1. Description of Double Beta Decay, Nuclear Structure and Physics beyond the Standard Model - Status and Prospects. Amand Faessler University of Tuebingen Nuclear Phy sics in Astrophysics-V. Eilat, April 5th. 2011

2. O νββ -Decay (forbidden in Standard Model)  Neutrino Mass P P n n Left ν Phase Space 10 6 x 2 νββ Amand Faessler, Tuebingen e1e1 e2e2  = c Majorana Neutrino Neutrino must have a Mass W 1 = cos  W L + sin  W R W 2 = -sin  W L + cos  W R Majorana, N L, N R

3. Neutrinoless Double Beta- Decay Probability Amand Faessler, Tuebingen

4. Quasi-Particle Random Phase Approximation (QRPA; Tübingen). Shell Model (Strasbourg-Madrid ). Angular Momentum Projected Hartee-Fock- Bogoliubov (Tuebingen; P. K. Rath et al.). Interacting Boson Model (Barea and Iachello). Amand Faessler, Tuebingen 1. Different Methods for the 0  -Matrix Elements for the Light Majorana Neutrino Exchange. A. Escuderos, A. Faessler, V. Rodin, F. Simkovic, J. Phys. G37 (2010) 125108; arXiv: 1001.3519 [nucl-th]

5. Amand Faessler, Tuebingen a)QRPA all the Ring diagrams: Ground State: 0, 4, 8, 12, … quasi- particles (seniority) b) The Shell Model Ground state: 0, 4, 6, 8, …. Problem for SM: Size of the Single Particle Basis.

6. Additive Contributions of 0, 4, 6, … Quasi-Particle States in the SM (Poves et al.). Amand Faessler, Tuebingen 128 Te 82 Se Not in QRPA Increasing Admixtures in the Ground State

7. Basis Size Effect for 82 Se on the Neutrinoless Double Beta Decay. Amand Faessler, Tuebingen 4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2 6levels: 0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2 9levels:0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2 4levels: Ikeda Sum rule 50 %; 5 levels 60 %;

8. Amand Faessler, Tuebingen Basis Size Effect for 128 Te on the Neutrinoless Double Beta Decay. 5 levels (Shell Model): 0g7/2, 1d572, 2s1/2, 1d3/2, 0h11/2 7 levels: 0g7/2, 1d572, 2s1/2, 1d3/2, 0h11/2, 0g9/2, 0h9/2 13 levels: N=3, N=4, 0h11/2, 0h9/2, 1f7/2, 1f5/2 Ikeda sum Rule: 60 %

9. Amand Faessler, Tuebingen

10. Different Seniority Contributions s for 82 Se and 128 Te in QRPA and the Shell Model Amand Faessler, Tuebingen M 0 s=0 s= 4, (6), 8,… total ISR% 82 Se 4lev QRPA 6.7 -5.6 1.1 50 82 Se 4lev SM 7.8 -5.8 2.0 82 Se 6lev QRPA 10.7 -6.6 4.1 100 82 Se 9lev QRPA 11.9 -7.6 4.3 100 128 Te 5lev QRPA 9.7 -8.3 1.4 60 128 Te 5lev SM 10.6 -8.4 2.2 128 Te 7lev QRPA 13.7 -10.3 3.4 100 128 Te 13lev QRPA 16.8 -13.0 3.8 100 4 level basis: p 3/2, f 5/2, p 1/2, g 9/2 6 level basis: f 7/2, p 3/2, f 5/2, p 1/2, g 9/2, g 7/2 9 level basis: d 5/2, s 1/2, d 3/2, f 7/2, p 3/2, f 5/2, p 1/2, g 9/2, g 7/2

11. Contribution of Higher Angular Momentum Pairs in Projected HFB. Only even Angular Momentum Pairs with Positive Parity can contribute. IBM: = 0 + and 2 + Pairs HFB 0  Amand Faessler, Tuebingen

12. QRPA (TUE), Shell Model (Madrid-Strassburg), IBM2, PHFB Amand Faessler, Tuebingen

13. QRPA (TUE), Shell Model IBM2, PHFB

14. Amand Faessler, Tuebingen 2. Can one measure the Matrix Elements of the 0  Decay? V. Rodin, A. F., Phys. Rev. C80 (2009), arXiv: 0906.1759 and 1012.5176 [nucl-th] to be published. Fermi part: Shell Model = (1/5) QRPA in 76 Ge

15. Amand Faessler, Tuebingen 3. Can one measure the Matrix Elements of the 0  Decay?

16. Fermi and Gamow-Teller 0  Transition Operator with Closure Amand Faessler, Tuebingen 0  Transition Matrix Element with Closure Relation:

17. |DIAS> = |T, T-2> |IAS> = |T, T-1> 0 + |g.s. i > =|T, T> |T-2,T-2> |g.s. f >=|0 f + > +  |DIAS> Amand Faessler, Tuebingen T-T- T-T- T-T- 0+0+ 0+0+ Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS> Isotensor force needed: T  T-2; Coulomb Interaction

18. Gamow Teller Strength not concentrated in one State broad Resonance. Fermi Transition: narrow Gamow-Teller: Main Contrib. Neutron Pairs: T =1, L=0  S=0  Gamow-Teller: g A s a s b |Pair> = - g A 3|Pair> Fermi: g V |Pair> = 1 |Pair> Shell Model for Fermi ~ (1/5) of QRPA Amand Faessler, Tuebingen

