Evolution of the Universe & Inert Phase: The Inert Model Today

1. USTROŃ 2009 15.09. 2009 Evolution of the Universe to the present Inert phase 2HDMs Z2 symmetry The Inert Model Various vacua Today= Inert phase Thermal evolutions Maria Krawczyk University of Warsaw I. Ginzburg, K. Kanishev (Novosibirsk University), D.Sokołowska (University of Warsaw)

2. Brout-Englert-Higgs mechanism Spontaneous breaking of EW symmetry SU(2) x U(1) → U(1) QED Standard Model Doublet of SU(2): vHi Masses for W, Z (tree =1) , no mass for the photon Fermion masses via Yukawa interaction Higgs particle HSM - spin 0, neutral, CP even couplings to WW/ZZ, Yukawa couplings to fermions mass  selfinteraction unknown

3. Brout-Englert-Higgs mechanism Spontaneous breaking of EW symmetry SU(2) x U(1) → ? Two Higgs Doublet Models Two doublets of SU(2) (Y=1, =1) - Φ₁ , Φ₂ Masses for W, Z , no mass for photon? Fermion masses via Yukawa interaction – various models: Model I, II, III, IV,X,Y,... 5 scalars: H+ and H- and neutrals: - CP conservation: CP-even h, H & CP-odd A - CP violation: h1,h2,h3 with undefinite CP parity* Sum rules (relative couplings to SM )

4. 2HDM Potential Lee'73, Haber, Gunion, Glashow, Weinberg, Paschos, Despande, Ma, Wudka, Branco, Rebelo, Lavoura, Ferreira, Barroso, Santos, Bottela, Silva, Diaz-Cruz, Grimus, Ecker, Ivanov, Ginzburg, Krawczyk, Osland, Nishi, Nachtmann, Akeroyd, Kanemura, Kalinowski, Grządkowski ,Hollik, Rosiek.. V = λ1(Φ₁†Φ₁)²+λ₂(Φ₂†Φ₂)²+λ₃(Φ₁†Φ₁)(Φ₂†Φ₂) + λ₄(Φ₁†Φ₂)(Φ₂†Φ₁)+ [λ₅(Φ₁†Φ₂)²+h.c] + [(λ₆(Φ₁†Φ₁)+λ₇(Φ₂†Φ₂))(Φ₁†Φ₂)+h.c] -m²₁₁(Φ₁†Φ₁)-m²₂₂(Φ₂†Φ₂)-[m²₁₂(Φ₁†Φ₂)+h.c.] Z₂ symmetry transformation: Φ₁→Φ₁ Φ₂→ - Φ₂ Hard Z₂ symmetry violation: λ₆, λ₇ terms Soft Z₂ symmetry violation: m²₁₂ term (Re m²₁₂=µ²) Explicit Z₂ symmetry in V: λ₆, λ₇, m²₁₂=0

5. - If Z2 symmetry holds in the Lagrangian L no CP violation in the scalar sector Lee' 73 Glashow, Weinberg'77, Paschos '77 Despande, Ma' 78 - Softly broken Z2→ Branco, Rebelo '85 CP violation possible, tree-level FCNC absent, Decoupling and non-decoupling possible Haber'95 - Hard breaking Z2→ CP violation possible [* even without CP mixing] Lavoura, Silva' 94 ; Kanishev, MK, Sokołowska' 2008 tree-level FCNC Z2 symmetry: Φ₁ → Φ₁ Φ₂→- Φ₂

6. Yukawa interactions (with or withoutZ2 symmetry) Model I - only Φ₁interacts with fermions Model II - Φ1 couples to down-type fermions d Φ2couplesup-type fermions u Model III - both doublets interact with fermions Model X - leptons interact with one doublet, quarks with other Top 2HDM – only top couples to one doublet + Extra dim 2HDM models ...

7. Inert or Dark 2HDM Ma'78 Barbieri'06 Z2 symmetry under Φ₁ → Φ₁ Φ₂→- Φ₂ both in L and in vacuum → Inert Model → Φ₁ as in SM, with Higgs boson h (SM-like) → Φ₂ - no vev, with 4 scalars (no Higgs bosons!) no interaction with fermions (inert doublet) Conservation of the Z2 symmetry; only Φ₂ has odd Z2 -parity → The lightest scalar – a candidate for dark matter (Φ2 dark doublet with dark scalars) . Conserved Z₂- parity only Φ₂ has Z₂-odd parity. Today <Φ₁T >= (0,v) <Φ2T >= (0,0)

8. Vacua for the potential with explicit Z2 symmetry and real parameters Finding extrema: VΦ₁Φ₁Φ₁and Φ₁ → Φ2 Finding minima → global minimum = vacuum Positivity (stability) constraints (for λ₆, λ₇, m²₁₂=0) Extremum fulfilling the positivity constraints with the lowest energy = vacuum Ginzburg, Kanishev, MK, Sokołowska'09

9. Possible vacuum states (V with explicit Z2) The most general vacuum state v1, v2, u , ξ - real,  0 v2 =v12 +v22 +u2 = (246 GeV)2 Inert I u = v2 = 0 Normal (CP conserving) N u = ξ = 0 Charge Breaking Ch u≠0 v2 =0 [ Vacuum B u = v1 = 0]

10. Various vacua on (λ4 , λ5) plane Positivity constrains on V: X=λ1λ2+λ3>0λ4 ± λ5 > - X Inert (or B) Y = MH+2 2/v2 Charge Breaking Ch Normal Note the overlap of the Inert with N and Ch !

