2-photon decay rate of the Scalar boson in the Inert Doublet Model Bogumiła Świeżewska in collaboration with Maria Krawczyk, based on arXiv:1212.4100 [hep-ph] Faculty of Physics, University of Warsaw 05.03.2013 Recontres de Moriond, La Thuile, Italy B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 1 / 7
The Inert Doublet Model (IDM) ❬◆✳ ●✳ ❉❡s❤♣❛♥❞❡✱ ❊✳ ▼❛✱ P❤②s✳ ❘❡✈✳ ❉ ✶✽ ✭✶✾✼✽✮ ✷✺✼✹✱ ❘✳ ❇❛r❜✐❡r✐✱ ▲✳ ❏✳ ❍❛❧❧✱ ❱✳ ❙✳ ❘②❝❤❦♦✈✱ P❤②s✳ ❘❡✈✳ ❉ ✼✹ ✭✷✵✵✻✮ ✵✶✺✵✵✼✱ ◗✳✲❍✳ ❈❛♦✱ ❊✳ ▼❛✱ ●✳ ❘❛❥❛s❡❦❛r❛♥✱ P❤②s✳ ❘❡✈✳ ❉ ✼✻ ✭✷✵✵✼✮ ✵✾✺✵✶✶✱ ❊✳ ▼✳ ❉♦❧❧❡✱ ❙✳ ❙✉✱ P❤②s✳ ❘❡✈✳ ❉ ✽✵ ✭✷✵✵✾✮ ✵✺✺✵✶✷✱ ▲✳ ▲♦♣❡③ ❍♦♥♦r❡③✱ ❊✳ ◆❡③r✐✱ ❋✳ ❏✳ ❖❧✐✈❡r✱ ▼✳ ❚②t❣❛t✱ ❏❈❆P ✵✼✵✷ ✭✷✵✵✼✮ ✵✷✽✱ ❉✳ ❙♦❦♦➟♦✇s❦❛✱ ❛r❳✐✈✿✶✶✵✼✳✶✾✾✶ ❬❤❡♣✲♣❤❪❪ � For a review of IDM see the talk by M. Tytgat Simple extension of the Standard Model (SM) Two scalar doublets φ ❙ and φ ❉ , �φ ❙ � = ✈ ✷ , �φ ❉ � = ✵ √ φ ❙ : ❤ – SM-like scalar, tree-level couplings to fermions and gauge bosons like in the SM. Deviation from SM in loop couplings possible! φ ❉ : ❍ , ❆ , ❍ ± – dark scalars, no tree-level couplings to fermions Exact ❉ symmetry: φ ❉ → −φ ❉ � lightest ❉ -odd particle stable � DM candidate ( ❍ ) Three regions of masses (low, medium or large) consistent with astrophysical observations B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 2 / 7
2-photon decay rate of the SM-like scalar ❬❏✳ ❘✳ ❊❧❧✐s✱ ▼✳ ❑✳ ●❛✐❧❧❛r❞ ❛♥❞ ❉✳ ❱✳ ◆❛♥♦♣♦✉❧♦s✱ ◆✉❝❧✳ P❤②s✳ ❇ ✶✵✻ ✭✶✾✼✻✮ ✷✾✷✱ ▼✳ ❆✳ ❙❤✐❢♠❛♥✱ ❆✳ ■✳ ❱❛✐♥s❤t❡✐♥✱ ▼✳ ❇✳ ❱♦❧♦s❤✐♥ ❛♥❞ ❱✳ ■✳ ❩❛❦❤❛r♦✈✱ ❙♦✈✳ ❏✳ ◆✉❝❧✳ P❤②s✳ ✸✵ ✭✶✾✼✾✮ ✼✶✶ ❬❨❛❞✳ ❋✐③✳ ✸✵✱ ✶✸✻✽ ✭✶✾✼✾✮❪✱ P✳ P♦s❝❤✱ P❤②s✳ ▲❡tt✳ ❇✻✾✻ ✭✷✵✶✶✮ ✹✹✼✱ ❆✳ ❆r❤r✐❜✱ ❘✳ ❇❡♥❜r✐❦✱ ◆✳ ●❛✉r✱ P❤②s✳ ❘❡✈✳ ❉✽✺ ✭✷✵✶✷✮ ✵✾✺✵✷✶❪ ❘ γγ – 2-photon decay rate ❘ γγ = σ ( ♣♣ → ❤ → γγ ) ■❉▼ σ ( ♣♣ → ❤ → γγ ) ❙▼ ≈ Γ( ❤ → γγ ) ■❉▼ Γ( ❤ ) ❙▼ Γ( ❤ → γγ ) ❙▼ Γ( ❤ ) ■❉▼ Two sources of deviation from ❘ γγ = ✶ : invisible decays ❤ → ❍❍ , ❤ → ❆❆ in Γ( ❤ ) ■❉▼ charged scalar loop in Γ( ❤ → γγ ) ■❉▼ � � ✹▼ ✷ �� � � ✷ Γ( ❤ → γγ ) ■❉▼ = ● ❋ α ✷ ▼ ✸ � A ❙▼ + ✷▼ ✷ ❍ ± + ♠ ✷ � � ❍ ± ❤ ✷✷ √ ❆ ✵ � ✷▼ ✷ ▼ ✷ ✷ π ✸ ✶✷✽ ❍ ± ❤ B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 3 / 7
