Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

1. Double Beta DecayandNeutrino MassesAmand FaesslerTuebingen Accuracy of the Nuclear Matrix Elements. It determines the Error of the Majorana Neutrino Mass extracted Amand Faessler, Erice, 20. September 2005

2. Oνββ-Decay (forbidden) only forMajoranaNeutrinos ν = νc P P Left ν Phase Space 106x2νββ Left n n Amand Faessler, Erice, 20. September 2005

3. GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass: Amand Faessler, Erice, 20. September 2005

4. P P e- ν ν e- L/R l/r n n Amand Faessler, Erice, 20. September 2005

5. L/R l/r P P l/r ν light ν heavy N Neutrinos l/r n n Amand Faessler, Erice, 20. September 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, Erice, 20. September 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, Erice, 20. September 2005

8. Neutrinoless Double Beta- Decay Probability Amand Faessler, Erice, 20. September 2005

9. Effective Majorana Neutrino-Mass for the 0nbb-Decay Tranformation from Mass to Flavor Eigenstates CP Amand Faessler, Erice, 20. September 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, Erice, 20. September 2005

11. ν1, ν2, ν3 Mass States νe, νμ, ντ Flavor States Theta(1,2) = 32.6 degrees Solar + KamLand Theta(1,3) < 13 degrees Chooz Theta(2,3) = 45 degrees S-Kamiokande Amand Faessler, Erice, 20. September 2005

12. Bilenky, Faessler, Simkovic P. R. D 70(2004)33003 Amand Faessler, Erice, 20. September 2005

13. Bilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250 • (Bild) Amand Faessler, Erice, 20. September 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, Erice, 20. September 2005

15. Amand Faessler, Erice, 20. September 2005

16. g(A)**4 = 1.25**4 = 2.44 fit to 2nbb Rodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063 Amand Faessler, Erice, 20. September 2005

17. Overlap of Wave Functions of the not involved core of the initial and final nuclei. Benesch, Faessler, Simkovic Preliminary (July 2005) Ge76 Benes, Faessler, Simkovic Amand Faessler, Erice, 20. September 2005

18. Overlap of the core added to the 0nbb-decay and new 2nbb-decay data (NEMO). Amand Faessler, Erice, 20. September 2005

19. 2.76 (QRPA) 2.34 (RQRPA) Muto corrected Amand Faessler, Erice, 20. September 2005

20. 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, Erice, 20. September 2005

21. 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, Erice, 20. September 2005

22. Influence on Short Range Correlations (Parametres from Miller and Spencer, Ann. Phys 1976) Amand Faessler, Erice, 20. September 2005

23. Comparison of 2nbbHalf Lives with Shell model Results from Strassburg Amand Faessler, Erice, 20. September 2005

24. 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, Erice, 20. September 2005

25. 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, Erice, 20. September 2005