1. Amand Faessler, Madrid, 8. June 20061 Double Beta Decay, a Test for New Physics Amand Faessler Tuebingen „The Nuclear Matrix Elements for the  are as important as the Data to extract the Neutrino Mass“ (and in general New Physics). (Frank Avignone in Erice, September 2005)

2. Amand Faessler, Madrid, 8. June 20062 O νββ -Decay (forbidden) only for Majorana Neutrinos ν = ν c P P nn Left ν Phase Space 10 6 x 2 νββ

3. Amand Faessler, Madrid, 8. June 20063 GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

4. Amand Faessler, Madrid, 8. June 20064 P P ν ν nn e-e- e-e- L/R l/r

5. Amand Faessler, Madrid, 8. June 20065 l/r P ν P n n light ν heavy N Neutrinos l/r L/R p p n n e-e- vcvc vcvc e-e- W W

6. Amand Faessler, Madrid, 8. June 20066 Supersymmetry Bosons ↔ Fermions ----------------------------------------------------------------------- Neutralinos PP e-e- e-e- nn u u u u dd Proton Neutron

7. Amand Faessler, Madrid, 8. June 20067 Theoretical Description: Tübingen: Simkovic, Rodin, Benes, Vogel, Bilenky, Salesh, Gutsche, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Stoica, Suhonen, Civitarese, Tomoda, Moya de Guerra, Sarriguren, Valle et al. 0+0+ 0+0+ 0+0+ 1+1+ 2-2- k k k e1e1 e2e2 P P ν EkEk EiEi n n 0 νββ

8. Amand Faessler, Madrid, 8. June 20068 Neutrinoless Double Beta- Decay Probability + …

9. Amand Faessler, Madrid, 8. June 20069 Effective Majorana Neutrino-Mass for the 0  Decay CP Tranformation from Mass to Flavor Eigenstates

10. Amand Faessler, Madrid, 8. June 200610 BilenkyBilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250 FaesslerSimkovic

11. Amand Faessler, Madrid, 8. June 200611 The best choice: Quasi-Particle-  Quasi-Boson-Approx.:  Particle Number non-conserv. (important near closed shells)  Unharmonicities  Proton-Neutron Pairing Pairing

12. Amand Faessler, Madrid, 8. June 200612 g(A)**4 = 1.25**4 = 2.44; fit of g pp to 2  RodinRodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063 and Nucl. Phys. A (2006)FaesslerSimkovicVogel

13. Amand Faessler, Madrid, 8. June 200613 Quasi-Particle Random Phase (QRPA), Renormalized QRPA (RRPA) and Selfconsistent QRPA (SRPA)for three Basis Sizes and three Forces g pp fixed to 2  No experimental error g A = 1.25

14. Amand Faessler, Madrid, 8. June 200614 Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass of planed Experiments expt.T 1/2 [y] [eV] DAMA ( 136 Xe) 1.2 X 10 24 2.3 MAJORANA ( 76 Ge) 3 X 10 27 0.044 EXO 10t ( 136 Xe) 4 X 10 28 0.012 GEM ( 76 Ge)7 X 10 27 0.028 GERDA II ( 76 Ge) 2 X 10 26 0.11 CANDLES ( 48 Ca) 1 X 10 26 0.2 MOON ( 100 Mo) 1 X 10 27 0.058

15. Amand Faessler, Madrid, 8. June 200615 Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass of planed Experiments expt.T 1/2 [y] [eV] XMASS ( 136 Xe) 3 X 10 26 0.10 CUORE ( 130 Te) 2 X 10 26 0.10 COBRA ( 116 Cd) 1 X 10 24 1 DCBA ( 100 Mo) 2 X 10 26 0.07 DCBA ( 82 Se)3 X 10 26 0.04 CAMEO ( 116 Cd) 1 X 10 27 0.02 DCBA ( 150 Nd) 1 X 10 26 0.02

16. Amand Faessler, Madrid, 8. June 200616 Overlap of the inert Core of the initial and final Nucleus due to changes in Deformation  Pairing and Hilbert Space.

