1. Conformal Higgs, or Technidilaton - Composite Higgs at Conformal Phase Transition K. Yamawaki @Lorentz Center Aug. 26, 2009

2. ORIGIN of MASS ? LHC

3. m Z,W m q,l gYgY g 1,2

4. SM Higgs is Nice ○ simplicity (technically) ○ renormalizability ○ unitarity SM Higgs is Bad × boring × m 2 <0 (tachyon) × triviality × many parameters (Yukawa) × naturalness

5. Naturalness == SUSY +

6. Dynamical Symmetry Breaking (Technicolor, top quark condensation, composite W/Z, etc) Extra dimension Nambu (1960) mNmN N NN N Attractive forces (BCS instability) (Tachyon) Gauge theories: Dim. transmutation Log separation

7. Walking/Conformal Technicolor Large separation NaturalnessConformal inv. UVFP Techni-dilaton

8. Walking/Conformal Technicolor a la Banks-Zaks IRFP UV IR independent Conformal sym IRFTUVFT β(α)β(α) IRFP

9. Conformal Phase Transition IR=UV Conformal Sym Naturalness Techni-dilaton (composite Higgs)

10. 1.Introduction 2.Walking/Conformal Technicolor 3.Conformal Phase Transition: Gross-Neveu Model Gauged NJL Model as W/C TC Phase Diagram of Large N f QCD 4. Conformal Higgs, or Technidilaton 5. Various Issues 6. Conclusion Miransky-K.Y. (1997)

11. X 2600 Technicolor: a Scale-Up of QCD

12. FCNC q R,l R q L,l L FLFL FRFR X FLFL q R,l R FRFR d Problems: Mass of Quarks/Leptons ETC Needs 10 3 enhancement

13. Anomalous Scaling Holdom (1981) QCD

14. Explicit Dynamics ?

15. 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*) Koichi YamawakiNagoya U.Masako BandoKyoto U.Ken-iti MatumotoToyama U. at Maskawa-Nakajima Solution (1974)

17. Schwinger-Dyson Gap Equation

18. Scale-inv. form Maskawa-Nakajima (1974) （Ｌａｄ ｄｅｒ） SSB solution < 0

19. 0 Miransky scaling

20. α ~ const ( ＞ α cr ) OPE DSB solution ≈ Fixed point Quasi-conformal

21. Realistic Dynamics for ?

22. α β(α)β(α) IRFP (Q)α ≈ Const. α ≈ * Walking/Conformal Coupling Large N f QCD 0 NfNf Banks, Zaks (1989)

23. Banks, Zaks （１９８ ２） IR Fixed Point

24. ``Conformal Window’’ N f cr < N f < 11N c /2 NfNf NfNf Chiral Symmetry Restoration at SD equation Appelquist,Terning,Wijewardhana (1996) Walking

25. Conformal sym. broken

26. α β(α)β(α) IRFP (Q)α ≈ Const. α ≈ * Walking/Conformal Technicolor

27. Conformal Phase Transition Essential singularity Miransky Scaling Miransky-K.Y. (1997)

28. essential singularity at Order parameter 1. No light spectrum for 2. No parameter s.t. Ginzburg-Landau

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

30. ・ 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

31. D (2<D<4) –dimensional Gross-Neveu Model Y. Kikukawa - K.Y. (1990) UV=IR repulsive No bound states

32. ・ Gross-Neveu Model Conformal sym.

33. Infrared free conformal Asymptotic free Broken conformal Conformal sym breaking PCDC massive dilaton

34. Gauged NJL Model as a W/C TC Resembles Large N f QCD with TC-induced ETC-origin Bardeen-Leung-Love (1986) Induced

35. (induced four-fermi) Phase Diagram Kondo-Mino-K.Y. (1988) Appelquist-Soldate-Takeuchi-Wijewardhana (1988)

36. 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

37. A=8/7 m=const. line (RG flow) A=10 (walking) Kondo-Shuto-K.Y. (1991)

38. A=100 (conformal)

39. Ginzburg-Landau

40. Broken phase Conformal sym. Broken Massive dilaton =Techni-dilaton

41. Phases in Large N f QCD First order p.t. Banks-Zaks (1982) Kogut-Susskind fermion bulk p.t. (first order) Coulomb phase ?

42. Conformal phase transition Coulomb phase Miransky-K.Y.(1997)

43. Deuzeman-Lombardo-Pallante (hep-ph/0904.4662) Four-fermion coupling ?

44. Conformal Higgs, or Techni-dilaton Mass estimate (SD via gauged NJL) Mass estimate (SD + BS in Large N f QCD) incl. Ps, V, A spectra

45. Shuto-Tanabashi-KY (1990) Carena-Wagner (1992) M. Hashimoto (1998) (PCDC) 1

46. (Improved) Ladder SD & BS Equations Straightforward Calculation SD + IBS SD + BS S parameter Light Spectra no induced/ETC four-fermi no mixing with glueball, multi-body bound states no KM-’t Hooft determinant Harada-Kurachi-K.Y. (2003-2006)

47. Light Spectra (SD+HBS) Harada-Kurachi-KY (2003) N f =11.92N f =11.42

48. Kurachi-Shrock (2006) S A V SD

49. Light spectra (one family TC F π ~125GeV) Techni-dilaton ~ 500 GeV Techni-rho/a 1 ~ 1.3 - 1.5 TeV

50. Search for Higgs Present Lower Limit （ LEP) ｍ H ＞ １１４ GeV/c 2 LHC （ 2009~ ） ： Could be searched for ｍ H ＜ 1 Ｔ eV/c 2 １３０１８０ SM ( No New Physics)Composite SUSY １１４ GeV/c 2 500 Techni-dilaton ?

51. 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: m t, explicit ETC, )

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

53. Dec. 8 (Tue.) - 11 (Fri.), 2009 http://www.eken.phys.nagoya-u.ac.jp/scgt09/ SCGT 88 SCGT 90 SCGT 96 SCGT 02 SCGT 06 6 th Nagoya SCGT Workshop See you @ ``Strong Coupling Gauge Theories in LHC Era’’