Sterile neutrino dark matter Oleg Ruchayskiy Ecole Polytechnique F´ ed´ erale de Lausanne together with A. Boyarsky, M. Shaposhnikov et al. The Dark Matter connection: Theory & Experiment GGI Florence May 21, 2010
Standard Model of Elementary Particles The Standard Model of elementary particle physics: from understanding the β -decay to the Large Hadron Collider. Is there a new physics beyond the Standard Model? Oleg Ruchayskiy S TERILE NEUTRINO DM 1/40
Why (and where) we expect new physics? � Dark matter (not a SM particle!) – particles with weak cross-section will have correct abundance Ω DM (“WIMP miracle”). New scale ∼ 1 TeV – Axions. New scale 10 10 − 10 12 GeV. � Baryon asymmetry of the Universe : what ensured that for each 10 10 anti-protons there was 10 10 + 1 proton in the early Universe? – Sakharov conditions: CP-violation; B-number violation; out-of- equilibrium particles. – Out-of-equilibrium decay of heavy lepton χ at temperatures M EW < T decay < M χ produces correct baryon-to-entropy ratio for M χ > 10 11 GeV – new energy scale � Fine-tuning problems: CP-problem, hierarchy problem, grand unification, cosmological constant problem Oleg Ruchayskiy S TERILE NEUTRINO DM 2/40
Hierarchy problem � Masses of fermions are provided by Quantum corrections to the the Higgs field Higgs mass: � Fermion corrections to the Higgs Higgs Higgs mass are proportional to their mass M 2 f . Fermion ? ⇓ � Contributions from heavy fermions ( M f ≫ 100 GeV) would make Higgs 100 GeV < M H < 300 GeV mass heavy M H ∼ M f ⇑ � To keep Higgs boson light, one should fine-tune the parameters of the model to cancel fermions’ Higgs Higgs contribution by that of Higgs Oleg Ruchayskiy S TERILE NEUTRINO DM 3/40
Alternatives? Build a model that resolves several BSM phenomena within its framework. Worry about fine-tunings later Oleg Ruchayskiy S TERILE NEUTRINO DM 4/40
Neutrino oscillations � Experiments on neutrino oscillations determined two mass differences between neutrino mass states � Sterile (right-handed) neutrinos provide the simplest and natural extension of the Minimal SM that describe oscillations. � Make leptonic sector of the SM symmetric. Oleg Ruchayskiy S TERILE NEUTRINO DM 5/40
See-saw Lagrangian Add right-handed neutrinos N I to the Standard Model 0 1 0 1 0 1 0 1 0 1 0 1 N c ν e ¯ N 1 N 1 1 L right = i ¯ A + N c N I / ∂N I + ν µ ¯ @ F � H � N 2 @ M N 2 @ A A @ @ A A @ A 2 ν τ ¯ . . . . . . . . . | {z } | {z } Dirac mass MD Majorana mass ν α = ˜ HL α , where L α are left-handed lepton doublets � Active masses are given via usual see-saw formula : 1 M T ( m ν ) = − M D ; M D ≪ M I D M I � Neutrino mass matrix – 7 parameters . Dirac+Majorana mass matrix – 11 (18) parameters for 2 (3) sterile neutrinos. Two sterile neutrinos are enough to fit the neutrino oscillations data. Scale of Dirac and Majorana masses is not fixed! Oleg Ruchayskiy S TERILE NEUTRINO DM 6/40
Some general properties of sterile neutrino � Sterile neutrinos are decaying particles M I < 1 MeV M I > 1 MeV M I > 150 MeV . . . N I → νe + e − N I → π ± e ∓ N I → νν ¯ ν N I → π 0 ν N I → νγ � Short lifetime – decay in the early Universe. Can have CP-violating phases. Leptogenesis? Affects BBN? � Lifetime τ ∝ θ − 2 I M − 5 . (Cosmologically) long lifetime – dark matter I candidate? � Mixing angle θ I : | F αI | 2 v 2 � θ 2 I = ≪ 1 M 2 I α = e,µ,τ Oleg Ruchayskiy S TERILE NEUTRINO DM 7/40
The scale of right-handed masses? “Popular” choices of see-saw parameters � Yukawa couplings F αI ∼ 1 , i.e. Dirac masses M D ∼ M t . Majorana masses M I ∼ 10 15 GeV. � Attractive features: – Provides a mechanism of baryon asymmetry of the Universe – Scale of Majorana masses is possibly related to GUT scale � This model does not provide the dark matter particle � Alternative? Choose Majorana masses M I of the order of masses of other SM fermions and make Yukawa couplings small Oleg Ruchayskiy S TERILE NEUTRINO DM 8/40
Neutrino minimal Standard Model ( ν MSM) eV t b c τ 10 10 N N 10 10 2 s 3 u µ N ν d 10 6 10 6 3 N e 1 ν N 2 10 2 10 2 ν 3 N ν 10 −2 10 −2 ν 1 2 ν quarks leptons 1 10 −6 10 −6 Dirac masses Majorana masses The model solves several beyond the Standard Model problems � . . . explains neutrino oscillations � . . . matter-antimatter asymmetry of the Universe � . . . provides a viable dark matter candidate that can be cold, warm or mixed (cold+warm) Oleg Ruchayskiy S TERILE NEUTRINO DM 9/40
