2-photon decay rate of the Scalar boson in the Inert Doublet Model - - PowerPoint PPT Presentation

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(❤ → γγ)❙▼ Γ(❤)❙▼ Γ(❤)■❉▼

Two sources of deviation from ❘γγ = ✶: invisible decays ❤ → ❍❍, ❤ → ❆❆ in Γ(❤)■❉▼ charged scalar loop in Γ(❤ → γγ)■❉▼

Γ(❤ → γγ)■❉▼ = ●❋α✷▼✸

❤

✶✷✽ √ ✷π✸

• A❙▼+✷▼✷

❍± + ♠✷ ✷✷

✷▼✷

❍±

❆✵ ✹▼✷

❍±

▼✷

❤

• ✷
• 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 Existence of the Inert vacuum (new) ♠✷

✷✷ ✾ · ✶✵✹ GeV✷

• 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❙) + ♠✷ ✷✷(φ† ❉φ❉)

• + ✶

✷

• λ✶(φ†

❙φ❙)✷ + λ✷(φ† ❉φ❉)✷

+ +λ✸(φ†

❙φ❙)(φ† ❉φ❉) + λ✹(φ† ❙φ❉)(φ† ❉φ❙)+ ✶ ✷λ✺

• (φ†

❙φ❉)✷ + (φ† ❉φ❙)✷

Z✷ symmetry (❉ symmetry): φ❉ → −φ❉, φ❙ → φ❙ Positivity constraints: a) λ✶ > ✵, λ✷ > ✵, b) λ✸ + √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

• nly 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

• f ❙ 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