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 10 34 GeV p Fine-tuning problem (10 . GeV) . = (10 34 GeV) . − (10 34 GeV) . p Higgs is close to critical: 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.
Argument by Bardeen W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 (1995). 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.
How to generate the scale in the hidden sector? Two ways: p Non-perturbative way p Perturbative way n Strong dynamics n Coleman-Weinberg n e.g. Λ >?@ n Scale anomaly n Dimensional transmutation n The mass term is dynamically generated. n The mass term is basically not generated.
Example of non-perturbative way Hidden sector Standard model sector Higgs portal coupling Strong dynamics e.g . Hidden QCD T. Hur and P. Ko, Phys. Rev. Lett. 106 141802 (2011) Hidden quark ( 𝑂 B flavor) Hidden gluon field strength Singlet scalar (mediator) Dynamical Chiral Symmetry Breaking (D 𝜓 SB) in hidden sector
Contents The model 1. Dark matter candidates 2. 1 st order phase transition of electroweak 3. symmetry (at finite temperature)
The model p Strongly interacting Hidden sector n SU(𝑂 F )×U 𝑂 B 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: < 𝑇 J 𝑇 >≠ 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. O𝜔 > → < 𝑇 > → 𝑛 Q = 𝜇 S < 𝑇 > → < ℎ > p Λ M>?@ ~ < 𝜔 p Λ M>?@ ~ < 𝑇 J 𝑇 > → 𝑛 Q = 𝜇 S < 𝑇 J 𝑇 > → < ℎ > n The DM candidate is CP even. p c.f. The DM in hidden (quark) QCD is CP odd. p Strong 1 st 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 D 𝜓 SB 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 < 𝑇 J 𝑇 >≠ 0 is dominant. n Ignore the breaking by scale anomaly.
Effective theory p Effective Lagrangian n Scale invariant Lagrangian. n 𝜇 U , 𝜇′ U and 𝜇 QU 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? Review: T. Hatsuda and T. Kunihiro, Phys. Rep. 247 221 (1994) p Mean-field approximation (MFA) n Many body system is reduced to 1 body system. n Methods: Introduce a “BCS” vacuum and a mean field: 1. Apply the following replacements to ℒ YBB 2. Normal ordering We obtain 3.
Effective potential p The mean-field approximated effective potential n Integrate out 𝜓 (Gauss integral) MS scheme Tr log p Constituent scalar mass
The solutions p The vacuum of Higgs p The scalar condensate p Constituent scalar mass
Where is the vacuum? p Minimum of 𝑊 \]^ ; Solving gap equations: p Three solutions: a >≠ 0, < 𝑁 . >= 0, 𝐻 = 0 < 𝑇 ` i. a >= 0, < 𝑁 . >= 0 < 𝑇 ` ii. a >= 0, < 𝑁 . >≠ 0, 𝐻 > 0 < 𝑇 ` iii. 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 Scale invariant standard model & hidden sector Described by the effective model TeV Dynamical scale symmetry breaking Electroweak symmetry breaking
Contents The model 1. Dark matter candidates 2. 1 st order phase transition of electroweak 3. symmetry (at finite temperature)
Dark matter candidate is p The excitation fields from the vacuum < 𝑇 J 𝑇 > n Assume the unbroken U(𝑂 B ) flavor symmetry: p Mean-field Lagrangian (before integrating 𝑇 )
Dark matter candidate is p Decay into Higgs through 𝑇 loop Forbidden by flavor symmetry p Coannihilation
Mass of dark matter p Mass = a pole of two point function n Inverse two point function of 𝜚 d (dark matter) n Find zero
Direct detection p Scattering off the Nuclei n Spin independent cross section 𝑛 e : nucleon mass 𝑠̂ : nucleonic matrix element
𝜏 ij vs. 𝑛 @\
Contents The model 1. Dark matter candidates 2. 1 st order phase transition of electroweak 3. symmetry (at finite temperature)
EW Baryogenesis scenario p Sakharov conditions Baryon number violation 1. C-symmetry and CP-symmetry violation 2. Interactions out of thermal equilibrium. 3. 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 Summation of thermal mass (remove the IR divergence) All SM particles ・ ・ ・ ・ ・ ・
Phase transition p 𝑊 YBB at zero temperature "# (EWPT) p 𝑊 YBB at critical temperature 𝑈 l ii (SSPT) p 𝑊 YBB at critical temperature 𝑈 l
Scale transition is strong 1 st order. J, Kubo and M. Y. , PTEP 2015 093B01 (arXiv:1506.06460)
Without dark matter case: 𝑂 B = 1 EW phase transition becomes strong 1 st order Two phase transition occur at the same time EWSB is triggered by SSB.
With dark matter case: 𝑂 B = 2 EW phase transition becomes weak 1 st order
Difference between two cases p The Higgs portal is important n Large 𝜇 QU : p The DM relic abundance becomes too small. n Small 𝜇 QU : p The strong 1 st order phase transition in hidden sector is not transmitted to the standard model sector. p Improved analysis might realize the strong EW 1 st order 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 < 𝑇 J 𝑇 >≠ 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 < 𝑇 J 𝑇 >≠ 0 n The EW symmetry breaking < ℎ >≠ 0 “Scalegenesis” is realized! p Dark matter candidate exists. p The EW 1 st order phase transition
Appendix
Argument by Bardeen W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 (1995).
In viewpoint of Wilson RG Broken phase Symmetric phase Phase boundary (massless) Fine-tuning problem = criticality problem Why is the Higgs close to critical?
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