Relic Neutrinos. Relic Neutrinos in the Standard Model. Beyond the Standard Model ! RELIC. BBN and CMB. Direct Detection by Coherent Scattering

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1 Relic Neutrinos! COSMIC RAY Relic Neutrinos in the Standard Model BBN and CMB! RELIC Beyond the Standard Model Direct Detection by Coherent Scattering D GZK ~50 Mpc Z 0 " 20 # } 10 2 nucleons 17 " - + e + -,!,! Direct Detection by Z-Bursts

2 The CMB Radiation decoupled at 380,000 yr Redshifted to 2.73 K 400/cm 3 Temperature anisotropies structure formation, cold dark matter, dark energy

3 Neutrino Masses CDHSW First extension of standard model 10 0 KARMEN2 LSND Bugey CHORUS NOMAD NOMAD CHORUS BNL E776 Solar: LMA (SNO, Kamland) 10 3 CHOOZ SuperK PaloVerde m ev 2, nonmaximal Atmospheric: m 2 Atm ev 2, near-maximal mixing m 2 [ev 2 ] SMA ν e ν X ν µ ν τ ν e ν τ ν e ν µ LMA KamLAND LOW Reactor: U e3 small VAC tan 2 θ 10 2

4 Mixings: let ν ± 1 2 (ν µ ± ν τ ): ν 3 ν + ν 2 cos θ ν sin θ ν e ν 1 sin θ ν + cos θ ν e ev ev 1 0 ev ev 0 ev Normal hierarchy Inverted hierarchy Degenerate patterns (add common mass < 0.2 ev); motivated by CHDM but no longer needed

5 Expectations for the Relic Neutrinos Reactions such as ν i ν i e + e kept ν s in equilibrium at high T ν i, ν i decoupled at T D few MeV f νi = F eq (p, m i, µ Di, T D ) [ ( ) (p 2 + m 2 i = exp )1/2 µ Di T D + 1 ] 1 f νi = F eq (p, m i, µ Di, T D )

6 Subsequently, p redshifted to p = p /η, where η R(t)/R(t D ) f νi F eq (p, m i, µ Di, T D ) = F eq (p, m i /η, µ Di /η, T D /η) [ ( ) (p 2 + m 2 eff = exp i ) 1/2 µ i T ν + 1 ] 1 m effi m i η m i, T ν T D η = ( 4 11 (µ i µ i for ν i ) ) 1/3 T γ 1.9K, µ i µ D i η Form of relativistic thermal distribution, but (negligible) m eff T ν Actually decoupled and may be non-relativistic

7 For µ i = 0, N νi = N νi = p 3.2T ν ev λ = 2π/ p 2.3 mm d 3 p e p/t ν + 1 T 3 50/cm 3 Non-zero asymmetry, µ i 0: N νi N νi = T 3 ν 6 [ ] ξ i + ξ3 i π 2, ξ i µ i T ν

8 For hierarchical pattern m ev, m ev, m 1 m 2 ( v , v ) For degenerate pattern, m 1 m 2 m 3 < 0.23 ev (WMAP), Clustering? v i ( 0.23 ev m i v esc 10 4 (Sun), (Galaxy), (Large Cluster) ) Little effect on velocities except degenerate case Little clustering unless m i > 0.3 ev, and then on supercluster scale (Singh, Ma; Ringwald, Wong)

9 Ringwald, Wong, hep-ph/ for a relativistic Fermi Dirac distribution are displayed in row one. n ν n ν p λ = 1 p Relativistic Fermi Dirac ev cm see (4.1) NFWhalo, m ν = 0.6 ev ev cm NFWhalo, m ν = 0.45 ev ev cm NFWhalo, m ν = 0.3 ev ev cm NFWhalo, m ν = 0.15 ev ev cm MWnow, m ν = 0.6 ev ev cm MWnow, m ν = 0.45 ev ev cm MWnow, m ν = 0.3 ev ev cm MWnow, m ν = 0.15 ev ev cm v

10 Big bang nucleosynthesis Production of light nuclei ( 4 He, D, 3 He, 7 Li) in early Universe Parameters η = n B /n γ (η Ω b h 2 ) N ν (any new source of energy density, relative to one active ν flavor) ξ e = µ νe /T, related to (n νe n νe )/n γ SBBN: N ν = ξ e = 0

