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

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

3. Brout-Englert-Higgs mechanism Brout-Englert-Higgs mechanism Spontaneous breaking of EW symmetry Spontaneous breaking of EW symmetry SU(2) x U(1) → ? SU(2) x U(1) → ? Two Higgs Doublet Models Two Higgs Doublet Models Two doublets of SU(2) (Y=1,  =1) - Φ₁, Φ₂ Two doublets of SU(2) (Y=1,  =1) - Φ₁, Φ₂ Masses for W , Z, no mass for photon? Masses for W , Z, no mass for photon? Fermion masses via Yukawa interaction – Fermion masses via Yukawa interaction – various models: Model I, II, III, IV,X,Y,... 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 conservation: CP-even h, H & CP-odd A - CP violation: h 1,h 2,h 3 with undefinite CP parity* - CP violation: h 1,h 2,h 3 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 = λ 1 (Φ₁†Φ₁)²+λ₂(Φ₂†Φ₂)²+λ₃(Φ₁†Φ₁)(Φ₂†Φ₂) V = λ 1 (Φ₁†Φ₁)²+λ₂(Φ₂†Φ₂)²+λ₃(Φ₁†Φ₁)(Φ₂†Φ₂) + λ₄(Φ₁†Φ₂)(Φ₂†Φ₁)+ [λ₅(Φ₁†Φ₂)²+h.c] + λ₄(Φ₁†Φ₂)(Φ₂†Φ₁)+ [λ₅(Φ₁†Φ₂)²+h.c] + [(λ₆(Φ₁†Φ₁)+λ₇(Φ₂†Φ₂))(Φ₁†Φ₂)+h.c] + [(λ₆(Φ₁†Φ₁)+λ₇(Φ₂†Φ₂))(Φ₁†Φ₂)+h.c] -m²₁₁(Φ₁†Φ₁)-m²₂₂(Φ₂†Φ₂)-[m²₁₂(Φ₁†Φ₂)+h.c.] -m²₁₁(Φ₁†Φ₁)-m²₂₂(Φ₂†Φ₂)-[m²₁₂(Φ₁†Φ₂)+h.c.] Z₂ symmetry transformation: Φ₁ → Φ₁ Φ₂ → - Φ₂ Z₂ symmetry transformation: Φ₁ → Φ₁ Φ₂ → - Φ₂ Hard Z₂ symmetry violation: λ₆, λ₇ terms Hard Z₂ symmetry violation: λ₆, λ₇ terms Soft Z₂ symmetry violation: m²₁₂ term (Re m²₁₂=µ²) Soft Z₂ symmetry violation: m²₁₂ term (Re m²₁₂=µ²) Explicit Z₂ symmetry in V: λ₆, λ₇, m²₁₂=0 Explicit Z₂ symmetry in V: λ₆, λ₇, m²₁₂=0

5. - If Z 2 symmetry holds in the Lagrangian L no CP violation in the scalar sector no CP violation in the scalar sector Lee' 73 Glashow, Weinberg'77, Paschos '77 Despande, Ma' 78 - Softly broken Z 2 → - Softly broken Z 2 → Branco, Rebelo '85 CP violation possible, tree-level FCNC absent, CP violation possible, tree-level FCNC absent, Decoupling and non-decoupling possible Haber'95 Decoupling and non-decoupling possible Haber'95 - Hard breaking Z 2 → - Hard breaking Z 2 → CP violation possible [* even without CP mixing] CP violation possible [* even without CP mixing] Lavoura, Silva' 94 ; Kanishev, MK, Sokołowska' 2008 Lavoura, Silva' 94 ; Kanishev, MK, Sokołowska' 2008 tree-level FCNC tree-level FCNC Z 2 symmetry: Φ₁ → Φ₁ Φ₂ → - Φ₂

6. Yukawa interactions ( with or without Z 2 symmetry) Model I - only Φ₁ interacts with fermions Model I - only Φ₁ interacts with fermions Model II - Φ 1 couples to down-type fermions d Model II - Φ 1 couples to down-type fermions d Φ 2 couples up-type fermions u Φ 2 couples up-type fermions u Model III - both doublets interact with fermions Model III - both doublets interact with fermions Model X - leptons interact with one doublet, quarks with other Model X - leptons interact with one doublet, quarks with other Top 2HDM – only top couples to one doublet Top 2HDM – only top couples to one doublet + Extra dim 2HDM models... + Extra dim 2HDM models...

