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Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen. Accuracy of the Nuclear Matrix Elements. It determines the Error of the Majorana Neutrino Mass extracted. O νββ -Decay (forbidden). only for Majorana Neutrinos ν = ν c. P. P. Left. ν. Phase Space 10 6 x 2 νββ. Left. n.

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Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

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  1. Double Beta DecayandNeutrino MassesAmand FaesslerTuebingen Accuracy of the Nuclear Matrix Elements. It determines the Error of the Majorana Neutrino Mass extracted Amand Faessler, 22. Oct. 2004

  2. Oνββ-Decay (forbidden) only forMajoranaNeutrinos ν = νc P P Left ν Phase Space 106x2νββ Left n n Amand Faessler, 22. Oct. 2004

  3. GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass: Amand Faessler, 22. Oct. 2004

  4. P P e- ν ν e- L/R l/r n n Amand Faessler, 22. Oct. 2004

  5. P P l/r ν light ν heavy N Neutrinos l/r n n Amand Faessler, 22. Oct. 2004

  6. Supersymmetry Bosons↔ Fermions ----------------------------------------------------------------------- Neutralinos P P e- e- Proton Proton u u u u d d Neutron Neutron n n Amand Faessler, 22. Oct. 2004

  7. Theoretical Description:Simkovic, Rodin, Pacearescu,Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta,Kaminski, Gutsche, Bilenky, Vogel, Stoica, Suhonen, Civitarese, Tomoda et al. P k 0+ P e2 k e1 k ν Ek 1+ 2- n n Ei 0+ 0+ 0νββ Amand Faessler, 22. Oct. 2004

  8. Amand Faessler, 22. Oct. 2004

  9. The best choice: Quasi-Particle- • Quasi-Boson-Approx.: • Particle Number non-conserv. (important near closed shells) • Unharmonicities • Proton-Neutron Pairing Pairing Amand Faessler, 22. Oct. 2004

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  13. M0ν (QRPA)O. Civitarese, J. Suhonen, NPA 729 (2003) 867 Nucleus their(QRPA, 1.254)our(QRPA, 1.25) 76Ge 3.33 2.68(0.12) 100Mo 2.97 1.30(0.10) 130Te 3.49 1.56(0.47) 136Xe 4.640.90(0.20) • A different procedure of fixing gpp to single beta decays. What is their g(pp) with error? How well is the 2-neutrino decay reproduced? • Higher order terms of nucleon Current included differently with Gaussian form factors based on a special quark model ( Kadkhikar, Suhonen, Faessler, Nucl. Phys. A29(1991)727). Does neglect pseudoscalar coupling (see eq. (19a)), which is an effect of 30%. We: Higher order currents from Towner and Hardy. • What is the basis and the dependence on the size of the basis? • We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)! Amand Faessler, 22. Oct. 2004

  14. M0ν (R-QRPA; 1.25) S. Stoica, H.V. Klapdor-Kleingrothaus, NPA 694 (2001) 269 • The same procedure of fixing g(pp) • Higher order terms of nucleon current not considered • Nucleus l.m.s s.m.s our 76Ge 1.87 (l=12) 3.74(s=9)2.40(.12) 100Mo 3.40 4.361.20(.15) 130Te 3.00 4.551.46(.46) 136Xe 1.02 1.570.85(.23) • Model space dependence ? • Disagreement also between his tables and figures for R-QRPA and S-QRPA! Amand Faessler, 22. Oct. 2004

  15. Neutrino-Masses from the 0νbband Neutrino Oscillations Solar Neutrinos (CL, Ga, Kamiokande, SNO) Atmospheric ν(Super-Kamiokande) Reactor ν(Chooz; KamLand) with CP-Invariance: Amand Faessler, 22. Oct. 2004

  16. Reactor Neutrinos (Chooz): CP Amand Faessler, 22. Oct. 2004

  17. Bilenky, Faessler, Simkovic P. R. D 70(2004)33003 Amand Faessler, 22. Oct. 2004

  18. (Bild) Amand Faessler, 22. Oct. 2004

  19. Summary:Accuracy of Neutrino Masses from 0nbb • Fit the g(pp) by 2nbb in front of the particle-particle NN matrixelement include exp. Error of 2nbb. • Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets (small about 2 shells, intermediate 3 shells and large 5 shells) the 0nbb. • Use QRPA and R-QRPA (Pauli principle) • Use: g(A) = 1.25 and 1.00 • Error of matrixelement 20 to 40 % (96Zr larger; largest errors from experim. values of T(1/2, 2nbb)). Amand Faessler, 22. Oct. 2004