Choosing parameters of the ν MSM � If M 2 , 3 ∼ 100 MeV − 20 GeV and ∆ M 2 , 3 ≪ M 2 , 3 ν MSM explains baryon asymmetry of the Universe. Asaka, Shaposhnikov � Neutrino experiments can be explained within the same choice of ’05 parameters. 10 -5 10 -6 No matter-antimatter asymmetry 10 -7 10 -8 2 10 -9 θ 2 10 -10 Constraints 10 -11 from primordial N synthes of light elements o n e u 10 -12 t r i n o o s c i l l a t i o n s 10 -13 0.1 1 10 M 2 [GeV] Oleg Ruchayskiy S TERILE NEUTRINO DM 10/40
Parameters of the third sterile neutrino? � The third sterile neutrino can couple to the SM arbitrarily weakly. Dark matter candidate? � Any DM candidate must be – Produced in the early Universe and have correct relic abundance – Be stable or cosmologically long-lived – Very weakly interacting with electromagnetic radiation (“dark”) – Allow to explain the observed large scale structure Oleg Ruchayskiy S TERILE NEUTRINO DM 11/40
Mass of sterile neutrino DM? � The model-independent lower limit on the mass of fermionic DM Tremaine, Gunn (1979) � The smaller is the DM particle mass – the bigger is the number of particles within some region of phase-space density (defined by velocity dispersion σ and size R ) � For fermions Pauli principle restricts number of fermions � Objects with highest phase-space density – dwarf spheroidal galaxies – lead to the lower bound on the DM mass m > 300 eV � New dSph’s are very dense Q obs = 10 4 − 10 5 M ⊙ kpc − 3 [ km s − 1 ] − 3 . � Bound on any fermionic DM improved to become M s > 0 . 41 keV Boyarsky, O.R. , � Can be further improved if production model of sterile neutrinos is Iakubovskyi’08 specified Oleg Ruchayskiy S TERILE NEUTRINO DM 12/40
How sterile neutrino DM is produced? � Phenomenologically acceptable values of θ 1 are so small, that the rate of this interaction Γ of sterile neutrino with the primeval plasma is much slower than the expansion rate ( Γ ≪ H ) ⇒ Sterile neutrino are never in thermal equilibrium � Simplest scenario: sterile neutrino in the early Universe interact with the rest of the SM matter via neutrino oscillations: Dodelson Widrow’93 e − q ′ e + q Asaka, Laine, Shaposhnikov’0 W ± Z 0 + + · · · e ∓ ν Ns ν Ns ¯ ¯ ν � Production is sharply peaked at � M s � 1 / 3 T max ≃ 130 MeV keV Oleg Ruchayskiy S TERILE NEUTRINO DM 13/40
Production through oscillations � Sterile neutrinos have non-equilibrium spectrum of primordial velocities, roughly proportional to the spectrum of active neutrinos θ 2 f s ( p ) ∝ exp( p T ν ) + 1 � Their amount less than that of active: P m ν Ω s h 2 ∝ θ 2 M s recall: SM neutrinos Ω ν h 2 = 94 eV 94 eV � Average momentum � p s � ∼ � p ν � ≫ M s – sterile neutrinos are produced relativistic Oleg Ruchayskiy S TERILE NEUTRINO DM 14/40
Resonant production � The presence of lepton asymmetry makes this production much more effective – resonant production Shi Fuller’98 Laine, Shaposhnikov’0 � To be effective this mechanism requires lepton asymmetry of the � 10 − 6 (compare with η B = n b − n ¯ order n ν − n ¯ ∼ 10 − 10 ) ν b s s � Typically, one expect the lepton asymmetry to be ∼ η B (sphalerons equilibrate the two) � In the ν MSM one can generate the lepton asymmetry below the sphaleron scale thus making it significantly large than η B Shaposhnikov’0 � The value of lepton asymmetry can be as large as L 6 ≡ 10 6 n ν e − n ¯ ν e � 700 s (present BBN bound L BBN � 2500 ) Serpico, 6 Raffelt’05 Oleg Ruchayskiy S TERILE NEUTRINO DM 15/40
RP sterile neutrino spectra 10 -2 L 6 = 10 L 6 = 25 L 6 = 16 M 1 = 3 keV 10 -3 Resonant q 2 f(q) component 10 -4 Non-resonant component 10 -5 0 1 2 3 4 5 6 7 q = p/T ν Laine, Shaposhnikov’08; Boyarsky, O.R. , Shaposhnikov’09 Oleg Ruchayskiy S TERILE NEUTRINO DM 16/40
Sterile neutrinos and structure formation � Sterile neutrinos are ultra-relativistic at production � t v ( t ′ ) dt ′ λ co F S = a ( t ′ ) � DM particles erase primordial spectrum of 0 density perturbations on scales up to the DM particle horizon – free-streaming length � Comoving free-streaming lengths peaks around t nr when � p � ∼ m � Free-streaming horizon determines suppression scale of power spectrum of density perturbations. � An order of magnitude estimate for the free-streaming scale? � � p s � � keV λ co FS ∼ 1 Mpc M s � p ν � Oleg Ruchayskiy S TERILE NEUTRINO DM 17/40
Power spectrum of density fluctuations Oleg Ruchayskiy S TERILE NEUTRINO DM 18/40
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