17. Amand Faessler, Madrid, 8. June 200617 Proton and Neutron Number conserved as and and improved spherical Overlap of the inert Core due to different Pairing. = Z; = Z 2 ~20 % Reduction due to (Pairing) Overlap g A = 1.25 3 basis sets:~3 and 4 and 5 oscillator shells; Force: Bonn

18. Amand Faessler, Madrid, 8. June 200618 Dependence of 0  on the size of the Basis after Fit of g pp to 2 

19. Amand Faessler, Madrid, 8. June 200619

20. Amand Faessler, Madrid, 8. June 200620 2  Matrix Elements depending on the initial and final Deformation Beta

21. Amand Faessler, Madrid, 8. June 200621 Phenomenological NN-Force for differen Particle-Particle Strength kappa   adjusted to log ft in 1. leg

22. Amand Faessler, Madrid, 8. June 200622 new standard

23. Amand Faessler, Madrid, 8. June 200623 new standard

24. Amand Faessler, Madrid, 8. June 200624

25. Amand Faessler, Madrid, 8. June 200625

26. Amand Faessler, Madrid, 8. June 200626 2.76 (QRPA) 2.34 (RQRPA) Muto corrected

27. Amand Faessler, Madrid, 8. June 200627 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 4.64 0.90(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. Short-range Brueckner Correlations not included.

28. Amand Faessler, Madrid, 8. June 2006 28 Differences 1.. Ajustment of g pp for the NN force to the total 2  decay probability (Tuebingen) or to (Jyväskylä): β-β- 0+0+ 0+0+ 2-2- 1+1+ 1+1+ pn -1 np -1 x x   This log ft value known in only three double beta decay nuclei: 100 Mo, 116 Cd, 128 Te

29. Amand Faessler, Madrid, 8. June 200629 Different ways for Determening the g pp 2. Leg: Log ft only known in 100 Mo, 116 Cd, 128 Te. 1. leg 2 

30. Amand Faessler, Madrid, 8. June 200630 2. leg: known only in these three nuclei For the first leg no agreement

31. Amand Faessler, Madrid, 8. June 200631 2. Uncorrelated and Correlated Relative N-N-Wavefunction in the N-N-Potential Short Range Correlations

32. Amand Faessler, Madrid, 8. June 200632 Influence of Short Range Correlations (Parameters from Miller and Spencer, Ann. Phys 1976)

33. Amand Faessler, Madrid, 8. June 200633 Grey Area: Uncertainty due to Deformation; Dashed: Spherical

34. Amand Faessler, Madrid, 8. June 200634 Comparison of 2  Half Lives with Shell model Results from Strassburg-Madrid For 0  one needs intermidiate negative Parity States and higher Multipoles

35. Amand Faessler, Madrid, 8. June 200635 Contributions of different Multipolarities for 0  Negative Parity States not described by  Shell Model Blue: Short Range Correlations and Higher Order Currents. Red: Short Range Correlations, no Higher Order Currents White: No Short range Correlations, no Higher order Currents 76 Ge    and  oscillator shells  to  oscillator shells 76 Ge  

36. Amand Faessler, Madrid, 8. June 200636 Summary: Accuracy of Neutrino Masses from 0  Fit the g(pp) by  in front of the particle- particle NN matrixelement include exp. Error of . 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  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, 2  )) 

37. Amand Faessler, Madrid, 8. June 200637 Summary: Results from  (  Ge  Exp. Klapdor)  0.47 [eV] Klapdor et al. from  Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV].  [GeV] > 5600 [GeV] SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4) Mainz-Troisk, Triton Decay: m(  2.2 [eV] Astro Physics (SDSS): Sum{ m( ) } < ~0.5 to 2 [eV] Do not take democratic averaged matrixelements !!!

38. Amand Faessler, Madrid, 8. June 200638 Open Problems: 1. Overlapping but slightly different Hilbert spaces in intermediate Nucleus for QRPA from intial and from final nucleus. 2. BCS Pairing does not conserve Nucleon number. Problem at closed shells. Particle projection. 3. Deformed nuclei? (e.g.: 150 Nd ) β-β- 0+0+ 0+0+ 2-2- 1+1+ 0+0+ pn -1 np -1

39. Amand Faessler, Madrid, 8. June 200639 Open Problems: 4. Ajustment of g pp for the NN force to the total 2  decay probability or to: β-β- 0+0+ 0+0+ 2-2- 1+1+ 0+0+ pn -1 np -1 x x  

40. Amand Faessler, Madrid, 8. June 200640 Open Problems: 5. What is the leading Mechanisme for the Neutrinoless double Beta- Decay ? a) Light Majorana Neutrino exchange b) Heavy Majorana Neutrino exchange c) Right handed Current at one Vertex d) Heavy Vector-boson at one Vertex e) Minimal Supersymmetry with R-parity Violation And Others 0  to Excited States

41. Amand Faessler, Madrid, 8. June 200641 Open Problems: shell model Contribution of Different Multipoles to the zero Neutrino Matrixelements in QRPA 6. Shell model needs to enlarge the single particle space to three oscillator shells to include negative parity states and five shells to include deformations: Different Multipoles Blue: Short Range Correlations and Higher Order Currents. Red: Short Range Correlations, no Higher Order Currents White: No Short range Correlations, no Higher order Currents THE END 76 Ge 100 Mo