  20. Summary:Results from 0nbb • <m(n)>(0nbb Ge76, Exp. Klapdor) < 0.47 [eV] • <M(heavy n)> > 1.2 [GeV] • <M(heavy Vector B)> > 5600 [GeV] • SUSY+R-Parity: l‘(1,1,1) < 1.1*10**(-4) • Mainz-Troisk: m(n) < 2.2 [eV] • Astro Physics (SDSS): Sum{ m(n) } < 1 to 2 [eV] • Klapdor et al. from 0nbb Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV], if confirmed. The Theory Groups must check their Results against each other. THE END Amand Faessler, 22. Oct. 2004

  21. Summary:Accuracy of Neutrino Masses by the Double Beta Decay Dirac versus Majorana Neutrinos Grand Unified Theories (GUT‘s), R-Parity violatingSupersymmetry →Majorana-Neutrino = Antineutrinos <m(n)> < 0.47 eV; l‘ < 1.1*10**(-4) Direct measurement in the Tritium Beta Decay in Mainz and Troisk Klapdor et al.: <mββ> = 0.1 – 0.9 [eV] ; R-QRPA: 0.15 – 0.72 [eV] P P u u u u P P d d d d u u n n n n Amand Faessler, 22. Oct. 2004

  22. 3. Neutrino Masses and Supersymmetry • R-Parity violating Supersymmetry mixes Neutrinos with Neutrinalinos (Photinos, Zinos, Higgsinos) and Tau-Susytau-Loops, Bottom-Susybottom-Loops → Majorana-Neutrinos (Faessler, Haug, Vergados: Phys. Rev. D ) • m(neutrino1) = ~0 – 0.02 [eV] • m(neutrino2) = 0.002 – 0.04 [eV] • m(neutrino3) = 0.03 – 1.03 [eV] • 0-Neutrino Double Beta decay <mββ> = 0.009 - 0.045 [eV] • ββExperiment: <mββ> < 0.47 [eV] • Klapdor et al.: <mββ> = 0.1 – 0.9 [eV] • Tritium (Otten, Weinheimer, Lobashow) <m> < 2.2 [eV] THE END Amand Faessler, 22. Oct. 2004

  23. ν-Mass-Matrix by Mixing with: Diagrams on the Tree level: Majorana Neutrinos: Amand Faessler, 22. Oct. 2004

  24. Loop Diagrams: Figure 0.1: quark-squark 1-loop contribution to mv X X Majorana Neutrino Amand Faessler, 22. Oct. 2004

  25. Figure 0.2: lepton-slepton 1-loop contribution to mv (7x7) Mass-Matrix: X Block Diagonalis. X Amand Faessler, 22. Oct. 2004

  26. 7 x 7 Neutrino-Massmatrix: Basis: Eliminate Neutralinos in 2. Order: separabel { Mass Eigenstate Vector in flavor space for 2 independent and possible Amand Faessler, 22. Oct. 2004

  27. Super-K: Amand Faessler, 22. Oct. 2004

  28. Horizontal U(1) Symmetry U(1) Field U(1) charge R-Parity breaking terms must be without U(1) charge change (U(1) charge conservat.) Symmetry Breaking: Amand Faessler, 22. Oct. 2004

  29. How to calculateλ‘i33 (andλi33)fromλ‘333? U(1)chargeconserved! 1,2,3 = families Amand Faessler, 22. Oct. 2004

  30. gPP fixed to 2νββ; M(0nbb) [MeV**(-1)] Each point: (3 basis sets) x (3 forces) = 9 values Amand Faessler, 22. Oct. 2004

  31. Assuming only Electron Neutrinos: (ES) 2.35*106 [Φ] (CC) 1.76*106 [Φ] (NC) 5.09*106 [Φ] Including Muon and Tauon ν: Amand Faessler, 22. Oct. 2004

  32. Amand Faessler, 22. Oct. 2004

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