11. TODAY 2HDM with explicit Z2 symmetry Φ₁ → Φ₁ Φ₂→- Φ₂ Model I (Yukawa int.) Charged breaking phase ? photon is massive, el.charge is not conserved... → no Neutral phases: Normal ok, many data, but no DM Inert OK! there are some data B no, all fermions massless, no DM

12. LEP: 2HDM (N vacuum) v1,v2 (tan );Model I,II..

13. Inert Model (Dark 2HDM) vs dataMa..' 78, Barbieri.. ' 2006 Exact Z₂ symmetry in L and in vacuum → Z2-parity: odd is only Φ₂ Φ₁ Nonzero vev has only doublet Φ₁ (Higgs doublet) only it couples to fermions (Model I) SM-like Higgs boson h M2h= m112 = 1 v2 Φ₂ Zero vev for Φ₂ (scalar doublet) and no Yukawa int. Four scalars with odd Z₂-parity (dark scalars D) The lightest dark scalar - stable

14. Dark scalars D = H+,H-,H,A Masses D couple to V = W/Z (eg. AZH, H⁻ W⁺H), not to V V! Selfcouplings DDDD proportional to  Couplings between Higgs boson h and D proportional toM2D + m222 /2

15. Intert Model – dark scalar massesusing X (positivity) andY = MH+2 2/v2 here H+ the heaviest here H is the dark matter candidate (λ5  0)

16. Testing Inert Model To consider properties of SM-like h (light and heavy) properties of dark scalars (produced only in pairs!) DM candidate Colliders signal/constraints Barbieri et al '2006 for heavy h Cao, Ma, Rajasekaren' 2007 for a light h

17. Dark 2HDM: LEP II exclusion Lundstrom et al 0810.3924 LEP II + WIMP Mh= 200 GeV MA- MH > 8 GeV

18. Inert Model: constraints LEP+DM → LHC E. Dolle, S. Su, 0906.1609 [hep-ph] LEP (exclusion and EW precision data) + relic density using MicroOMEGA/CalCHEP S=H Su, CERN, August 2009

19. S = H (DM)

20. Dark 2HDM – additional decays for h Ma' 2007

21. Dark 2HDM – total width of h

23. Conclusion on gamma lines Gustafsson et al.2007: Striking DM line signals -promising features to search with GLAST Mass of: H = 40-80 GeV, H+ = 170 GeV, A = 50-70 GeV, h = 500 and 120 GeV Honorez, Nezri, Oliver, Tytgat 2006-7: H as a perfect example or arcgetype of WIMP – within reach of GLAST (FERMI) Here mass of h = 120 GeV, large mass H+ close to A = 400 - 550 GeV

24. Evolution of the Universe – different vacua in the past ? We consider 2HDM with an explicit Z2 symmetry assuming that today the Inert Model is realized. Useful parametrization with k and δ Yukawa interaction – Model I → all fermions couple only to Φ₁

25. Possible vacua: Ch Inert B u=0 N Depending on value of δ → a true vacuum (with the minimal energy) u≠0

26. Possible vacua at differentδ

27. Termal corrections of parameters Matsubara method (temperature T>> m2) – -only quadratic (mass) parameters change with T δ(T) with T  → different phases

28. Phase transitions from the EW symmetric phase For to the present INERT phase

29. Conclusions Rich content of 2HDMs Intert Model in agreement with present data – soon tests at FERMI and LHC What was in the Past? Various scenarios Can we find clear signals ? excluded if DM neutral !

30. Conclusions 2HDM – a great laboratory for physics BSM In many Standard Models SM-like scenarios can be realized: [Higgs mass >114 GeV, SM tree-level couplings] In models with two doublets: - MSSM with decoupling of heavy Higgses → LHC-wedge - 2HDM with and without CP violation both h or H can be SM-like - Dark 2HDM (Intert Model) Loop effects = a window to heavy sector

31. SM-like scenarios In many Standard Models SM-like scenarios are realized (Higgs mass >114 GeV, SM tree-level couplings) In models with two doublets: - MSSM with decoupling of heavy Higgses → LHC-wedge - 2HDM with and without CP violation both h or H can be SM-like - Dark 2HDM (Intert Model)

32. Dark 2HDM: h 