Walking on the Weak Scale with/without Extra Dimensions

1. Walking on the Weak Scale with/without Extra Dimensions K. Yamawaki Oct. 10-11,　２００５ @KIAS-KAIST WORKSHOP

2. Walking/Conformal Coupling β(α) β(α) UVFP IRFP α α ≈ ≈ α (Q) Const. α *

3. Walking/Conformal Coupling β(α) β(α) Large Anomalous Dimensions UVFP IRFP α α ≈ ≈ α (Q) Const. α *

4. PART IWALKING WITH MANY FLAVORS )

5. PART IIWalkingwith Extra Dimensions

6. References: • Walking with Many Flavors (Large Nf QCD) M. Harada, M. Kurachi & K.Y., hep-ph/0509193 PR D70 (2004) 033009-(1-11) PR D68 (2003) 076001-(1-16) V.A. Miransky & K.Y., PR D55 (1997) 5051 • Walking with Extra Dimensions H. Fukano & K.Y. , hep-ph/0508065 M. Hashimoto, M. Tanabashi & K. Y., PR D69 (2004) 076004-(1-23) PR D64 (2001) 056003-(1-19) V.P. Gusynin, M. Hashimoto, M. Tanabashi & K. Y. , PR D70 (2004) 096005-(1-32) PR D65 (2002) 116008-(1-25) • Walking/Conformal DSB (before 1996) K. Y., “Dynamical Symmetry Breaking with Large Anomalous Dimension”, (Cheju Symposium, July 1995) hep-ph/9603293

7. PART IWALKING WITH MANY FLAVORS )

8. ORIGIN of MASS ?

9. g1,2 gY mq,l • mZ,W

10. What is Higgs ? Origin of Weak Scale • Fundamental Parameter ? • Dynamically Generated ? In the Past …

11. Spontaneous Symmetry Breaking Microscopic Macroscopic Superconductor Ginzburg-Landau Bardeen-Cooper-Schriefer (ψ↑ψ↓) φ Cooper Pair Order parameter

12. Hadron Physics Linear Sigma Model QCD <σ>=fπ＝　93MeV σ π Compositeness/UnderlyingTheory

14. 2. Technicolor S. Weinberg (1976) L. Susskind (1979) h UnderlyingQCD

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

16. FL qR,lR FCNC FCNC Problem : ETC qL,lL FR Mass of Quarks/Leptons qR,lR FL X qL,lL FR dd Needs 103 enhancement

17. Light Pseudo NG Bosons Typical Model: Farhi, Susskind (1979) qiα Qiα Li li ΛQCD2 ~ αem SU(8)L x SU(8)R 82 – 1 = 63 NG Bosons: 3 MW,Z m2 ~ αc ΛTC2 60 psuedo NGs Qbar L Qbar Q - 3 Lbar L + - - - - + - - - - τα α1,2 ΛTC2 m2 ~ techniaxion ΛTC６ m2 ~ (1/ΛETC2 )　・ P0,P0’ 10-6 ~ GeV2

18. Anomalous Scaling B. Holdom (1981) QCD

19. 3. Walking/Conformal Technicolor ・K.Y., Bando, Matumoto (1986) ・Akiba, Yanagida (1986) ・Appelquist, Karabali, Wijewardhane (1986) (Holdom (1985))

20. Schwinger-Dyson Gap Equation

21. + UVBC & IRBC Oscillating Sol= SSB Solution

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

23. Electroweak Constraints S(exp)=L10= 0.32 ±0.04 (QCD) S(pert)=NDNc /(6π) 0.16 (QCD) ? S(exp) < 0.1

25. Walking FCNC ? Solves S,T,U

26. 4．Large Nf QCD Realistic Field Theoretical Model of Walking/Conformal Technicolor IR Fixed Point

27. Banks, Zaks　（１９８２） IR Fixed Point

28. ``Conformal Window’’ Banks, Zaks　（１９８２） 8.05 < Nf < 16.5 Nf Nf Chiral Symmetry Restoration at SD equation Appelquist,Terning,Wijewardhana (1996)

29. Miransky scaling Conformal Phase Transition Miransky & K.Y. (1997) Ginzburg-Landau

31. M. Harada, M. Kurachi & KY, hep-ph/0509193 PRD68 (2003) 076001-(1-16) PRD70 (2004) 033009-(1-11) ５. , S

32. (Improved) Ladder SD & BS Equations Works in Real-life QCD Harada, Kurachi, KY (2004)

33. Walking/Conformal Artificial cut

34. Harada, Kurachi, KY (2004)

37. Miransky scaling Nfcrit= 11.9 αcr= π/4=0.785

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45. Walking

47. S parameter ?

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