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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, GERDA, 11. November 2005

  2. Oνββ-Decay (forbidden) only forMajoranaNeutrinos ν = νc P P Left ν Phase Space 106x2νββ Left n n Amand Faessler, GERDA, 11. November 2005

  3. GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass: Amand Faessler, GERDA, 11. November 2005

  4. P P e- ν ν e- L/R l/r n n Amand Faessler, GERDA, 11. November 2005

  5. L/R l/r P P l/r ν light ν heavy N Neutrinos l/r n n Amand Faessler, GERDA, 11. November 2005

  6. Supersymmetry Bosons↔ Fermions ----------------------------------------------------------------------- Neutralinos Neutralinos P P e- e- Proton Proton u u u u d d Neutron Neutron n n Amand Faessler, GERDA, 11. November 2005

  7. Theoretical Description:Simkovic, Rodin, Benes, Vogel, Bilenky, Salesh,Gutsche,Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, 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, GERDA, 11. November 2005

  8. Neutrinoless Double Beta- Decay Probability Amand Faessler, GERDA, 11. November 2005

  9. Effective Majorana Neutrino-Mass for the 0nbb-Decay Tranformation from Mass to Flavor Eigenstates CP Amand Faessler, GERDA, 11. November 2005

  10. 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, GERDA, 11. November 2005

  11. ν1, ν2, ν3 Mass States νe, νμ, ντ Flavor States Theta12 = 32.6 degrees Solar + KamLand Theta13 < 13 degrees Chooz Theta23 = 45 degrees S-Kamiokande D m 212(solar ) ~ 8*10**(-5) [eV**2] Dm223(atmospheric ) ~ 2.5*10**(-3) [eV**2] Amand Faessler, GERDA, 11. November 2005

  12. Bilenky, Faessler, Simkovic P. R. D 70(2004)33003 Amand Faessler, GERDA, 11. November 2005

  13. Bilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250 Amand Faessler, GERDA, 11. November 2005

  14. The best choice: Quasi-Particle- • Quasi-Boson-Approx.: • Particle Number non-conserv. (important near closed shells) • Unharmonicities • Proton-Neutron Pairing Pairing Amand Faessler, GERDA, 11. November 2005

  15. Amand Faessler, GERDA, 11. November 2005

  16. Contribution of Different Multipoles to M(0n) Amand Faessler, GERDA, 11. November 2005

  17. g(A)**4 = 1.25**4 = 2.44 fit to 2nbb Rodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063 Amand Faessler, GERDA, 11. November 2005

  18. 2.76 (QRPA) 2.34 (RQRPA) Muto corrected Amand Faessler, GERDA, 11. November 2005

  19. 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) • g(pp) fitted differently • 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? • Short-range Brueckner Correlations not included. But finite size effects included. • We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)! Amand Faessler, GERDA, 11. November 2005

  20. Neutrinoless Double Beta Decay The Double Beta Decay: 0+ 1+ x x x 2- β- β- e- e- 0+ E>2me 0+ xxx Gamov-Teller single beta decay in the second leg fitted with g(pp) by Suhonen et al.. Underestimates the first leg. We fit the full 2nbb decay by adjusting g(pp). Amand Faessler, GERDA, 11. November 2005

  21. Fit of g(pp) to the single beta (2. leg) and the 2n double beta decay (small and large basis). Fit to 1+ to 0+ Fit to 2nbb Amand Faessler, GERDA, 11. November 2005

  22. Uncorrelated and Correlated Relative N-N-Wavefunctionin the N-N-Potential Short Range Correlations Amand Faessler, GERDA, 11. November 2005

  23. Jastrow-Function multiplying the relative N-N wavefunction (Parameters from Miller and Spencer, Ann. Phys 1976) Amand Faessler, GERDA, 11. November 2005

  24. Influence of Short Range Correlations (Parameters from Miller and Spencer, Ann. Phys 1976) Amand Faessler, GERDA, 11. November 2005

  25. Contribution of Different Multipoles to the zero Neutrino Matrixelements in QRPA s.r.c. = short range correlations h.o.t. = higher order currents Different Multipoles • a) 76Ge small model space ( 9 levels) b) 76Ge large model space (21 levels) • C) 100Mo small model space ( 13 levels) d) 100Mo large model space ( 21 levels) Amand Faessler, GERDA, 11. November 2005

  26. Comparison of 2nbbHalf Lives with Shell model Results from Strassburg Amand Faessler, GERDA, 11. November 2005

  27. Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Massof planed Experiments Amand Faessler, GERDA, 11. November 2005

  28. Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Massof planed Experiments Amand Faessler, GERDA, 11. November 2005

  29. 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)). • Core overlap reduction by ~0.85 (preliminary) Amand Faessler, GERDA, 11. November 2005

  30. Summary:Results from 0nbb • <m(n)>(0nbb Ge76, Exp. Klapdor) < 0.47 [eV] • Klapdor et al. from 0nbb Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [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, Triton Decay: m(n) < 2.2 [eV] • Astro Physics (SDSS): Sum{ m(n) } < ~0.5 to 2 [eV] Do not take democratic averaged matrix elements !!! THE END Amand Faessler, GERDA, 11. November 2005

  31. Open Problems: 1. Overlapping but slightly different Hilbert space in intermediate Nucleus for QRPA from intial and from final nucleus. 2. Pairing does not conserve Nucleon number. Problem at closed shells. Particle projection. Lipkin-Nogami <N>, <N2> 3. Deformed nuclei? Amand Faessler, GERDA, 11. November 2005

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