1. Dynamical EWSB and Fourth Generation Michio Hashimoto (KEK) 2009.10.28@KEK Mt. Tsukuba M.H., Miransky, 0901.4354. M.H., Miransky, in preparation.

2. Introduction Standard Model (SM) is phenomenologically successful. However, several points are theoretically unnatural: Fine-tuning Why 3 generation? No explanation for the mass hierarchy Why not? The 4th generation The KM theory requires 3 or more.

3. ★What is it for? Dynamical Electroweak Symmetry Breaking ★ The LHC has a discovery potential for the chiral 4th family at early stage. ◎ B Physics, EW Baryogenesis, etc.

4. contents Introduction Status of the 4th generation model Super heavy quarks and multi-Higgs doublets M.H., Miransky, in preparation.M.H., Miransky, 0901.4354. Summary 

5. Constraints for the 4th family

6. ◎ constraints for the masses For quarks, CDF, Public Note 9446 CDF, Public Note 9759 Summer, 2009 July, 2008 Particle Data Group (PDG) 2008 For leptons, (invisible case)

7. ★ Z boson invisible width at LEP by invisible Z width (PDG2008) ◎ Is it proof of the 3 generation? is allowed !! ◎ Number of light neutrinos

8. ◎ Constraints from the oblique corrections LEP EWWG 68% and 95% C.L. constraints viable parameter region ● PDG2008, ● LEPWG, 1 Higgs + 4th family G.D.Kribs, T.Plehn, M.Spannowsky, T.M.P.Tait, PRD76(‘07)075016.

9. The LHC can discover or exclude b’ at early stage. For example, (significance) (exclusion 95% C.L.) talk by Kai-Feng Chen (NTW), the CMS collaboration August, 2009

10. Perturbative unitarity bound: N.B. Chanowitz, et. al., PLB78(‘78)285; NPB153(‘79)402. It will be a milestone for the experiments. ☆ The quark masses above 1TeV will be constrained by gg  ZZ. Chanowitz, et. al., PLB352(‘95)376.

11. ◎ The generation structure is a mystery in the particle physics. Probably, the LHC will answer the question. The chiral 4th generation has not yet been excluded by experiments.

12. If the 4th family may exist, what is interesting? Dynamical Electroweak Symmetry Breaking The 4th generation quarks can be closely connected with the DEWSB through their condensations. (TeV) The yukawa coupling runs very quickly and reaches the Landau pole at most several tens TeV. This is a signal for the DEWSB!!

13. Superheavy quarks and multi-Higgs doublets ◎ The yukawa couplings have the Landau pole, so that the theory is effective only up to this scale < O(10TeV). ★ Besides t’ and b’ condensations, the top condensation also contributes to the EWSB. ★ The Nambu-Jona-Lasinio description is applicable in low energy. M.H., Miransky, 0901.4354; in preparation. ○ The point is that the masses of t’, b’ and t are O(v=246GeV). Multiple Higgs doublet model

14. Model kinetic term for the fermions kinetic term for the gauge bosons Nambu-Jona-Lasinio couplings effectively induced in low energy Three Higgs doublet model low energy effective theory @ composite scale M.H., Miransky, in preparation. We consider only t’, b’ and t.

15. Topcolor gauge boson exchange topcolor instanton flavor changing neutral interaction between t’-t We don’t know a natural candidate of the origin. How to get them:

16. Auxiliary Field Method Let us introduce the auxiliary field, etc. If yukawa int. Higgs mass terms

17. ◎ The low energy effective theory @ EWSB scale The Higgs bosons get the kinetic terms and quartic couplings.

18. ★ Higgs potential @ 1/Nc leading approximation @ 1/Nc LO Higgs quartic coupling --- 2 Higgs part + 1 Higgs part (2+1)-Higgs doublet model

19. ○ The RGE approach is more convenient. NJL model = RGE + compositeness conditions Bardeen, Hill, Lindner, PRD41(‘90)1647. (composite scale) Compositeness conditions

20. ◎ Even in the RGE analysis, the (2+1)-Higgs structure is kept, if we ignore the EW 1-loop effect. The quartic term is then written as ★ The EW 1-loop diagram yields, for example, When we consider the full 1-loop RGE, we should analyze a general 3 Higgs model, instead of the (2+1)-Higgs.  45 parameters in the quartic couplings

21. Numerical Analysis We have 8 theoretical parameters; The physical quantities are composite scale (Landau pole) of t’ and b’ composite scale (Landau pole) of the top 3 Higgs doublets:CP even Higgs -- 3 CP odd Higgs -- 2 charged Higgs -- 2+2 VEV -- 3 etc.

22. ◎ Definition of the angles of the VEVs ◎ It is natural to take similar composite scales. ◎ Owing to yt’ = yb’, the T parameter constraint implies Also,

23. By using we approximately obtain We here took

24. ◎ It is convenient to take the following parameters: ★ The outputs are decay widths of yukawa couplings between the fermions and the Higgs bosons

25. We calculate the mass spectrum by using the RGE: RGE for the (2+1)-Higgs doublets + compositeness conditions and for various The bold curves are for The dashed curves are for

26. The mass spectrum of the Higgs bosons for various We also used and

27. constraint is potentially dangerous. How about the Higgs contributions to the S,T-parameter bounds yield the constraint to TeV for TeV The sensitivity of is small. and and it corresponds to ★

28. ◎ The 4th generation quarks drastically increases

29. ◎ An example for the scenario with Inputs: Outputs:

30. yukawa couplings Decay width into WW, ZZ Enhancement of Higgs production

31. ◎ An example for the scenario with Inputs: Outputs:

32. yukawa couplings Decay width into WW, ZZ Enhancement of Higgs production

33. Summary and discussions There exists an allowed parameter region for the 4th generation model. Probably, the LHC will answer to this problem. If the 4th generation exist, the t’ and b’ will be closely connected with the EWSB. The top quark also contributes to the EWSB. The dynamical model with the 4th generation naturally yields multi-Higgs doublets. We analyzed the (2+1)-Higgs model.

34. In Progress: Branching ratio of the Higgs Decay mode of the Higgs bosons etc. Lepton sector Majorana neutrinos etc. Under construction: Thank you,