Dark matter and electroweak scalegenesis

from a bilinear scalar condensate

Masatoshi Yamada(Kanazawa University)

Collaborator: Jisuke Kubo (Kanazawa University)

Based on J, Kubo and M. Y., arXiv:1505.05971 (to be published in PRD)

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

Workshop of elementary particle physics in Matsue @Shimane Univ.

Introductionp The SM is complete.p Still unsolved problems.p In this talk,

n Fine-tuning problem (criticality problem)n The origin of electroweak symmetry breakingn Dark matter

p Suggest a model based on the classical scale invariance.

Classical scale invariance and Scalegenesisp The Higgs mass is prohibited.

n The SM becomes scaleless.p How to generate a scale?

n Coleman-Weinberg mechanismp Perturbativep The mass term is not generated.

n Strong dynamicsp Non-perturbativep The dynamical mass term is generated.

Contents1. The model

2. Dark matter candidates

3. 1st order phase transition of electroweak symmetry (at finite temperature)

Contents1. The model

2. Dark matter candidates

3. 1st order phase transition of electroweak symmetry (at finite temperature)

Modelp Strongly interacting Hidden sector

n SU(𝑁%)×U 𝑁( invariant + classically scale invariant

J, Kubo and M. Y., arXiv:1505.05971

Dynamical Scale Symmetry Breaking

Effective theoryp Low energy effective Lagrangian

n Assume that DSSB is dominant.n Attempt to describe the genesis of scale a la

Coleman-Weinberg.n Scale invariant Lagrangian.n Renormalizablen 𝜆*, 𝜆′* and 𝜆-*: effective coupling constants.

p which contain the quantum effects of hidden gluon.

Effective model

Order parameter

meson

Scale invariant

Chiral invariant

Comparison

Effective potentialp The mean-field approximated effective potential

n Integrate out 𝜒 (Gauss integral)

p Solving the gap equations

Tr logMS scheme

p The vacuum of Higgs

p The scalar condensate

p Constituent scalar mass

Solutions

Input & free parametersp Input

n Higgs massn EW vacuumn DM relic abundance

p 7 free parameters.

Contents1. The model

2. Dark matter candidates

3. 1st order phase transition of electroweak symmetry (at finite temperature)

Dark matter candidate

Dark matter candidate is p The excitation fields from the vacuum < 𝑆2𝑆 >

n Assume the unbroken U(𝑁() flavor symmetry:

p Mean-field Lagrangian (before integrating 𝑆)

c.f.

p Decay into Higgs through 𝑆 loop

p Coannihilation

Dark matter candidate is

Forbidden by flavor symmetry

𝜎56 vs. 𝑚89

Contents1. The model

2. Dark matter candidates

3. 1st order phase transition of electroweak symmetry (at finite temperature)

Electroweak 1st order phase transition

EW Baryogenesis scenariop Sakharov conditions

1. Baryon number violation2. C-symmetry and CP-symmetry violation3. Interactions out of thermal equilibrium.

p Electroweak strong first-order phase transition

The SM cannot satisfy this condition

Phase transitionp 𝑉;(( at zero temperature

p 𝑉;(( at critical temperature 𝑇%=>(EWPT)

p 𝑉;(( at critical temperature 𝑇%55(SSPT)

Scale transition is strong 1st order.J, Kubo and M. Y., PTEP 2015 093B01 (arXiv:1506.06460)

Without dark matter case: 𝑁( = 1EW phase transition becomes strong 1st order

EW-PT is triggered by SS-PT

With dark matter case: 𝑁( = 2EW phase transition becomes weak 1st order

Difference between two casesp The Higgs portal is important

p Need more precisely analysis

EW-PT is triggered.

Not enough to trigger

Summary p We suggested a new model based on classically

scale invariance.n Strongly interacting hidden sector with the scalar fieldn Explain the mechanism of generation of “scale”n Dynamical Scale Symmetry Breaking < 𝑆2𝑆 >≠ 0n 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 fieldn Explain the mechanism of generation of “scale”n Dynamical Scale Symmetry Breaking < 𝑆2𝑆 >≠ 0n The EW symmetry breaking < ℎ >≠ 0

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

“Scalegenesis” is realized!

Prospectsp More precise analysis is needed.

n Lattice simulationp C and CP violation

Appendix

Hierarchy problem p Nothing between Λ=>andΛJK?

n Λ=>~𝒪 10N GeV ⇔ΛJK~𝒪 10ST GeV

p Fine-tuning problem

p Fermion and gauge field have not the problem.n Gauge symmetry:

n Chiral symmetry:

(10NGeV)N = (10STGeV)N − (10STGeV)N

Argument by Bardeen p The quadratic divergences are spurious.

n Λ always is 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.

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

The non-zero beta function 𝛽 ≠ 0

p The RG equation of Higgs mass

n If 𝑚 ΛJK = 0, the mass dose not run.

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

n If 𝑀~𝒪(TeV), fine-tuning is not needed.p Even if so, the origin of 𝑚Y with TeV order is unknow.

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

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

Broken phase Symmetric phase

Phase boundary(massless)

Fine-tuning problem in viewpoint of Wilson’s RG [Cf. H. Aoki, S. Iso, ’14]

Fine-tune problem = Why is the Higgs close to critical?

Broken phase Symmetric phase

Phase boundary(massless)

Fine-tuning problem in viewpoint of Wilson’s RG [Cf. H. Aoki, S. Iso, ’14]

The classical scale invariance = The bare mass is exactly put on the critical line. The massless theory (critical theory) is realized.The classical scale invariance makes the Higgs critical.

Classical scale invariancep The classical scale invariance prohibits 𝑚Y .

p Boundary condition: 𝑚Y = 𝑚 ΛJK = 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.

How to generate radiative corrections?

Advantages of our modelp The number of parameters is less.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 < 𝜓\𝜓 >→< 𝑆 >→ 𝑚- →< ℎ >p < 𝑆2𝑆 >→ 𝑚- →< 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.(will see later)

Where is the vacuum?p Minimum of 𝑉9^_; Solving gap equations:

p Three solutions:i. < 𝑆ab >≠ 0,< 𝑀N >= 0, 𝐺 = 0ii. < 𝑆ab >= 0,< 𝑀N >= 0iii. < 𝑆ab >= 0,< 𝑀N >≠ 0, 𝐺 > 0

The solution (iii) is suitable.

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 ℒ;((

3. We obtain

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

Normal ordering

Mean-field approximationp Bogoliubov-Valatin vacuum

p Wick contractions

Mean-field approximationp Lagrangian

p Constituent scalar mass

Effective potential

Mass of dark matterp Mass = a pole of two point function

n Inverse two point function of 𝜙f (dark matter)

n Find zero

Coannahilation

Velocity averaged annihilation cross section

Dark matter candidate is p The excitation fields from the vacuum < 𝑆2𝑆 >

n Assume the unbroken U(𝑁() flavor symmetry:

p Mean-field Lagrangian (before integrating 𝑆)

Direct detectionp Scattering off the Nuclei

n Spin independent cross section

𝑚g: nucleon mass�̂�: nucleonic matrix element

Inverse two-point function

𝜎56

Dark matter relic abundancep DM relic abundance

n Entropy density

n Critical density/Hubble parameter

n DM number density

At finite temperaturep Momentum integral

n Matsubara frequency

Effective potentialp There are four components.

Zero temp. part

Finite temp. part

All SM particles

Summation of thermal mass(remove the IR divergence)

・・・

・・・

Scale transition is strong 1st order.J, Kubo and M. Y., PTEP 2015 093B01 (arXiv:1506.06460)