What I learned on Dark Matter while preparing a lecture on it Andr - PowerPoint PPT Presentation

What I learned on Dark Matter while preparing a lecture on it Andr´ as Patk´ os Institute of Physics, E¨ otv¨ os University, Budapest Outline: • Astrophysical DM evidences: rotation-curve, grav. lensing, CMB, DD-ID detections • Seminar theme:Rotational curves in standard and modified gravity models • Neutrinos: excluding SM ν ’s; the WIMP paradigm • Seminar theme:Sterile neutrino DM • Basic theory tools of WIMP search: Effective Theories, Simplified Models • Seminar theme:Inflationary Higgs fluctuations might account for DM and explain the present ground state of SM simultanously

Galactic star distribution and rotation curves mv 2 = G mM ( <r ) r 2 r F .Zwicky (1930) → V. Rubin (1980): DM content ≈ 80% X-ray energy distribution measurement in galaxy clusters – in excess to the virial T = V T theorem ( 2 E kin pot ) with luminous matter only Gravitational lensing: map of the whole of the gravitating matter content (cca. 2003-04)

Modeling cosmological Background radiation (WMAP, PLANCK) Ω b h 2 = 0 . 02226(23) , Ω DM h 2 = 0 . 1186(20) , H h = 100 km/Mpc/s = 0 . 678(9) Claims for direct and indirect DM observations

There is enough uncertainty for investigating alternatives! Example: Dark Matter content from rotation curves of 40 galaxies ( Almeida, Amendola, Niro, arXiv:1805.11.067 ) Specific MOND model: 5th force mediated by scalar field Φ( x ) , assuming different coupling α i to DM and BM T µ T µ ( BM ) ν ; µ = − α BM T ( BM ) Φ ; ν , ( DM ) ν ; µ = − α DM T ( DM ) Φ ; ν T µ T = T µ (Φ) ν ; µ = ( α BM T ( BM ) + α DM T ( DM ) )Φ ; ν , µ Local gravity experiments: α BM � 10 − 2 → MOND-contribution of BM is negligible ρ ( x ′ ) | x − x ′ | e −| x − x ′ | /λ , β = α BM α DM � DM MOND potential: Ψ MOND ( x ) = − Gβ x ρ s DM matter distribution of Navarro-Frenk-White (1996): ρ NF W ( r ) = 2 rs ( 1+ r r rs ) � � Ψ ( N ) gas + Ψ ( N ) disk + Ψ ( N ) + Ψ ( N ) circular = r d Ψ v 2 dr , Ψ = DM + Ψ MOND bulge

Data set, fitting, results SPARC database: measurements performed with SPITZER satellite (arXiv:1606.09251), 175 galaxies Combined fits to 4 randomly chosen set, consisting of 10 galaxies each Number of parameters β, λ + 2 constants for FRW-profile, 18-19 further constants characterising the structure of BM Result: β = 0 . 34 ± 0 . 04 , λ = 5 . 61 ± 0 . 91 kpc 8 σ deviation from β = 0 , DM density reduced by 20%

Dark Matter: non-luminous, at most weakly interacting matter with lifetime longer than the age of the Universe Textbook material: D.H. Perkins: Particle Astrophysics, Oxford U.P ., 2003,2009 Natural first candidate: relic SM neutrinos (Marx, Szalay 1976) At T > 3 MeV in thermal equilibrium through γ ↔ e + + e − ↔ ν i + ¯ ν i Decoupling: weak reaction rate W weak < expansion rate of the universe H rad H rad = 2 . 07 · 10 5 g 1 / 2 ( k B T ) 2 , g ∗ = 43 / 2 ∗ G 2 F (3 . 15 kBT )2 ρ l = 3 × 2 . 404 4 π 2 h 3 c 3 ( k B T ) 3 , W weak = < ρ l σ weak v >, σ weak = , v ≈ c 3 π 25 ( k B T ) 5 1 W weak ≈ → k B T dec ≈ 3 MeV

Actual number density of neutrinos/flavor: 113 / cm 3 , neutrinos would represent dark matter fully with � i m νi ∼ 12 eV ρν the closure ratio Ω ν = ρcrit for relativistic species increases linearly with m ν Problems which discard this option: • � m ν too large compared to existing upper bounds ( < 0 . 5 eV) • Hot dark matter would smooth out density fluctuations, contrary the observed large scale structure

The WIMP option χχ -annihilation into γ maintains the thermal equilibrium until decoupling: fT 2 � 3 / 2 e − ( MW IMP /Tdec ) = 2 M W IMP v 2 = 3 � MW IMP Tdec 1 dec <σannv>MP L , 2 T dec 2 π Annihilation cross-section dependence on M W IMP : σ ann ∼ G 2 F M 2 for M W IMP < M EW , W IMP σ ann ∼ g 4 M − 2 for M W IMP > M EW , W IMP fT 2 � 3 � T 0 dec N W IMP, 0 = × Number density at present: Tdec <σannv>MP L 3 H 2 0 c 2 MW IMP NW IMP, 0 Closure parameter today: Ω W IMP, 0 = , ρ crit, 0 = ρcrit, 0 8 πG Allowed windows for WIMP ”miracle”:

Appealing WIMP-candidate: sterile neutrinos Latest review: A. Boyarsky et al. arXiv:1807.07938 Motivations and hints • Dynamical interpretation of ν oscillations • Interpretation of very small non-zero m ν of active ν ’s ( << m e ) • Arbitrarily weaker interaction with baryonic matter than that of active ν ’s • Miniboone and LSND oscillation experiments admit the existence of fourth neutrino generation Construction: n gauge singlet RH neutrinos + 3 SM-neutrinos; all Majorana particles � � ∂ν R − l L F ν R ˜ Φ − ˜ R M M ν R + ν R M † (˜ Φ † ν R F † l L − 1 M ν c ν c L = L SM + iν R / , Φ = ǫ Φ) R 2 ν R : n sterile flavors, M M : the n × n mass-matrix of the sterile sector, F : 3 × n matrix of the Yukawa-couplings of the sterile neutrinos to singlets formed from the Higgs-dublet Φ and the SM l L ’s.