Scan of the parameter space Parameters: ( λ ✶ , λ ✷ , λ ✸ , λ ✹ , λ ✺ , ♠ ✷ ✷✷ ) or ( ▼ ❤ , ▼ ❍ , ▼ ❆ , ▼ ❍ ± , ♠ ✷ ✷✷ , λ ✷ ) We took into account: Vacuum stability Perturbative unitarity Electroweak Precision Tests (EWPT) LEP bounds LHC data: ▼ ❤ = ✶✷✺ GeV ❍ as DM candidate ✷✷ � ✾ · ✶✵ ✹ GeV ✷ Existence of the Inert vacuum (new) � ♠ ✷ B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 4 / 7
❘ γγ vs Dark Matter mass ❬s❡❡ ❛❧s♦✿ ❆✳ ❆r❤r✐❜✱ ❘✳ ❇❡♥❜r✐❦✱ ◆✳ ●❛✉r✱ P❤②s✳ ❘❡✈✳ ❉✽✺ ✭✷✵✶✷✮ ✵✾✺✵✷✶❪ Invisible channels open � no enhancement in ❤ → γγ possible Enhanced ❘ γγ for ▼ ❍ , ▼ ❍ ± , ▼ ❆ > ✻✷ . ✺ GeV B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 5 / 7
❘ γγ vs charged scalar mass Enhanced ❘ γγ possible for ✷✷ < − ✾ . ✽ · ✶✵ ✸ GeV ✷ ♠ ✷ any value of ▼ ❍ ± If ❘ γγ > ✶ . ✸ , then: ▼ ❍ ± , ▼ ❍ � ✶✸✺ GeV Only medium DM mass! B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 6 / 7
Summary IDM in agreement with the data (LHC and WMAP) ❤ → γγ can provide important information about IDM, because is sensitive to ▼ ❍ and ▼ ❍ ± If ❘ γγ > ✶ . ✸ ✻✷ . ✺ GeV < ▼ ❍ ± , ▼ ❍ � ✶✸✺ GeV � Only medium masses of DM! � Light charged scalar! − ✶ . ✹✻ < λ ❤❍ + ❍ − , λ ❤❍❍ < − ✵ . ✷✹ I eagerly wait for the experimental results! B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 7 / 7
Back up B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 8 / 7
❘ γγ vs λ ❤❍❍ and λ ❤❍ + ❍ B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 9 / 7
❤ → ❩ γ - Preliminary ❬❙❡❡ ❛❧s♦ t❛❧❦ ❜② ❆✳ ❆r❤r✐❜ ❛t ❚♦②❛♠❛ ❈♦♥❢❡r❡♥❝❡ ✵✷✳✷✵✶✸❪ B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 10 / 7
Potential ❬◆✳ ●✳ ❉❡s❤♣❛♥❞❡✱ ❊✳ ▼❛✱ P❤②s✳ ❘❡✈✳ ❉ ✶✽ ✭✶✾✼✽✮ ✷✺✼✹✱ ❏✳ ❋✳ ●✉♥✐♦♥✱ ❍✳ ❊✳ ❍❛❜❡r✱ ●✳ ❑❛♥❡✱ ❙✳ ❉❛✇s♦♥✱ ❚❤❡ ❍✐❣❣s ❍✉♥t❡r✬s ●✉✐❞❡ ✱ ✶✾✾✵ ❆❞❞✐s♦♥✲❲❡s❧❡②✱ ■✳ ❋✳ ●✐♥③❜✉r❣✱ ❑✳ ❆✳ ❑❛♥✐s❤❡✈✱ ▼✳ ❑r❛✇❝③②❦✱ ❉✳ ❙♦❦♦➟♦✇s❦❛✱ P❤②s✳ ❘❡✈✳ ❉ ✽✷ ✭✷✵✶✵✮ ✶✷✸✺✸✸❪ � � � ❉ φ ❉ ) ✷ � ❙ φ ❙ ) ✷ + λ ✷ ( φ † ✶✶ ( φ † ✷✷ ( φ † λ ✶ ( φ † ❱ = − ✶ ❙ φ ❙ ) + ♠ ✷ ❉ φ ❉ ) + ✶ + ♠ ✷ ✷ ✷ + λ ✸ ( φ † ❙ φ ❙ )( φ † ❉ φ ❉ ) + λ ✹ ( φ † ❙ φ ❉ )( φ † ❉ φ ❙ )+ � ❉ φ ❙ ) ✷ � ❙ φ ❉ ) ✷ + ( φ † ( φ † ✶ ✷ λ ✺ Z ✷ symmetry ( ❉ symmetry): φ ❉ → −φ ❉ , φ ❙ → φ ❙ Positivity constraints: b) λ ✸ + √λ ✶ λ ✷ > ✵ , a) λ ✶ > ✵ , λ ✷ > ✵ , c) λ ✸ + λ ✹ + λ ✺ + √λ ✶ λ ✷ > ✵ B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 11 / 7
