1. Amand Faessler, Tuebingen1 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Neutrino Masses and the Neutrinoless Double Beta Decay: Dirac versus Majorana Neutrinos Accuracy of the Nuclear Matrix Elements

2. Amand Faessler, Tuebingen2 Neutrinoless Double Beta Decay The Double Beta Decay: 0+0+ 0+0+ 0+0+ β-β- 1+1+ 2-2- β-β- e-e- e-e- E>2m e

3. Amand Faessler, Tuebingen3 2 νββ -Decay (in SM allowed) Thesis Maria Goeppert-Mayer 1935 Goettingen PP nn

4. Amand Faessler, Tuebingen4 O νββ -Decay (forbidden) only for Majorana Neutrinos ν = ν c P P nn Left ν Phase Space 10 6 x 2 νββ

5. Amand Faessler, Tuebingen5 GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

6. Amand Faessler, Tuebingen6 P P ν ν nn e-e- e-e- L/R l/r

7. Amand Faessler, Tuebingen7 l/r P ν P n n light ν heavy N Neutrinos

8. Amand Faessler, Tuebingen8 Supersymmetry Bosons ↔ Fermions ----------------------------------------------------------------------- Neutralinos PP e-e- e-e- nn u u u u dd Proton Neutron

9. Amand Faessler, Tuebingen9 Theoretical Description: Simkovic, Rodin, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel 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

10. Amand Faessler, Tuebingen10

11. Amand Faessler, Tuebingen11 The best choice: Quasi-Particle-  Quasi-Boson-Approx.:  Particle Number non-conserv. (important near closed shells)  Unharmonicities  Proton-Neutron Pairing Pairing

12. Amand Faessler, Tuebingen12

13. Amand Faessler, Tuebingen13 Nucleus 48 Ca 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 128 Te 130 Te 134 Xe 136 Xe 150 Nd T1/2 (exp) [years] >9.5 10 21 >1.9 10 25 >1.4 10 22 >1.0 10 21 >5.5 10 22 >7.0 10 22 >8.6 10 22 >1.4 10 22 >5.8 10 22 >7.0 10 23 >1.7 10 21 Ref.:YouKlap- dor Elli- ott Arn.EjiriDane- vich Ales. Ber.Stau dt Klime nk. [eV]<22.<0.47<8.7<40.<2.8<3.8<17.<3.2<27.<3.8<7.2 η ~m(p)/M(  <200.<0.79<15.<79.<6.0<7.0<27.<4.9<38.<3.5<13. λ‘(111)[10 -4 ] <8.9<1.1<5.0<9.4<2.8<3.4<5.8<2.4<6.8<2.1<3.8 Only for Majorana ν possible.

14. Amand Faessler, Tuebingen14 g PP fixed to 2 νββ; M(0  ) [MeV**(-1)] Each point: (3 basis sets) x (3 forces) = 9 values

15. Amand Faessler, Tuebingen15

16. Amand Faessler, Tuebingen16 Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass of planed Experiments

17. Amand Faessler, Tuebingen17 Neutrino-Masses from the 0 ν  and Neutrino Oscillations Solar Neutrinos (CL, Ga, Kamiokande, SNO) Atmospheric ν (Super-Kamiokande) Reactor ν (Chooz; KamLand) with CP-Invariance:

18. Amand Faessler, Tuebingen18 Solar Neutrinos (+KamLand): (KamLand) Atmospheric Neutrinos: (Super-Kamiok.)

19. Amand Faessler, Tuebingen19 Reactor Neutrinos (Chooz): CP

20. Amand Faessler, Tuebingen20 ν 1, ν 2, ν 3 Mass States ν e, ν μ, ν τ Flavor States Theta(1,2) = 32.6 degrees Solar + KamLand Theta(1,3) < 13 degrees Chooz Theta(2,3) = 45 degrees S-Kamiokande

21. Amand Faessler, Tuebingen21 OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies: m ν Normal m 3 m 2 m 1 m 1 <<m 2 <<m 3 Inverted m 2 m 1 m 3 m 3 <<m 1 <<m 2 Bilenky, Faessler, Simkovic P. R. D 70(2004)33003

22. Amand Faessler, Tuebingen22 (Bild)

23. Amand Faessler, Tuebingen23 Summary: Accuracy of Neutrino Masses from 0  Fit the g(pp) by  in front of the proton- neutron Gamow-Teller NN matrixelement include exp. Error of . Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets the  Use QRPA and R-QRPA (Pauli principle) Use: g(A) = 1.25 and 1.00 Error of matrixelement 20 to 50 % (large errors from experim value of T(1/2, 2  )) 

24. Amand Faessler, Tuebingen24 Summary: Results from  (  Ge  Exp. Klapdor)  0.47 [eV]  [GeV] > 5600 [GeV] SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4) Mainz-Troisk: m(  2.2 [eV] Astro Physics (SDSS): Sum{ m( ) } < 1 to 2 [eV] Klapdor et al. from  Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV], if confirmed. THE END 

25. THE END25 Summary: Accuracy of Neutrino Masses by the Double Beta Decay Dirac versus Majorana Neutrinos Grand Unified Theories (GUT‘s), R-Parity violatingSupersymmetry → Majorana- Neutrino = Antineutrinos <m(  eV; ‘ < 1.1*10**(-4) Direct measurement in the Tritium Beta Decay in Mainz and Troisk Klapdor et al.: = 0.1 – 0.9 [eV] ; R-QRPA: 0.15 – 0.72 [eV] nn nn P P PP d d d d u u u u u u

26. Amand Faessler, Tuebingen26 3. Neutrino Masses and Supersymmetry R-Parity violating Supersymmetry mixes Neutrinos with Neutrinalinos (Photinos, Zinos, Higgsinos) and Tau-Susytau-Loops, Bottom-Susybottom-Loops → Majorana-Neutrinos (Faessler, Haug, Vergados: Phys. Rev. D ) m(neutrino1) = ~0 – 0.02 [eV] m(neutrino2) = 0.002 – 0.04 [eV] m(neutrino3) = 0.03 – 1.03 [eV] 0-Neutrino Double Beta decay = 0.009 - 0.045 [eV] ββ Experiment: < 0.47 [eV] Klapdor et al.: = 0.1 – 0.9 [eV] Tritium (Otten, Weinheimer, Lobashow) < 2.2 [eV] THE END

27. Amand Faessler, Tuebingen27 ν -Mass-Matrix by Mixing with: Diagrams on the Tree level: Majorana Neutrinos:

28. Amand Faessler, Tuebingen28 Loop Diagrams: Figure 0.1: quark-squark 1-loop contribution to m v X X Majorana Neutrino

29. Amand Faessler, Tuebingen29 Figure 0.2: lepton-slepton 1-loop contribution to m v (7x7) Mass-Matrix: X X Block Diagonalis.

30. Amand Faessler, Tuebingen30 7 x 7 Neutrino-Massmatrix: Basis: Eliminate Neutralinos in 2. Order: separabel { Mass Eigenstate Vector in flavor space for 2 independent and possible

31. Amand Faessler, Tuebingen31 Super-K:

32. Amand Faessler, Tuebingen32 Horizontal U(1) Symmetry U(1) Field U(1) charge R-Parity breaking terms must be without U(1) charge change (U(1) charge conservat.) Symmetry Breaking:

33. Amand Faessler, Tuebingen33 How to calculate λ ‘ i33 (and λ i33 ) from λ ‘ 333 ? U(1) charge conserved! 1,2,3 = families