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KATRIN and the Cosmic Neutrino Background Amand Faessler University of Tuebingen Germany Amand Faessler, Rastislav Hodak, Sergey Kovalenko, Fedor Simkovic: arXiv: [nucl-th] 20. April 2013.

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Cosmic Microwave Background Radiation (Photons in the Maximum 2 mm) Decoupling of the photons from matter about years after the Big Bang,when the electron are captured by the protons and He4 nuclei and the universe gets neutral. Photons move freely.

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Penzias and Wilson; Bell Telephon Nobel Price 1978

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Planck Satellite Temperature Fluctuations Comic Microwave Background (March )

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6 Curvature of the Univers flat xxx We know the size of the hot spots.

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The Universe is flat. The density has the critical value: = We can only see till the sphere of the the last photon- electron scattering: ~14 x10 12 light years

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Black body radiation. Temperature adjusted (pdg 2012): T=2.7255(6) K Experiment Microwave Background Radiation T = (6) Kelvin

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The relative number abundance of the light nuclei formed in the big bang allows to determine the absolute baryon density and relative to the critical density (flat universe). Baryon = Baryon / critical = 0.02h -2 = 0.04 n B = 0.22 m -3 e B = 210 MeV/m -3 h = 0.71 h 2 = 0.5 Hubble-Konstant= H = 100 h [km/(sec Mpc)] B h 2 = 0.02

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Planck‘s Black Body Radiation

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Photons and Neutrinos e, W

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Decoupling of Photons and Neutrinos from Matter „Re“-combination of Electrons with Protons and -Particles (1 out of 1.7x10 9 from upper tail) 3000 Kelvin; years after Big Bang; e- + p neutral Hydrogen-Atom 2e- + neutral Helium-Atom Photons move freely since 14x10 years. Last sphere of scattering: Radius = 14x10 12 light years. Today T = (6) Kelvin independent of the direction.

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Neutrino Decoupling and Cosmic Neutrino Background For massless-massive Neutrinos:

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Temperature of Photons and Neutrinos The Neutrinos decouple before the Photons due to te weak interaction at about: T decoupl (Neutrinos) ~ 1 MeV ~ [Kelvin] T decoupl (Photons) ~ 0.3 [eV] ~ 3000 [Kelvin] Entropy ~ g i x T i 3 = g f T f 3 = const e‘s + Photons: g i = 4x(7/8) +2 = 11/2; Photons only: g f = 2 g f /g i = 4/11 = (T i= /T f ) 3 = ( T /(T f = 2.725)) 3 T (today) = (4/11) 1/ = 1.95 Kelvin

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Estimate of Neutrino Decoupling Universe Expansion rate: H=(da/dt)/a Interaction rate: n e-e H = \sqrt{8 G total /3} = \sqrt{8 /(3 M Planck 2 )} = = O(T 2 ) [1/time] ~ T 3 = T 3 G F 2 T 2 = G F 2 T 5 [Energy = 1/time] hbar = h/(2 ) = c = 1

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Neutrino Decoupling /H = ( k B T/ 1MeV) 3 ~ 1 T(Neutrinos) decoupl ~ 1MeV ~ Kelvin; Today: 1.95 K Time after Big Bang: 1 Second T(Photons) decoupling = 3000 Kelvin; heute: K Time(Photons) decoupling = years Below T = 1 MeV:

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(Energy=Mass)-Density of the Universe log a(t)~1/T Matter dominated: ~ 1/a 3 ~ T 3 Dark Energy 1/Temp 1 MeV 1sec dec. 1 eV 3x10 4 y heute 3000 K y dec. 8x10 9 y T = K = 1.95 K

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Hamburg, March (Bild) Results from Oscillations: No Hierarchy, no absolute Mass Scale Fogli, Lisi, Marrone, Palazzo: Phys. Rev. D86 (2012)

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Hamburg, March Tranformation from Mass to Flavor Eigenstates

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Mass of the Electron Neutrino? Tritium decay (Mainz + Troisk) With: Hamburg, March

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Measurement of the upper Limit of the Neutrino Mass in Mainz: m < 2.2 eV 95% C.L. Kurie-Plot Q = keV m 2 >0 m 2 <0 Electron Energy Eur. Phys. J. C40 (2005) 447

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Negatives Squares of the Measured Neutrino Masses Ch. Kraus, B. Bornschein, L. Bornschein, J. Bonn, B. Flatt, A. Kovalik, B. Ostrick, E. W. Otten, J. P. Schall, Th. Thümmler, Ch Weinheimer: Eur. Phys. J. C40 (2005)

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relic D GZK =50Mpc Neutrino E = 4x10 22 eV Energy Momentum conservation: 1 (GZK,4x10 22 eV) + 2 (CB) Z 0 (4x10 22 eV)burst 10 0, 2 nucleons, 17 +- Anihilation of Relic Neutrinos with extreme High Energy Neutrinos > eV Z0Z0 Above GZK Anihilation below Greisen-Zatsepin-Kuzmin Radius of 50 Mpc

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Cosmic Radiation from Z-Burst expected at eV

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Free magnetic floating cylinder with half absorbing material Permanent Magnet Superconducting Magnet Cylinder shaped One half absorbing, the other sterile. Balanced. The system rotates 90 degrees. Thomas Müller pointed this out to me. A. Ringwald: arXiv:hep- ph/031157v1; 2003.

