

m=const. line (RG flow)

A=10 (walking)

Kondo-Shuto-K.Y. (1991)

A=100 (conformal)

Ginzburg-Landau

Broken phase

Conformal sym. Broken

Massive dilaton =Techni-dilaton

Phases in Large Nf QCD

First order p.t.

Banks-Zaks (1982)

Kogut-Susskind fermion

bulk p.t. (first order)

Coulomb phase

?

Conformal phase transition

Coulomb phase

Coulomb phaseMiransky-K.Y.(1997)

Deuzeman-Lombardo-Pallante (hep-ph/0904.4662)

Four-fermion coupling ?

Conformal Higgs, or Techni-dilaton

• Mass estimate (SD via gauged NJL)

• Mass estimate (SD + BS in Large Nf QCD)

incl. Ps, V, A spectra

Shuto-Tanabashi-KY (1990)

Shuto-Tanabashi-KY (1990)Carena-Wagner (1992)M. Hashimoto (1998)

(PCDC)

1

(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)

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

Nf=11.92 Nf=11.42

　　　 Kurachi-Shrock (2006) 　　　

S

A

V

SD

Light spectra (one family TC Fπ ~125GeV)

• Techni-dilaton ~ 500 GeV

• Techni-rho/a1 ~ 1.3 - 1.5 TeV

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, )

Prof. Nambu’s reply to my congratulations on Nobel prize

Dec. 8 (Tue.) - 11 (Fri.), 2009

http://www.eken.phys.nagoya-u.ac.jp/scgt09/

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6th NagoyaSCGTWorkshop

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