Invisible Sterile Neutrinos March 25, 2010
Outline Overview of Sterile Neutrino Dark Matter The Inert Doublet Model with 3 Singlet Fermions Non-thermal Dark Matter Conclusion Work done in collaboration with Sergio Palomares-Ruiz and Graciela Gelmini
Sterile Neutrino Dark Matter In Standard Model (SM), the 3 active neutrinos are massless. Neutrino oscillations tells us that neutrinos have mass. Right-handed or sterile neutrinos can explain neutrino masses Sterile Neutrinos produced through active-sterile oscillations are good dark matter (DM) candidates. Typical masses in the kev range.
10-6 10-7 Ω N1 > Ω DM NRP 10-8 X-ray constraints sin 2 (2θ 1 ) 10-9 10-10 10-11 10-12 10-13 Phase-space density constraints L 6 =25 L 6 =70 L 6 max =700 BBN limit: L 6 BBN = 2500 10-14 10-15 Ω N1 < Ω DM 1 5 10 50 M 1 [kev] Figure: Sterile Neutrino Dark Matter (Boyarsky, Ruchayskiy and Shaposhnikov 2009)
Ingredients of the Model Inert Doublet Model with 3 Singlet Fermions (Ma, 2006),(Barbieri, Rychkov, Hall 2006) L Y = f ij (φ ν i + φ 0 l i )l c j + h ij (ν i η 0 l j η + )N j + h.c. Ingredients of the Model 3 singlet fermions N i Second scalar doublet that consists of η ± and η 0, η H = 2Im(η 0 ), η L = 2Re(η 0 ). SM particles are even under Z 2 symmetry and the additional particles are odd.
Ingredients of the Model Scalar Potential µ 2 1 Φ Φ + µ 2 2 η η + λ 1 (Φ Φ) 2 + λ 2 (η η) 2 + λ 3 (Φ Φ)(η η) + λ 4 (Φ η)(η Φ) + 1 2 λ 5[(Φ η) 2 + h.c.] η does not acquire a vev. λ 5 provides a mass splitting between the neutral η L and η H m 2 η H m 2 η L = λ 5 v 2.
Ingredients of the Model Z 2 discrete symmetry prevents active-sterile oscillations. Moreover, the lightest of N i or η is a viable dark matter candidate. Various models consider η 0 as the DM candidate (Dolle,Su 2009), (Tytgat et al. 2007). We will consider N 1 to be the DM candidate.
Neutrino Masses The active neutrinos acquire Majorana masses at the one loop level. φ 0 φ 0 η 0 η 0 ν L N ν L Figure: One-loop radiative neutrino mass (Ma,Kubo, Suematsu 2006) The neutrino masses depend on the Yukawa type couplings h ij
Model Specification A mass hierarchy of N 1,2 η ± > η H > η L N 1. Small h ij to ensure that N i s are never in chemical equilibrium in the early universe. h ij should also be small enough to ensure that flavor changing transitions don t occur, µ eγ. But h ij have to be large enough to ensure active neutrinos have mass, 0.01eV. h ij 10 7 fulfill all the requirements.
Non-Thermal Dark Matter Processes that keep η L in chemical equilibrium λ l = λ 3 + λ 4 + λ 5 η L decays into N 1 after freeze-out, η L N 1 + ν From the relic density of η L, we obtain the relic density of N 1 ( ) Ω N1 h 2 = Ω ηl h 2 MN1, m ηl
0.3 0.25 0.2 0.01 0.1 0.2 0.3 0.5 Ω h 2 0.15 0.1 0.05 0 10 20 30 40 50 60 70 80 90 100 m S [GeV] Figure: Relic Density of η L with various values of λ L, M Higgs = 120GeV, = 8 GeV (Dolle, Su 2009)
Additional constraints Stability of Scalar Potential λ 1,2 > 0,λ 2 < 1 λ 3,λ L λ 5 λ 5 > 2 λ 1 λ 2, Pertubativity of the Scalar Potential λ 3 2 + (λ L λ 5 ) 2 + λ 5 2 < 12λ 1 2. From LEP I measurements, M w < M η ± + M ηl,h and M z < M η 0. Considerations from LEP II lead to m ηl < 80GeV and m ηh > 120 GeV.
0.9 0.6 0.3 λ L 0-0.3-0.6 10 3 M 1 [MeV] 10 2 10 1 10 0 10-1 CDM WDM Possible λ L = 10-2 λ L = 10-3 λ L = 10-4 10-2 10-3 HDM 10 20 30 40 50 60 70 80 90 100 m ηl [GeV] Figure: In both panels, M Higgs = 160 GeV, m ηh m η ± = 130 GeV. = 125 GeV and
4 2 0 λ L -2-4 -6 10 3 M 1 [MeV] 10 2 10 1 10 0 10-1 CDM WDM Possible λ L = 10-1 λ L = 10-2 λ L = 10-3 10-2 10-3 HDM 10 20 30 40 50 60 70 80 90 100 m ηl [GeV] Figure: M Higgs = 500 GeV, m ηh = 150 GeV and m η ± = 300 GeV.
Conclusion A CDM candidate with mass > 1 10 MeV or WDM candidate with mass in the range of 10 kev to a few MeV. DM virtually non-detectable in direct or indirect searches of dark matter. Collider searches of other particles in the model can reveal the existence of this type of dark matter.