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Search for Cosmic Neutrino Background C B by Beta decay (KATRIN): Tritium Kurie-Plot of Beta and induced Beta Decay: (CB ) + 3 H(1/2 + ) 3 He (1/2 + ) + e - Electron Energy 2xNeutrino Masses Emitted electron Q = keV Infinite good resolution Resolution Mainz: 4 eV m < 2.3 eV Resolution KATRIN: 0.93 eV m < 0.2 eV 90% C.L. Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B

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Search for Cosmic Neutrino Background C B by Beta decay: 187 Re Kurie-Plot of beta and induced beta Decay: (CB ) Re 112 (5/2 + ) Os 111 (1/2 - ) + e - Electron Energy 2xNeutrino Masses Emitted electron Q = keV Infinite good resolution MARE-Genova: E ~ 11 eV m ~ 2 eV 90% C.L. Milano-Bicocca: E ~24 eV m ~ 3-4 eV Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B

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28 Solution of the Nuclear Structure Problem: Pairing Quasi-Boson Approximation

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Tritium Beta Decay: 3 H 3 He+e - + c e

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Neutrino Capture: (relic) + 3 H 3 He + e - 50 microgram of Tritium 5x10 18 T 2 -Molecules: N capture(KATRIN) = 4.2x10 -6 n / [year -1 ] Every years a count!!

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Neutrino Capture: (relic) + 3 H 3 He + e - 20 g(eff) of Tritium 2x10 18 T 2 -Molecules: N capture(KATRIN) = 1.7x10 -6 n / [year -1 ] Every years a count!! for = 56 cm -3

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Kaboth, Formaggio, Monreal: Phys. Rev. D82 (2010) g(eff) of Tritium 6.6x10 18 T 2 -Molecules: N capture(KATRIN) =5.5x10 -6 n (year -1 ) Every years a count. (For n = ) Faessler et al.: J. Phys. G38 (2011) g(eff) of Tritium 5x10 18 T 2 -Molecules N capture(KATRIN) = 4.2x10 -6 n / (year -1 ) Every years a counts.(For n = ) Drexlin April 2013: 20 g(eff) of Tritium 2x10 18 T 2 -Molecules N capture(KATRIN) = 1.7x10 -6 n / (year -1 ) Every years a counts.(For n = )

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Beta-Decay Re 112 Os 111 +e - + c e

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Kurie-Plot Electron Energy 2xNeutrino Masses Emitted electron Resolution KATRIN: 0.93 eV m < 0.2 eV 90% C.L. Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B Two Problems 1.Number of Events with average Neutrino Density of n e = 56 [ Electron-Neutrinos/cm -3 ] Katrin: 1 Count in Years Gravitational Clustering of Neutrinos!!!??? 2. Energy Resolution (KATRIN) E ~ 0.93 eV

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Gravitational Clustering of Dark Matter and Neutrinos in Galaxies Was kompensiert die Zentrifugalkraft? Dunkle Materie ? Faktum erwartet

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Gravitational Clustering of Neutrinos A. Ringwald, Y. Wong: arXiv:hep-ph/ ; solved Vlasov eq. for ; Dark Matter from Navarro et al. Ap J490 (1997) 493 Circles: 1h -1 kpc; Pentagons: 10h -1 kpc; Squares: 100h -1 kpc; Triangles 1000h -1 kpc. h -1 = 1.4 The solar system is 8 kpc = ly from the galactic center. Virial Mass: M vir = 5v2R/G; v = velocity in sight

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Gravitational Clustering of Neutrinos R.Lazauskas,P. Vogel and C.Volpe, J. Phys.g. 35 (2008) ; Light neutrinos: Gravitate only on Mpc (50 Mpc Galaxy Cluster) scale: n / ~ n b / ~ 10 3 – 10 4 ; = cm -3 A. Ringwald and Y. Wong: Vlasov trajectory simulations Clustering on Galactic Scale possible n / = n b / ~ 10 6 ; (R = 30 kpc) N capture(KATRIN) = 1.7x10 -6 n / (year -1 ) = 1.7 ( 170 for 2 milligram) [counts per year] R. Wigmans, Astroparticle Physics 19 (2003) 379 discusses up to: n / = but for us unrealistic.

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Capture: e (relic) Re(5/2) + Os(1/2) - + e - MARE Genova and Milano 760 grams of AgReO 4 N capture(MARE) = 6.7x10 -8 n / [year -1 ] For n = : Every 15 Million years a count. For: n / = 10 6 : Every 15 years a count. (KATRIN: 1.7 per year) Main Contribution: s(1/2); e - p(3/2)

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Summary 1 The Cosmic Microwave Background allows to study the Universe year after the BB. The Cosmic Neutrino Background 1 sec after the Big Bang (BB): T (today) = 1.95 Kelvin. Extremly difficult to detect: Small Cross Section and low Density 56 ‘s/cm 3 and low Energies (1.95 Kelvin = 2x10 -4 eV).

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2xNeutrino Masses Emitted electron Resolution KATRIN:.93 eV m < 0.2 eV 90% C.L. Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B Kurie-Plot Electron Energy Summary 2 1.Average Density: n e = 56 [ Electron-Neutrinos/cm -3 ] Katrin (20 g eff. mass 3 H): 1 Count in Years Gravitational Clustering of Neutrinos n / < 10 6 1.7 counts (2 milligram of 3 H 170 counts) per year. 2. Measure only an upper limit of n ENDE

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