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Fourth Generation and Dynamical Electroweak Symmetry Breaking Michio Hashimoto (KEK) 2010.02.20 @KEK Kairaku-en M.H., Miransky, 0912.4453. M.H., Miransky, PRD80(2009)013004. M.H., 1001.4335.

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Introduction It is a fundamental problem whether or not there exists a new generation. Notice that concept of the SM allows more than three generations: No theoretical reason to reject the 4th generation The Kobayashi-Maskawa theory is NOT limited to 3 generations. Anomaly free QCD is asymptotic free. @ 1-loop Also, it is NOT excluded by the EW precision data… (repetition of 1,2,3 generations )

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◎ If the 4th generation exists… NEW PHYSICS which is well-defined and familiar in some aspect Elementary Higgs may not be needed any longer Dynamical Electroweak Symmetry Breaking Free from the problem of naturalness!? Landau pole of yukawa The LHC can discover/exclude it at early stage.

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contents Introduction Status of the 4th generation Super heavy quarks and multi-Higgs doublets M.H., Miransky, 0912.4453.M.H., Miransky, PRD80(2009)013004. Summary M.H., 1001.4335.

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Constraints on the 4th family

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◎ constraints on the masses For quarks, CDF, 0810.3349. CDF, 0912.1057. (PDG 2009) For leptons, (stable case) Particle Data Group (PDG) 2009

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★ Z boson invisible width at LEP by invisible Z width (PDG2008) ◎ Is it proof of the 3 generation? ◎ Number of light neutrinos is allowed !! NO !

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Constraints from the oblique parameters

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G.D.Kribs, T.Plehn, M.Spannowsky, T.M.P.Tait, PRD76(‘07)075016. Favorable mass spectrum: ---------------- Higgs potential quickly falls down and hence becomes unstable at the scale less than 1 TeV!! ◎ Constraints from the S and T parameters LEP EWWG 68% and 95% C.L. constraints

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★ Very recently, I reanalyzed the (S,T) constraints. I also took into account the RGE’s: ・ Instability bound for the Higgs potential ・ Tree-level unitarity bounds for the yukawa and Higgs quartic couplings Theoretical cutoff In earlier works, people considered only S,T or assumed (M.H., 1001.4335) etc… I have varied all masses of the fermions and Higgs boson, and then obtained favorable mass spectra. (If the Higgs mass is so small, the Higgs potential is unstable at some scale.) (If the couplings are so large, they diverge at some scale. ) The cutoff should not be so small. Otherwise, such a model is unlikely to be valid in the LHC physics…

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Red Blue Violet Green We varied (M.H., 1001.4335) for Dirac-type neutrnos are assumed. The 1-loop RGE’s are employed. (SM4)

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The mass difference of the fermions is allowed in a wide parameter space!! is also possible. (Both of them are unlikely.) Favorable mass spectrum is contained in the following region: (I took)

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Kribs, et al, PRD76(‘07)075016. Comparison with the earlier work light Higgs scenario, say, Our work The Higgs boson in the SM4 is likely to be heavy, say, ○ △ The strategies are different. Not necessarily contradict each other Several decay channels are still allowed! etc. (S,T) 95%CL limit + RGE’s probably, (S,T) 68% CL limit

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LEP direct search Heavy Higgs does not contradict the EW precision data in the 4th generation model. This means that a tension between the Higgs mass fit in the SM3 and the LEP lower bound can be removed. SM3

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evidence/exclusion at LHC with early data 4th generation quarks

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@Taiwan National University If no excess is observed, (my estimate) discovery or exclusion of b’ at LHC ★ If we get evidence of the 4th family quarks, it will bring “New Era of Strong Dynamics”.

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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!! Holdom, PRL57(‘86)2496.

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Superheavy quarks and multi-Higgs doublets ◎ The yukawa couplings have the Landau pole ～ O(few TeV). It suggests compositeness, i.e., ★ The t’ and b’ condensations can dynamically trigger the EWSB and also the top may contribute somewhat. the Nambu-Jona-Lasinio description is applicable in low energy. M.H., Miransky, PRD80(2009)013004; 0912.4453. ○ The point is that the masses of t’, b’ and t are O(v=246GeV). Multiple composite Higgs doublet model 2,3,4,5 Higgs doublets A nonperturbative model

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4th generation!? Why?

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Prediction of the top mass in the 3 generation model Too Large!! (PDG2009) The minimal 3 gen. model does not work. ◎ Top See-saw ◎ Top mode standard model with extra dimensions Dobrescu and Hill, PRL81(‘98)2634. MH, Tanabashi, Yamawaki, PRD64(‘01)056003. 4th generation model Holdom, PRL57(‘86)2496.

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NJL-Model Three Higgs doublet model low energy effective theory @ composite scale M.H., Miransky, 0912.4453. We consider only t’, b’ and t. Such a NJL-type model can be produced by a topcolor model, for example.

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◎ The low energy effective theory @ EWSB scale Higgs potential @ 1/Nc leading approximation

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Higgs quartic coupling --- 2 Higgs part + 1 Higgs part (2+1)-Higgs doublet model ◎ When we ignore the EW 1-loop effect, the (2+1)-Higgs structure is safely kept. The quartic term is then written as Cf) is absent. (The mass terms are general one.)

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We calculate the mass spectrum by using the BHL approach: RGE for the (2+1)-Higgs doublets + compositeness conditions and for various Numerical Analysis composite scale (Landau pole) of t’ and b’

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The mass spectrum of the Higgs bosons for various We also used (2+1) Higgs structure within 95% CL limit of the (S,T)-constraint ◎ ◎ We took a large, so we can evade constraint.

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The physical Higgs bosons in the 3 Higgs doublet model are CP even Higgs -- 3 CP odd Higgs -- 2 charged Higgs -- 2+2

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What is the signature?

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◎ An example data for the scenario with Inputs: Outputs:

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yukawa couplings Decay width into WW, ZZ Enhancement of Higgs production of H1

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・ resonances in ttbar channel ・ The heavier Higgs H2 resonance may exist in the ZZ mode. ・ Also, in the t’t’bar channels, there may appear scalar resonances. ・・・・・・ Higgs Phenomenology is quite rich!

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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 somewhat. The dynamical model with the 4th generation naturally yields multi-Higgs doublets. We analyzed the (2+1)-Higgs model.

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

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