19. Fermi 0  Transition Operator Amand Faessler, Tuebingen

20. |IAS> = |T, T-1> 0 + |g.s. i > =|T, T> |g.s. f > = |T-2,T-2> +  |DIAS> Amand Faessler, Tuebingen T-T- 0+0+ Transition Matrix Elements for Fermi Transitions: First Leg Second Leg T-T- Exp. (d, 2 He): Frekers; Sakai; Zegers

21. Light left handed Majorana Exchange Heavy left handed Majorana Exchange Heavy right handed Majorana Exchange SUSY Lepton Number Violating Mechanis. Amand Faessler, Tuebingen 3. How to find the Leading Mechanism for the o  ? F. Simkovic, J. Vergados, A. Faessler, Phys. Rev. D82, 055502 (2010) A. Faessler, A. Meroni, S. T. Petcov, F. Simkovic, J. Vergados, to be published.

22. 5/2/2015Fedor Simkovic22 n Smallness of neutrino masses - Seesaw mnmn mDmD MRMR T. Yanagida, M. Gell-Mann, P. Ramond, R. Slansky If n R exists  then neutrino are naturaly massive  mass is unprotected by symmetry, can be large at a scale of LNV Sterile neutrinos n R Familiar light masses N m 1 =m D 2 /M R «m D m 2 ≈M R n 1 = n L -m D /M R ( n R ) c n 2 =n R +m D /M R ( n L ) c Assumption M R » m D Eigenvalues and eigenvectors

23. Amand Faessler, Tuebingen du d u WLWL WLWL kM mass e-e- e-e- GUT: Light and Heavy left handed Majorana Neutrino Exchange U ek=1,2,3  kL mass U  ek=4,5,6

24. Amand Faessler, Tuebingen du d u WRWR WRWR NRNR e-e- e-e- Light and Heavy left handed Majorana Neutrino Exchange V N ek

25. Amand Faessler, Tuebingen SUSY: R-Parity Breaking Lepton Number-Violating Minimal Supersymmetric Model Superfields:

26. 5/2/2015Fedor Simkovic26 R-parity Breaking MSSM R-parity breaking terms In superpotential Neutrino-Neutralino mixing matrix (see-saw structure) Radiative corrections to neutrino mass Gozdz, Kaminski, Šimkovic, PRD 70 (2004) 095005

27. Fedor Simkovic27 Gluino/neutralino exchange R-parity breaking SUSY mechanism of the 0  - decay quark-level diagrams exchange of squarks, neutralinos and gluinos d+d → u + u + e - + e -  ‘ 111

28. Amand Faessler, Tuebingen Neutrinoless Inverse Half Life propto Transition Probability

29. Transition Probability prop to Inverse Half Life; SUSY Contribution ‘. Amand Faessler, Tuebingen Dominance of Gluino echange in short range part assumed. Similar expression for Dominance of Neutralino exchange.

30. Dominance of Neutralino Exchange Faessler, Gutsche, Kovalenko, Simkovic Phys. Rev. D77 (2008) 113012 Amand Faessler, Tuebingen

31. 5/2/2015Fedor Simkovic31 Squark mixing SUSY mechanism Mixing between scalar Super-partners of the left- and right- handed fermions

32. Two leading non-interfering Mechanisms: Light Majorana and Heavy R Neutrino Amand Faessler, Tuebingen i = different nuclei, e.g. 76 Ge, 100 Mo, 130 Te; |    and our matrix element for g A = 1.25 Due to ratios only minimal changes for g A =1.00

33. Two leading non-interfering Mechanisms: Quenched g A ; Light Majorana and Heavy R Neutrino Amand Faessler, Tuebingen i = different nuclei, e.g. 76 Ge, 100 Mo, 130 Te; |    and quenched g A = 1.00 Due to ratios only minimal changes for g A =1.00

34. Two interfering Mechanisms: Light Majorana and Heavy Left Neutrino Amand Faessler, Tuebingen Three different transitions needed, e.g. 76 Ge, 100 Mo, 130 Te, to determine the three parameters.

35. Neutrino Mass from   Experiment Klapdor et al. 76 Ge  Mod. Phys. Lett. A21,1547(2006) ;  T(1/2; 0  ) = (2.23 +0.44 -0.31) x 10 25 years; 6  Matrix Elements: QRPA Tuebingen = 0.24 [eV] (exp+-0.02; theor+-0.01) [eV] Amand Faessler, Tuebingen

36. 1) Summary Comparing four different approaches for the  matrix elements: a.Shell model only small basis; violates the Ikeda sum rule by 50 to 60%. b.Interacting boson Model: only s (0 + ) and d (2 + ) pairs. c.Projected Hartee Fock Bogoliubov: Only 0 + pairs. d.QRPA large basis; fulfils Ikeda sum rule; realistic forces. Amand Faessler, Tuebingen

37. T-T- 0+0+ 2) Summary T-T- Shell model for Fermi Transition ~ 1/5 of QRPA IAS

38. Amand Faessler, Tuebingen 3) Summary Search for the Leading Mechanism  One Leading Mechanism: Determine the    m ?) in two systems. Is it the same?  Two leading non-interfering mechanisms: Determine  1 and  2 in three systems  Two interfering mechanisms: Determine  1,  2 and the relative phase theta in three nuclei and verify it in three nuclei with at least one other. THE END