Dynamical EWSB andFourth Generation

Michio Hashimoto

(KEK)

2009.10.28@KEK

Mt. Tsukuba

M.H., Miransky, 0901.4354.

M.H., Miransky, in preparation.

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.

★What is it for?

Dynamical Electroweak Symmetry BreakingDynamical Electroweak Symmetry Breaking

★The LHC has a discovery potential for the chiral 4th family at early stage.

◎ B Physics, EW Baryogenesis, etc.

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

Constraints for the 4th family

◎ 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)

★ Z boson invisible width at LEP

by invisible Z width (PDG2008)

◎ Is it proof of the 3 generation?

is allowed !!

◎ Number of light neutrinos

◎ 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.

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 collaborationAugust, 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.

◎ 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.

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!!

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

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.

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:

Auxiliary Field MethodLet us introduce the auxiliary field,

etc.

If

yukawa int.

Higgs mass terms

◎The low energy effective theory @ EWSB scale

The Higgs bosons get the kinetic terms and quartic couplings.

★ Higgs potential @ 1/Nc leading approximation

@ 1/Nc LO

Higgs quartic coupling --- 2 Higgs part + 1 Higgs part

(2+1)-Higgs doublet model

○ The RGE approach is more convenient.

NJL model = RGE + compositeness conditionsBardeen, Hill, Lindner, PRD41(‘90)1647.

(composite scale)

Compositeness conditionsCompositeness conditions

◎ 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

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 -- 2charged Higgs -- 2+2

VEV -- 3 etc.

◎ 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,

By using

we approximately obtain

We here took

◎It is convenient to take the following parameters:

★ The outputs are

decay widths of

yukawa couplings between the fermions and the Higgs bosons

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

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

★

◎ The 4th generation quarks drastically increases

◎ An example for the scenario with

Inputs:

Outputs:

yukawa couplings

Decay width into WW, ZZ

Enhancement of Higgs production

◎ An example for the scenario with

Inputs:

Outputs:

yukawa couplings

Decay width into WW, ZZ

Enhancement of Higgs production

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 sectorMajorana neutrinosetc.

Under construction:

Thank you,