Electroweak and Dark matter scalegenesis from a bilinear scalar - - PowerPoint PPT Presentation

Electroweak and Dark matter scalegenesis from a bilinear scalar condensate

Masatoshi Yamada

Kanazawa University Kyoto University (since July) Heidelberg University (since Sep.) In collaboration with Jisuke Kubo (Kanazawa university)

• Phys. Rev. D93 075016 (arXiv:1505.05971)

PTEP 2015 093B01 (arXiv:1506.06460)

What’s next after discovery of Higgs?

p The Higgs boson was discovered at CERN. p The SM is still incomplete.

n Neutrino mass n Dark matter n Baryogenesis n Origin of electroweak scale n Hierarchy problem (Fine-tuning problem) n GUT n Quantum gravity n …etc.

Our targets

p The Higgs boson was discovered at CERN. p The SM is still incomplete.

n Neutrino mass n Dark matter n Baryogenesis n Origin of electroweak scale n Hierarchy problem (Fine-tuning problem) n GUT n Quantum gravity n …etc.

Hierarchy problem

p Nothing between Λ"# and Λ()?

n Λ"#~𝒫 10. GeV ⇔ Λ()~𝒫 1034 GeV

p Fine-tuning problem p Higgs is close to critical:

(10. GeV). = (1034 GeV). − (1034 GeV).

Fine-tuning problem = Criticality problem

Is the quadratic divergence physical?

p The quadratic divergences are spurious.

n Λ is always subtracted by renormalization. n The dimensional regularization automatically subtracts

the quadratic divergence.

p Only logarithmic terms related to the scale

anomaly survive in the perturbation.

p The RG equation of Higgs mass

p If 𝑛 Λ() = 0, the mass dose not run.

Classical scale invariance

p The classical scale invariance prohibits 𝑛:.

n Boundary condition: 𝑛: = 𝑛 Λ() = 0

p The bare theory does not have the scale. p The massless theory is realized.

n The classical scale invariance makes the theory critical.

p If the Higgs field is coupled to a new particle with

mass 𝑁,

n If 𝑁~𝒫(TeV), fine-tuning is not needed. n If 𝑁 ≫ TeV, fine-tuning problem appears.

p The origin of observed mass is radiative

corrections with TeV scale.

p Consider the hidden sector.

n The scale is generated in the hidden sector. n The scale breaking propagates to the SM sector.

Argument by Bardeen

W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 (1995).

How to generate the scale in the hidden sector? Two ways:

p Non-perturbative way

n Strong dynamics n e.g. Λ>?@ n The mass term is

dynamically generated.

p Perturbative way

n Coleman-Weinberg n Scale anomaly n Dimensional transmutation n The mass term is basically not

generated.

Example of non-perturbative way

Standard model sector

Hidden sector

Strong dynamics e.g. Hidden QCD

Hidden quark (𝑂B flavor) Singlet scalar (mediator) Dynamical Chiral Symmetry Breaking (D𝜓SB) in hidden sector

• T. Hur and P. Ko, Phys. Rev. Lett. 106 141802 (2011)

Hidden gluon field strength Higgs portal coupling

Contents

1.

The model

2.

Dark matter candidates

3.

1st order phase transition of electroweak symmetry (at finite temperature)

The model

p Strongly interacting Hidden sector

n SU(𝑂F)×U 𝑂B invariant + classically scale invariant

Hidden color index Flavor index

Mechanism

p The standard model connects to the hidden

sector through the Higgs portal coupling.

p Strong dynamics in hidden sector dynamically

breaks scale invariance: < 𝑇J𝑇 >≠ 0

p The Higgs mass term is generated:

Advantages of our model

p The mediator is the strongly interacting particle.

n Observing the hidden sector is easier than other models

such as the hidden (quark) model.