Constraints Vacuum stability: For a stable vacuum state to exist it is necessary that the potential ❱ is bounded from below, which leads to: � � λ ✶ > ✵ , λ ✷ > ✵ , λ ✸ + λ ✶ λ ✷ > ✵ , λ ✸✹✺ + λ ✶ λ ✷ > ✵ . Perturbative unitarity: For the theory to be perturbatively unitary it is required that the eigenvalues Λ ✐ of the high-energy scattering matrix fulfill the condition | Λ ✐ | < ✽ π . Existence of the Inert vacuum: The Inert vacuum can be realized only if the following conditions are fulfilled: ♠ ✷ > ♠ ✷ ▼ ✷ ❤ , ▼ ✷ ❍ , ▼ ✷ ❆ , ▼ ✷ ✶✶ ✷✷ ❍ ± � ✵ , √λ ✶ √λ ✷ . From the existence of the Inert vacuum and the Higgs boson with mass ▼ ❤ = ✶✷✺ GeV, and unitarity bounds on λ ✷ , follows a bound on ♠ ✷ ✷✷ : ✷✷ � ✾ · ✶✵ ✹ GeV ✷ . ♠ ✷ B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 12 / 7
Constraints ❍ as DM candidate: We assume that ❍ is the DM candidate, so ▼ ❍ < ▼ ❆ , ▼ ❍ ± . Studies of the DM in the IDM show that if ❍ is to account for the observed relic density of DM, it should have mass in one of the three regions: ▼ ❍ < ✶✵ GeV, ✹✵ GeV < ▼ ❍ < ✽✵ GeV or ▼ ❍ > ✺✵✵ GeV. Electroweak Precision Tests (EWPT): We demand that the values of ❙ and ❚ parameters calculated in the IDM lie within ✷ σ ellipses in the ❙ , ❚ plane, with the following central values: ❙ = ✵ . ✵✸ ± ✵ . ✵✾ , ❚ = ✵ . ✵✼ ± ✵ . ✵✽ , with correlation equal to 87%. LEP: We use the LEPI and LEPII bounds on the scalar masses: ▼ ❍ ± + ▼ ❍ > ▼ ❲ , ▼ ❍ ± + ▼ ❆ > ▼ ❲ , ▼ ❍ ± > ✼✵ GeV ▼ ❍ + ▼ ❆ > ▼ ❩ , ✷ ▼ ❍ ± > ▼ ❩ , and exclude the region where: ▼ ❍ < ✽✵ GeV and ▼ ❆ < ✶✵✵ GeV and ▼ ❆ − ▼ ❍ > ✽ GeV . B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 13 / 7
DM signals ❬s❡❡ ❡✳❣✳✿ ▼✳ ●✉st❛❢ss♦♥✱ ❙✳ ❘②❞❜❡❝❦✱ ▲✳ ▲♦♣❡③ ❍♦♥♦r❡③✱ ❊✳ ▲ö♥❞str♦♠✱ P❤②s✳ ❘❡✈✳ ❉ ✽✻ ✭✷✵✶✷✮ ✵✼✺✵✶✾❪ gamma-ray lines cosmic and neutrino fluxes direct detection signals B. Świeżewska (University of Warsaw) γγ decay of BSMS in IDM 05.03.2013 14 / 7
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