11 ν e n e p and e + n ν e p keep n n /n p in equilibrium as long as it is rapid enough Freezeout at T 1 MeV, when Γ weak H Γ weak = cg 2 F T 5 H = [ 8π 3 G Nρ ] 1/2 1.66g 1/2 T 2 /M P l g = g B g F, with g F = N ν ( ) 1/3 T n n n p g 1/2 G 2 F M P l = e (m n m p +µ ν e )/T 4 He 4 He mass fraction: Y p = 4n 4 He depends strongly on N n ν H ( Y p N ν ) and ξ e, weakly on η Y 2 = D depends on η (baryometer) H Independent determination of η from CMB

12

13 Central 4 He somewhat low Best fit for N ν < 0, but consistent with zero Most new physics yields N ν > 0 strongly constrained Z ν R ν R ; sterile neutrinos (LSND); ξ µ,τ Can compensate by ξ e 0.1; naively expect 10 10

14 2 2!m m /ev LMA ATM Exclusion on sterile for N ν < ! s "! e! s "! µ,! sin 2 2! sin 2 0 2! 0 Compensation of ξ e and N ν

15 Large-scale structure (LSS) and CMB Hot Dark Matter (HDM) Ω ν h 2 = l m ν i /92.5 ev HDM excluded by free-streaming: not enough time for large structures to fragment Mixed CHDM models, typically Ω matter 1 and i m ν i few ev motivated degenerate ν spectra Now excluded by (a) Ω matter 0.3 (clusters, etc); (b) Ω total = Ω DE +Ω matter 1, DE = dark energy (1st CMB peak, WMAP); (c) Ω DE 0 (Type Ia supernovae)

16 Small admixture of HDM still possible LSS (2dF, SDSS) sensitive to Σ ν i m ν i CMB (WMAP) fixes other (degenerate) parameters 6000 CMB TT power spectrum l(l + 1)C l / 2! [µ" 2 ] P g (k) [(h -1 Mpc) 3 ] Multipole l k [h/mpc] Σ ν = 0.28 ev (solid), 1.5 ev (dotted), 3.0 ev (dashed)

17 Current: Σ ν < ev m νi < ev Future: sensitive to 0.1 ev, weak lensing, LSS, CMB cf. tritium β decay: m ν < 2.4 ev (future: KATRIN, 0.3 ev) cf. ββ 0ν < few 10 1 ev (future: 0.02 ev)

18 CMB has some sensitivity to N ν (matter-radiation transition)

19 Non-Standard Physics and Relic Neutrinos Neutrino Asymmetries BBN + CMB: 0.01 < ξ e < 0.22, ξ µ,τ < 2.6 CMB + BBN + equilibration: ξ i < 0.07 (Lunardini, Smirnov; Dolgov et al; Wong; Abazajian, Beacom, Bell) Can evade by new energy source But, naive expectation is ξ = O(10 11 ) Neutrino annihilation no relic neutrinos (Beacom, Bell, Dodelson) Neutrino decay modified spectrum (unlikely for small m ν )

20 Ways Out if LSND Confirmed Large ν asymmetries to suppress or compensate steriles Late time phase transitions to suppress masses and sterile mixings until after decoupling (T < 1 MeV) (Chacko, Hall, Oliver, Perelstein) Time varying masses (coupling to special scalar fields) sterile too massive to produce cosmologically (possible implications for matter effects and for dark energy) (Fardon, Nelson, Weiner, Kaplan, Zurek; Bi, Gu, Wang, Zhang) Low reheating temperature after inflation (Gelmini, Palomares-Ruiz, Pascoli)

21 Direct Detection β decay Neutrino winds scattering coherently from macroscopic target Neutrinos as target for high energy particle

22 ν e absorption in inverse β decay Absorption ν e + 3 H e + 3 He of relic ν e produces a peak above endpoint (Turner, Weinberg; Humphries) Irvine, Need huge asymmetry with µ e ev, ξ e > 10 5 excluded (P. F. Smith)

23 Incoherent scattering from fixed target σ ν G 2 F E2 ν cm 2 (m ν = 0), cm 2 (m ν 0.1 ev ) Rate per target atom: σ ν j ν (10 38 )/yr for j ν /cm 2 s Rate for kiloton target (10 33 scatterers): 10 9 (10 5 )/yr No signature

