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

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 1-loop

◎ 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.

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

Constraints on the 4th family

◎ constraints on the masses For quarks, CDF, CDF, (PDG 2009) For leptons, (invisible case) Particle Data Group (PDG) 2009

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.

★ 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 !

★ Exclusion of the SM-like Higgs mass at Tevatron SM3!! For SM4, the Tevatron exclusion should be severer, because of the enhancement of the gluon fusion process. Keep in mind a suggestion by Schmidt, et. al, arXiv: It might be better to wait for an official combined data of CDF and D0. (SM4)

◎ Constraints from the oblique corrections LEP EWWG 68% and 95% C.L. constraints ★ For the degenerate masses, For quarks, N=3, Y=1/6 For leptons, N=1, Y= ｰ 1/2 is favorable.

G.D.Kribs, T.Plehn, M.Spannowsky, T.M.P.Tait, PRD76(‘07) Favorable mass spectrum: cf.) A well-known paper  Higgs potential quickly falls down and hence becomes unstable at the scale less than 1 TeV!!

★ 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., ) etc… I have varied all masses of the fermions and Higgs boson(s), 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…

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

is allowed in a wide parameter space.

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)

Data samples for several senarios

An example of the branching ratio of the Higgs boson G.D.Kribs, T.Plehn, M.Spannowsky, T.M.P.Tait, PRD76(‘07)

Effects of the mixing between 3rd and 4th generations

★ We can take into account the effects of the mixing between the 3rd and 4th family quarks. (I didn’t consider the mixing in the lepton sector.) M. S. Chanowitz, Phys. Rev. D79, (2009). ◎ It contributes to the T-parameter (and also the RGE’s).

Data samples and (S,T)-contour Mass diff.

Data samples and (S,T)-contour Mass diff.

Kribs, et al, PRD76(‘07) 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

Must the Higgs mass be heavy ?  NOT necessarily Multiple Higgs models allow a light Higgs boson! in the SM4

Two Higgs doublet model of type II (M.H., ) The light CP even Higgs h is completely SM-like. the heavy Higgs decoupling regime. Schematically speaking, corresponds to The low mass region is exotic! is possible due to dyn. of quartic couplgs.

The RGE’s for the quartic couplings in the 2HDM II

Heavy Higgs masses Data samples and (S,T)-contour The 2HDM is better than the SM4! Detailed studies are needed. Type I, type X, etc.

4th generation quarks Discovery reach

◎ discovery potential for the 4th generation quarks V.E.Ozcan, S.Sultansoy, G.Unel, arXiv: Required Luminosity for

@Taiwan National University If no excess is observed,

Impact on the constraint of the mass spectrum in the SM4

If the LHC exclude at early stage, a wide parameter space in the SM4 will be gone. In this case, essentially, a nonperturbative regime will be left to be explored. ◎ If so, what kind of study is significant ?

Required luminosity for 3 and 5 sigma significance Higgs boson in the SM4

Schmidt, et. al, arXiv:

◎ The generation structure is a mystery in the particle physics. The Tevatron/LHC will answer the question. The chiral 4th generation has not yet been excluded by experiments. ★ If the Tevatron or LHC discover the 4th family quarks, it would bring a “New Era of Strong Dynamics”.

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.

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; ○ The point is that the masses of t’, b’ and t are O(v=246GeV). Multiple Higgs doublet model 2,3,4,5 Higgs doublets A nonperturbative model

4th generation!? Why?

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)  4th generation model

Estimate for the contributions of t’, b’ and t to the EWSB

◎ Estimate for the contributions of t’, b’ and top quarks to the EWSB (Pagels-Stokar formula) t’, b’ provide main contributions and the top plays a minor role!

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 composite scale M.H., Miransky, We consider only t’, b’ and t.

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:

◎ A topcolor model (extension of the QCD sector) For anomaly cancellation, we introduce weak singlet and the hypercharge is the same as M.H., Miransky, PRD80(2009)

Spontaneous topcolor breaking is very strong is relatively strong and is around QCD coupling. ★ ★ ★ massive gauge boson --- coloron

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

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

Higgs quartic coupling 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.)

◎ Number of parameters for the general 3 Higgs doublet model For mass terms, We can erase some of the phases of the mass mixing terms by redefining the phases of the Higgs fields. For quartic couplings,

The potential of the general 3 Higgs doublet model

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 VEV -- 3 etc.

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

◎ 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,

BHL approach Bardeen, Hill, Lindner, PRD41(‘90)1647. The NJL model is equivalent to a linear sigma model with the compositeness conditions: (composite scale) Compositeness conditions

RGE’s Compositeness Conditions

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

The mass spectrum of the Higgs bosons for various We also used and  (2+1) Higgs structure

How about the Higgs contributions to the S,T-parameter constraint is potentially dangerous. bounds yield the constraint to TeV for TeV The sensitivity of is small. and and it corresponds to ★  If the model is within 95%CL limit of S,T.

★ CKM structure sample data for CKM CKM matrix elements  Let us consider only two parameters.

What is the signature?

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

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

・ We may have ttbar resonances of H1 and H3. ・ The heavier Higgs H2 resonance may exist in the ZZ mode. ・ Also, in the t’t’bar and b’b’bar channels, there may appear scalar resonances H3 and H2. ・・・・・・ Higgs Phenomenology is quite rich!

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.

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

Thank you, Outlook: If the LHC excludes a large parameter space and then only a nonperturbative regime is left to be explored, what kind of studies are significant? For example, is there some nonperturbative effect in the nonresonant gg  ZZ mode? ★ ★ Is a bound state owing to the Higgs exchange possible? ★ etc… ◎ Can the BHL approach be refined by lattice?