p ΛM>?@~ < 𝜔

O𝜔 > → < 𝑇 > → 𝑛Q = 𝜇S < 𝑇 > → < ℎ >

p ΛM>?@~ < 𝑇J𝑇 > → 𝑛Q= 𝜇S < 𝑇J𝑇 > → < ℎ >

n The DM candidate is CP even.

p c.f. The DM in hidden (quark) QCD is CP odd.

p Strong 1st order of EW phase transition can be

realized.(as will be seen later)

Strong interaction is difficult…

p It is hard to analytically solve the strongly

interacting system.

p In QCD, effective model approaches are

successful.

n e.g. Nambu—Jona-Lasinio (NJL) model for D𝜓SB

p We formulate an effective theory of our model.

How to formulate?

p An effective model describing dynamical scale

symmetry breaking (DSSB)

p Scale invariance is broken by scale anomaly. p The breaking is only logarithmic.

n The non-perturbative scale breaking due to the

condensation < 𝑇J𝑇 >≠ 0 is dominant.

n Ignore the breaking by scale anomaly.

Effective theory

p Effective Lagrangian

n Scale invariant Lagrangian. n 𝜇U, 𝜇′U and 𝜇QU are effective coupling constants. n Renormalizable n We attempt to describe the dynamical genesis of

scale using the Coleman-Weinberg mechanism.

How to evaluate physical values?

p Mean-field approximation (MFA)

n Many body system is reduced to 1 body system. n Methods: 1.

Introduce a “BCS” vacuum and a mean field:

2.

Apply the following replacements to ℒYBB

3.

We obtain

Review: T. Hatsuda and T. Kunihiro, Phys. Rep. 247 221 (1994)

Normal ordering

Effective potential

p The mean-field approximated effective potential

n Integrate out 𝜓 (Gauss integral)

p Constituent scalar mass

Tr log

MS scheme

p The vacuum of Higgs p The scalar condensate p Constituent scalar mass

The solutions

Where is the vacuum?

p Minimum of 𝑊

\]^; Solving gap equations:

p Three solutions:

i.

< 𝑇`

a >≠ 0, < 𝑁. >= 0, 𝐻 = 0 ii.

< 𝑇`

a >= 0, < 𝑁. >= 0 iii.

< 𝑇`

a >= 0, < 𝑁. >≠ 0, 𝐻 > 0

The solution (iii) is suitable.

Input & free parameters

p Input

n Higgs mass n EW vacuum n DM relic abundance

p There are 7 free parameters.

Summary so far

Planck TeV Dynamical scale symmetry breaking Electroweak symmetry breaking Scale invariant standard model & hidden sector

Described by the effective model

Contents

1.

The model

2.

Dark matter candidates

3.

1st order phase transition of electroweak symmetry (at finite temperature)

Dark matter candidate is

p The excitation fields from the vacuum < 𝑇J𝑇 >

n Assume the unbroken U(𝑂B) flavor symmetry:

p Mean-field Lagrangian (before integrating 𝑇)

p Decay into Higgs through 𝑇 loop p Coannihilation

Dark matter candidate is

Forbidden by flavor symmetry

Mass of dark matter

p Mass = a pole of two point function

n Inverse two point function of 𝜚d (dark matter) n Find zero

Direct detection

p Scattering off the Nuclei

n Spin independent cross section

𝑛e: nucleon mass 𝑠̂: nucleonic matrix element

𝜏ij vs. 𝑛@\

Contents

1.

The model

2.

Dark matter candidates

3.

1st order phase transition of electroweak symmetry (at finite temperature)

EW Baryogenesis scenario

p Sakharov conditions

1.

Baryon number violation

2.

C-symmetry and CP-symmetry violation

3.

Interactions out of thermal equilibrium.

p Electroweak strong first-order phase transition

The SM cannot satisfy this condition

At finite temperature

p Momentum integral

n Matsubara frequency

Effective potential

p There are four components.

