1. Amand Faessler University of Tuebingen
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

2. Oνββ-Decay (forbidden in Standard Model)  Neutrino MassP e1 P
Left ν
Phase Space
106 x 2νββ
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. Amand Faessler, Tuebingen
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) ; arXiv: [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. Amand Faessler, Tuebingen
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. Amand Faessler, Tuebingen
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. Amand Faessler, Tuebingen
2. Can one measure the Matrix Elements of the 0nbb Decay? V. Rodin, A. F. , Phys. Rev. C80 (2009), arXiv: and [nucl-th] to be published.
Fermi part: Shell Model = (1/5) QRPA in 76Ge
Amand Faessler, Tuebingen

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

12. Amand Faessler, Tuebingen
Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS>
|DIAS> = |T, T-2> |IAS> = |T, T-1> 0+ |g.s.i> =|T, T> |T-2,T-2> |g.s.f>=|0f+> + e|DIAS>
Isotensor force needed: T  T-2; Coulomb Interaction 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. How to find the Leading Mechanism for the onbb ?
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, (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 ExchangeWL e-
Unek=1,2,3
nkM mass
NkL mass
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. Amand Faessler, Tuebingen
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. Amand Faessler, Tuebingen
Neutrino Mass from 0nbb
Experiment Klapdor et al. 76Ge
Mod. Phys. Lett. A21,1547(2006) ;
T(1/2; 0nbb) = ( ) x 1025 years; 6s
Matrix Elements: QRPA Tuebingen
<m(n)> = [eV]
(exp+-0.02; theor+-0.01) [eV]
Amand Faessler, Tuebingen

23. Amand Faessler, Tuebingen
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 T- IAS T- 0+
Amand Faessler, Tuebingen

25. Amand Faessler, Tuebingen
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 h2 in three systems
Two interfering mechanisms: Determine h1, h2 and the relative phase theta in three nuclei and verify it in three nuclei with at least one other.
THE END
Amand Faessler, Tuebingen