Amand Faessler University of Tuebingen

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. Oνββ-Decay (forbidden in Standard Model)  Neutrino Mass e2 P e1 P Left ν Phase Space 106x2νββ Left n n W1 = cos q WL+ sin q WR W2= -sin q WL+ cos q WR n = nc Majorana Neutrino Neutrino must have a Mass nMajorana, NL, NR Amand Faessler, Tuebingen

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

4. 1. Different Methods for the 0nbb-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] • 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

5. 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. Amand Faessler, Tuebingen

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

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

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

9. QRPA (TUE), Shell Model IBM2, PHFB Amand Faessler, Tuebingen

10. 2. Can one measure the Matrix Elements of the 0nbb 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 76Ge Amand Faessler, Tuebingen

11. Fermi and Gamow-Teller 0nbbTransition Operator with Closure 0nbb Transition Matrix Element with Closure Relation: Amand Faessler, Tuebingen

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

13. Fermi 0nbb Transition Operator Amand Faessler, Tuebingen

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

15. 3. Howto find theLeadingMechanismfortheonbb ? • Light left handed Majorana n Exchange • Heavy left handed Majorana n Exchange • Heavy right handed Majorana n Exchange • SUSY Lepton Number Violating Mechanis. 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. Amand Faessler, Tuebingen

16. GUT: Light and Heavy left handed Majorana Neutrino Exchange d u WL e- nkM mass NkL mass Unek=1,2,3 UNek=4,5,6 e- WL u d Amand Faessler, Tuebingen

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

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

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

20. Two leading non-interfering Mechanisms: Light Majorana and Heavy R Neutrino i = different nuclei, e.g. 76Ge, 100Mo, 130Te; |h|2 > 0 and our matrix element for gA = 1.25 Due to ratios only minimal changes for gA=1.00 Amand Faessler, Tuebingen

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

22. Neutrino Mass from 0nbb • Experiment Klapdor et al. 76Ge • Mod. Phys. Lett. A21,1547(2006) ; • T(1/2; 0nbb) = (2.23 +0.44 -0.31) x 1025 years; 6s Matrix Elements: QRPA Tuebingen • <m(n)> = 0.24 [eV] (exp+-0.02; theor+-0.01) [eV] Amand Faessler, Tuebingen

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

24. 2) Summary Shell model for Fermi Transition ~ 1/5 of QRPA 0+ IAS T- T- Amand Faessler, Tuebingen

25. 3) Summary Search for the Leading Mechanism • One Leading Mechanism: Determine the h1(mn ?) in two systems. Is it the same? • Two leading non-interfering mechanisms: Determine h1 and h2in three systems • Two interfering mechanisms: Determine h1, h2and the relative phase theta in three nuclei and verify it in three nuclei with at least one other. THE END Amand Faessler, Tuebingen