Zero temp. part Finite temp. part

All SM particles

Summation of thermal mass

(remove the IR divergence) ・ ・ ・ ・ ・ ・

Phase transition

p 𝑊

YBB at zero temperature

p 𝑊

YBB at critical temperature 𝑈 l "#(EWPT)

p 𝑊

YBB at critical temperature 𝑈 l ii (SSPT)

Scale transition is strong 1st order.

J, Kubo and M. Y., PTEP 2015 093B01 (arXiv:1506.06460)

Without dark matter case: 𝑂B = 1

EW phase transition becomes strong 1st order

Two phase transition

• ccur at the same time

EWSB is triggered by SSB.

With dark matter case: 𝑂B = 2

EW phase transition becomes weak 1st order

Difference between two cases

p The Higgs portal is important

n Large 𝜇QU:

p The DM relic abundance becomes too small.

n Small 𝜇QU:

p The strong 1st order phase transition in hidden sector is not

transmitted to the standard model sector.

p Improved analysis might realize the strong EW 1st

• rder phase transition and the existence of DM at

the same time.

Summary

p We suggested a new model based on classically

scale invariance.

n Strongly interacting hidden sector with the scalar field n Explain the mechanism of generation of “scale” n Dynamical Scale Symmetry Breaking < 𝑇J𝑇 >≠ 0 n The EW symmetry breaking < ℎ >≠ 0

“Scalegenesis” is realized!

Summary

p We suggested a new model based on classically

scale invariance.

n Strongly interacting hidden sector with the scalar field n Explain the mechanism of generation of “scale” n Dynamical Scale Symmetry Breaking < 𝑇J𝑇 >≠ 0 n The EW symmetry breaking < ℎ >≠ 0

p Dark matter candidate exists. p The EW 1st order phase transition

“Scalegenesis” is realized!

Appendix

Argument by Bardeen

W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 (1995).

Fine-tuning problem = criticality problem

Broken phase Symmetric phase

Phase boundary (massless)

In viewpoint of Wilson RG

Why is the Higgs close to critical?

p The RG equation of Higgs mass

n If 𝑛 Λ() = 0, the mass dose not run.

p If the Higgs field is coupled to a new particle with mass

𝑁,

n If 𝑁~𝒫(TeV), fine-tuning is not needed.

p Even if so, the origin of 𝑛: with TeV order is unknown.

n If 𝑁 ≫ TeV, fine-tuning problem appears.

p How to kill the bare mass term?

Argument by Bardeen

W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 (1995).

Classical scale invariance

p The classical scale invariance prohibits 𝑛:.

p Boundary condition: 𝑛: = 𝑛 Λ() = 0

p The origin of observed mass is radiative

corrections with TeV scale.

p The classical scale invariance is one of

candidates for the solution of fine-tuning problem.

What’s classical scale invariance?

p The phase boundary (critical line) corresponds to the

massless theory.

p The quadratic divergence determines the position of the

phase boundary.

n The position depends on renormalization scheme. n Rotating the coordinate of theory space, the position always can

be given at 𝑛 = 0 line.

p If the bare parameters is exactly put on phase boundary,

the massless theory is realized.

p The classical scale symmetry makes the theory critical. p How to generate the scale from the scaleless theory?

Coleman-Weinberg mechanism

p Scale anomaly p In the SM, p Dimensional transmutation

n N dimensionless free parameters n one dimensionful parameter and N-1 dimensionless free

parameters

p The mass term does not generated. p Cannot explain the Higgs mass and the top mass

Mean-field approximation

p Bogoliubov-Valatin vacuum p Wick contractions

Mean-field approximation

p Lagrangian p Constituent scalar mass

Effective potential

Coannahilation

Velocity averaged annihilation cross section

𝜏ij

Dark matter relic abundance

p DM relic abundance

n Entropy density n Critical density/Hubble parameter n DM number density

Comparison with NJL model

p Lagrangian p Effective model p Order parameter p Meson

D Scale SB D Chiral SB