Dynamical Symmetry Breakingand

Collider Physics

201７.1２.２３at Osaka U.

Michio Hashimoto(Chubu U)

(Review Talk)

1. Concept of Dynamical Symmetry Breaking Scenarios

2. Introduction to DSB Approaches

3. Introduction to my recent work and recent MCHM analysis

4. Summary

I will talk

Concept of DSB Scenarios

Spontaneous Symmetry Breaking (SSB) and DSB

When a continuous group G spontaneously breaks down to H,there appear Nambu-Goldstone Bosons (NGB’s) associated with the broken currents J:

order parameter

If it is a composite operator, we may call this SSB

Dynamical Symmetry Breaking(This topics is appropriate to this room ^_^;;)

f: decay constant(scale of SSB)

Good example is the low-energy QCD:

NGB:

DSB!!order param:

f = 93 MeVThe scale is or

Nambu-Goldstone theorem tells us

For the EW gauge symmetry breaking,

The SM answers that the order param. is the elementary scalar field H,so called the Higgs doublet:

we know the scale is v=246 GeV, which corresponds to

v v

Is this really elementary?

However, the SM looks like the linear sigma model for QCD:

This is OK as an effective theory of Hadron Physics,but, in reality, we know the fundamental theory is QCD.

For the EWSB, it is still one of a central problem whether the Higgs field is elementary or composite.

If composite,

there must exist more fundamentaltheory beyond the SM!!

DSB approaches

There are many DSB approaches:

1. Technicolor/Walking TC2. Little Higgs models3. Strongly Interacting Light Higgs (SILH)4. Pseudo Nambu-Goldstone Boson (pNGB)

etc.

Related

1. Technicolor (TC) S. Weinberg,PRD13,974(1976);PRD19,1277(1979);L. Susskind, PRD20,2619(1979).

We may just scale up the QCD scale to the EW scale,

The experiments already have showed that Nature is Not so Simple.

Existence of h(125) Higgless/heavy Higgs

Precision Test, S < 0.1 Big S-parameter

No exotica Many Technihadrons, etc.,

(1 Family type = 4 weak doublets)QCD-like TC

Constraint from Precision measurements

Peskin & Takeuchi; Holdom & Terning, Gorden & Landall

For NTC

= 4

S = 1.6 !!

No Z’ and W’ CERN-EP-2017-25019th December 2017

arXiv: 1712.06518

arXiv: 1710.07235

No Top partner arXiv: 1707.03347

In the Little Higgs models, we introduce

f: typical scale of LH

Canceling mechanism of the top-loop quadratic divergence

2. Little Higgs models

(also W’ is introduced for cancellation of W loop)

No W’ and/or T severely constrain the LH models…

3. SILH approach

We assume only one light Higgs boson and some underlying dynamics yields higher dim. operator:

Relations between the model parameters and obs.

The triple gauge couplings are also modified.

I don’t show the global fit, because so complicated…

A composite Higgs doublet field can be realized as a pNGB. Base on the DSB of SO(5) SO(4), whose scale is f,Minimal Composite Higgs Models (MCHM’s), which containonly one Higgs doublet, have been proposed.These are concrete models of the SILH approach.However, there are many variations depending on the representation of the fermions.

4. Higgs as pNGB

Later, I will show you a recent work of MCHM.

Deviations from the SM:

Possibility of Enhanced top Yukawa coupling

The top Yukawa coupling is still unclear and thusthere is a room of BSM.However, simple models cannot yield an enhanced top Yukawacoupling consistently with the experimental constraints.

The Simplest Vector-like Quark model

Yt Always suppressed!

Other Simple Cases

gg h inevitably enhanced when Yt is bigger.

Big Yt requires more extra fields!

Recently, I studied the vector-like quark model with exotic hyperchargeassuming one composite Higgs doublet:

MH, arXiv: 1704.02615

MH, arXiv: 1704.02615

In the lowest order of the 1/M expansion,

In our case, we can show

If an enhanced Yt is confirmed, the mass of VLQ must be

Quite recently, numerical analyses of several MCHM’s are performed:

arXiv: 1712.07494

Several patterns of fermion representations are studied:

The constraint is relaxed for

up to 10% smaller

Summary

There is a longstanding problem concerning with the origin ofthe Higgs field. The Higgs compositeness is still important issue.

I’d like to emphasize that the size of the top Yukawa coupling is still unclear and some of BSM, for example, the VLQ models and MCHM’s, can be testable via Yt.

Based on DSB approach, many studies are uninterruptedly performed. In my impression (prejudice), the pNGB approach seems to get popular now.

Thank you!