24 Coherent scattering For N particles in coherence volume of radius λ = 1/p 2.3 mm σ ν j ν N 2 1/yr May see forces/torques on macroscopic bodies, or induced currents or pumping of coherent sound waves Net neutrino flux due to motion of Solar System through ν sea ( 220 km/s), modulated by Earth sidereal period (23 hr 56 min)

25 (P. F. Smith)

26 Forces, Torques on Macroscopic Objects Coherent forward elastic scattering. λ 2.3 mm atomic spacing suggests ray optics, with refractive indices n ν, ν 1 = 2π N p 2 a f a ν, ν (0) f a ν, ν (0) = 1 G F E K(p, m ν ) [ g a V π + ga A σ a ˆp ], 2 where K (1, 1 2 ) for (m ν = 0, p m ν ), and L = G F 2 νγ µ (1 + γ 5 )ν ψ a γ µ (g a V + ga A γ 5)ψ a For polarized iron and SM couplings, n νe, ν e 1 = [ σ e ˆp] n νµ, ν µ 1 = ± [ σ e ˆp] a

27 Net force from refraction for asymmetric geometry? Movement through ν sea needed? ν ν cancellation? Total external reflection (Opher) Net force of O(G F ) for θ < θ c = 2(1 n) 10 µrad for n < 1 (ν e, ν µ, ν τ ) No ν ν cancellation Need stack of reflectors and motion through ν rest frame Concrete proposal (actually O(G 3/2 F )) (Lewis)

28 Effect actually vanishes to O(G F, G 3/2 Cabibbo, Maiani) F ) (PL, Leveille, Sheiman; Total external reflection only occurs for reflector thickness > skin depth d λ/ 1 n = O(20 m) Diffraction at ends unless length L > 10 7 m Theorem (directly from field equations): All O(G F ) forces vanish if time averaged ν flux is spatially homogeneous (isotropy not needed) (PL, Leveille, Sheiman)

29 Net torque allowed to O(G F ) for magnetized, shielded target for large ξ i (Stodolsky; LSS) τ = E 2 ˆv e σ e E = 2G F v e [ (Nνe N νe ) (N νµ N νµ ) (N ντ N ντ ) ] E ev for ξ i = O(1) (too small)

30 Coherent elastic scattering to order G 2 F (Smith, Lewin; Ferreras, Wasserman; Duda, Gelmini, Nussinov; Hagmann) Coherent reflection from homogeneous target (effects tiny) Coherent scattering from individual granules Large recoil distances for Dirac ν (strong Majorana suppression) Need to monitor huge numbers individually

31 Granules embedded in foam-like or lamindated material inside of torsion balance (Hagmann) Largest for ev scale Dirac ν, a cm/s 2 Suppressed by (v ν /c) 2 for Majorana A B Neutrino Target Laser Resonator Persistent Magnet Suspension Magnet Balancing Mass Conventional Cavendish sensitive to cm/s 2 Hagmann proprosal (superconducting levitation): cm/s 2

32 Other coherent scattering proposals Coherent electron scattering to induce current in superconductor (Lewin, Smith) Expect induced current of A after 10 days. Quantization? Inelastic scattering: coherence volume reduced by to volume of produced phonon (Müller)

33 Transfer energy from one coherent excitation to another, i.e., between perpendicular standing acoustic waves in a solid (Tupper, Müller, Rafelski, Danos) Acoustic energy must exceed binding energy of target!

34 Relic ν s as target Scattering of accelerator beams on relic ν s hopelessly small! COSMIC RAY Scattering of high energy cosmic ray neutrinos (Z-burst) (Weiler) ν i ν i Z particles, D GZK ~50 Mpc Z! RELIC 0 " 20 # } 10 2 nucleons 17 " - + e + -,!,! at E R ev ( 0.1 ev m ν ).

35 Account for E p > GZK? (Best fit m ν = Ringwald; Gelmini, Varieschi) ev, Fodor, Katz,

36 Future observation? Depends on unknown flux of UHE ν Too large for thin sources from π decay (π 0 γγ) Exotic sources, such as topological defects?

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38 Cosmic rays: Auger Neutrinos: Amanda, Antares IceCube Antares

39 Could be absorption dips even if too small for E p > GZK (Eberle, Ringwald, Song, Weiler)

40 Conclusions Relic neutrinos important for BBN, CMB, structure, ν mass spectrum, exotica Direct detection extremely difficult. granules? Z burst? Coherent scattering from