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

8. Vacua for the potential with explicit Z 2 symmetry and real parameters Finding extrema:  V  Φ₁  Φ₁  Φ₁    and  Φ₁ → Φ 2  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 Z 2 ) The most general vacuum state v 1, v 2, u, ξ - v 1, v 2, u, ξ - real,  0 real,  0 v 2 =v 1 2 +v 2 2 +u 2 = (246 GeV) 2 v 2 =v 1 2 +v 2 2 +u 2 = (246 GeV) 2 Inert I u = v 2 = 0 Inert I u = v 2 = 0 Normal (CP conserving) N u = ξ = 0 Normal (CP conserving) N u = ξ = 0 Charge Breaking Ch u ≠ 0 v 2 =0 Charge Breaking Ch u ≠ 0 v 2 =0 [ Vacuum B u = v 1 = 0] [ Vacuum B u = v 1 = 0]

10. Various vacua on ( λ 4, λ 5 ) plane Various vacua on ( λ 4, λ 5 ) plane Positivity constrains on V: X=  λ 1 λ 2 +λ 3 >0 λ 4 ± λ 5 > - X Inert (or B) Inert (or B) Y = M H+ 2 2/v 2 Y = M H+ 2 2/v 2 Charge Breaking Charge Breaking Ch ChNormal Note the overlap of the Inert with N and Ch ! Note the overlap of the Inert with N and Ch !

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

12. LEP: 2HDM (N vacuum) v 1,v 2 (tan  );Model I,II..

13. Inert Model (Dark 2HDM) vs data Ma..' 78, Barbieri.. ' 2006 Inert Model (Dark 2HDM) vs data Ma..' 78, Barbieri.. ' 2006 Exact Z₂ symmetry in L and in vacuum → Exact Z₂ symmetry in L and in vacuum → Z 2 -parity: odd is only Z 2 -parity: odd is only Φ₂Φ₁ Nonzero vev has only doublet Φ₁ (Higgs doublet) Nonzero vev has only doublet Φ₁ (Higgs doublet) only it couples to fermions (Model I) only it couples to fermions (Model I) SM-like Higgs boson h SM-like Higgs boson h M 2 h = m 11 2 = 1 v 2Φ₂ Zero vev for Φ₂ (scalar doublet) and no Yukawa int. Zero vev for Φ₂ (scalar doublet) and no Yukawa int. Four scalars with odd Z₂- parity (dark scalars D) Four scalars with odd Z₂- parity (dark scalars D) The lightest dark scalar - stable The lightest dark scalar - stable

14. Dark scalars D = H+,H-,H,A Masses Masses D couple to V = W/Z (eg. AZH, H ⁻ W ⁺ H), D couple to V = W/Z (eg. AZH, H ⁻ W ⁺ H), not to V V! not to V V! Selfcouplings DDDD proportional to Selfcouplings DDDD proportional to  Couplings between Higgs boson h and D proportional to M 2 D + m 22 2 /2

15. Intert Model – dark scalar masses using X (positivity) and Y = M H+ 2 2/v 2 here H+ here H+ the heaviest the heaviest here H is the dark matter candidate ( λ 5  0) here H is the dark matter candidate ( λ 5  0)

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

17. Dark 2HDM: LEP II exclusion Lundstrom et al 0810.3924 LEP II + WIMP M h = 200 GeV M h = 200 GeV M A - M H > 8 GeV M A - M H > 8 GeV

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

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

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

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

26. Possible vacua at different δ

27. Termal corrections of parameters Matsubara method (temperature T>> m 2 ) – -only quadratic (mass) parameters change with T -only quadratic (mass) parameters change with T δ(T)  with T  → different phases

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

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

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

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

32. Dark 2HDM:  h 