The type-I see-saw mechanism Neutrino oscillation due to distinction between interaction ( α ) and mass ( i ) eigenstates: ν Lα = ( V ν ) αi ν i , V ν = (1 + η ) U ν η characterises the unitarity violation due to probability escape into unknown particles. Perturbative mass generation via ν R static exchange among ˜ L and l L ˜ Φ T l c Φ singlets: � � M F T � � l L ˜ ˜ → 1 F M − 1 Φ T l c Φ + h.c. L 2 Higgs-effect: Φ → (0 , v ) T and choosing the ”cut-off” Λ = min { eigenvalues of M M } dimension-5 effective (non-renormalisable) operator is produced: m ν = − m D M − 1 m T D ∼ O ( v 2 / Λ) , m D = F v

The type-I see-saw mechanism Exact diagonalisation of the mass-term � � 0 � � � � � ν c � � m diag ν ( M ) � 0 m D � 1 ν � ν c L ν L + h.c. = ν ( M ) N ( M ) m T M diag N ( M ) R 2 M M ν R 0 D N with the mass-eigenstates expressed through interaction states ν ( M ) = ν L + ν c ν ν ( W ) ν ν ( W ) c ν θν ( W ) c ν θ ∗ ν ( W ) L − θν c R − θ ∗ ν R = V † + V T − U † − U T , L L R R N ( M ) = ν R + ν c N ν ( W ) N ν ( W ) c N θν ( W ) c N θ † ν ( W ) L + θ † ν L = V † + U † R + θ T ν c + V T + U T . R R L L (mixing matrix: θ = m D M − 1 M ) Weak interaction of N suppressed by the action of Θ = θU ∗ N : � � L N − int = − g N Θ † γ µ e L W + µ + e L γ µ Θ NW − √ µ 2 � � � � gMN g N Θ † γ µ ν L + ν L γ µ Θ N Θ hν L N + Θ † hNν L − 2 cos Θ W Z µ − . √ mW 2

Type-I see-saw, remarks, experimental (observational) hints Simplified (less general) construction: – associate exactly 1 heavy neutrino with 1 light flavor – perform see-saw computation for each of them separately. Strategy (Shaposhnikov, 2004): – 2 of them can be used to account for ∆ m 2 solar , ∆ m 2 atmospheric , – 1 is used to arrange BAU via lepton number asymmetry Thermal Θ -suppressed production of N : ultraweak interaction prevents thermalisation → n N << n ν Gunn-Tremaine mass lower bound (1979): The Fermi velocity of degenerate Fermi-Dirac gas of mass m min in a sphere of radius R and mass M should not exceed the escape velocity � 1 / 3 � � 2 GNM 9 πM → � = → m min ∼ 100 − 400 eV 2 fdof m 4 minR 3 R Refined analysis using dwarf spheroidal galaxies: Boyarsky et al. , JCAP 0903 (2009) 005

Decay-constraint from main channel N → ν α ν β ν β τ − 1 = Γ N → 3 ν = G 2 F M 5 α | θ α | 2 , τ < τ Universe = 4 . 4 · 10 17 s � 96 π 3 α | θ α | 2 < 3 . 3 · 10 − 4 � 10 keV � 5 � M Possible clear X-ray signal from 1-loop level N → γ + ν decay Γ N → γν = 9 αG 2 F M 5 α | θ α | 2 ≈ 1 � 128 Γ N → 3 ν 256 π 4 Galactic 3.5 keV line confirmed at 11 σ level!!! No accepted interpretation yet.

Basic theory tools of DM search Review article: Simplified models vs. Effective Field Theory Approaches, by A. de Simone and T. Jacques, EPJ C76 (2016) 367 Search strategies: • DM-production at colliders • Direct Detection (DD) of scattering of DM-particles off nuclei • Indirect Detection (ID) of decay products from self-annihilation of DM-particles WIMP phenomenology should offer a unified treatment of the corresponding observables, keeping the number of parameters minimal

Basic theory tools of DM search Two methods widely used: I. Effective Field Theory (EFT): most general contact interactions of DM and SM particles emerges by ”integrating” over mediating force fields at a characteristic scale, expansion in powers of (energy/scale). • fits well DD-ID experiments (applicable in several channels), • questionable validity of the expansion in annihilation channel ( E ∼ 2 M W IMP ), • misses resonant enhancement, when E ≈ M force • many terms in the effective theory, if no specific model is employed Scattering experiments Typical characteristics of DAMA, XENON, etc. experiments: v ∼ 10 − 3 c, E recoil � 10 MeV Differential event rate: dσ χA n χ dR v>v min d 3 vvf ( v ) � dE recoil = m χ m A dE recoil

Basic theory tools of DM search: the EFT-approach Nuclear cross-section constructed from σ χN , computable in Born-approximation of NR quantum mechanics 12 invariant Fourier-transformed non-relativistic χ − N contact interaction potentials σi s i = ξ † 2 ξ s s ′ Spin-independent scattering σ N SI ; the unit operator dominates it; O NR = 1 1 ( O NR also contributes, velocity dependent terms are subdominant) 11