1. Amand Faessler, Tuebingen Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen 1. Solution of the Solar Neutrino Problem by SNO. 2. Neutrino Masses and the Neutrinoless Double Beta Decay: Dirac versus Majorana Neutrinos 3. Neutrino Masses and Supersymmetry

2. Amand Faessler, Tuebingen (1) Solar Neutrino Problem Reaction Network: Oscillations: Fewer ν e on Earth detected than produced in the Sun. Oscillations depend on:

3. Amand Faessler, Tuebingen Sudburry Neutrino Observatory Creighton Mine Ontario / Canada (Zink Mine)

4. Amand Faessler, Tuebingen THE SNO CHERENKOV DETECTOR WITH HEAVY WATER 9456 Photomultipliers Ø 20 cm 55 % of 4 π Cherenkow radiation of e - Trigger ≥ 23 PMT E ν (Threshold) = 6.75 MeV Ø 17 m; view from below

5. Amand Faessler, Tuebingen Cherenkov - Detectors: (ES) Elastic Neutrino Scattering: e- forward scattering S-KAMIOKANDE + SNO e - (fast) νeνe W+W+ νeνe e-e- e-e- νxνx νxνx Z0Z0 + 6:1:1:1

6. Amand Faessler, Tuebingen Charged Current (CC): e- backward SNO e-e- νeνe W+W+ P P Deuteron (p + n)

7. Amand Faessler, Tuebingen (NC) Neutral Current: n-capture in salt NaCl (n, γ) νxνx νxνx Z0Z0 Pn Deuteron SNO

8. Amand Faessler, Tuebingen Assuming only Electron Neutrinos: (ES) 2.35*10 6 [ Φ ] (CC) 1.76*10 6 [ Φ ] (NC) 5.09*10 6 [ Φ ] Including Muon and Tauon ν : Φ ( ν e)=1.76*10 6 (CC) Φ ( νμ + ν τ)=3.41*10 6 (CC+ES) Φ ( ν e+ νμ + ν τ)=5.09*10 6 (NC) Φ ( ν -Bahcall)=5.14*10 6

9. Amand Faessler, Tuebingen 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

10. Amand Faessler, Tuebingen (Bild)

11. Amand Faessler, Tuebingen (2) 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

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

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

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

15. Amand Faessler, Tuebingen P P ν ν nn e-e- e-e- L/R l/r

16. Amand Faessler, Tuebingen l/r P ν P n n light ν heavy N Neutrinos

17. Amand Faessler, Tuebingen 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

18. Amand Faessler, Tuebingen

19. Supersymmetry Bosons ↔ Fermions ----------------------------------------------------------------------- Neutralinos PP e-e- e-e- nn u u u u dd Proton Neutron

20. Amand Faessler, Tuebingen Majorana;

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

22. Amand Faessler, Tuebingen

23. 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.

24. Amand Faessler, Tuebingen g PP fixed to 2 νββ Each point: (3 basis sets) x (3 forces) = 9 values

25. Amand Faessler, Tuebingen

27. Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass of planed Experiments  from R-QRPA; m  ) =  )

28. Amand Faessler, Tuebingen Neutrino-Masses for the Double 0 νβ- Decay and Neutrino Oscillations Solar Neutrinos Atmospheric ν Reactor ν (Chooz; KamLand) with CP-Invariance:

29. Amand Faessler, Tuebingen Solar Neutrinos (+KamLand): (KamLand) Atmospheric Neutrinos: (Super-Kamiok.)

30. Amand Faessler, Tuebingen Reactor Neutrinos (Chooz): CP

31. Amand Faessler, Tuebingen 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

32. Amand Faessler, Tuebingen Normal: Inverted:

33. Amand Faessler, Tuebingen (Bild)

34. Amand Faessler, Tuebingen

36. Summary: Neutrinos Oscillations, Neutrino Masses and the Double beta Decay 1. Solution of the Solar Neutrino Problem by theSudburry-Neutrino-Observatory (SNO): Elastic Scattering (S-KAMIOKANDE): Heavy Water (SNO: Charged Currents): νxνx νxνx Z0Z0 e-e- e-e- e-e- e-e- νcνc νcνc W+W+ νcνc d d e-e- W+W+ PP P n n n P P νxνx νxνx Z0Z0

37. Amand Faessler, Tuebingen 2. Neutrinoless Double Beta Decay Dirac versus Majorana Neutrinos Grand Unified Theories (GUT‘s), R-Parity violating Supersymmetry → Majorana-Neutrinos = Antineutrinos Direct measurement in the Tritium Beta Decay in Mainz and Troisk nn nn P P PP d d d d u u u u u u

38. Amand Faessler, Tuebingen 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

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

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

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

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

43. Amand Faessler, Tuebingen Super-K:

44. Amand Faessler, Tuebingen 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:

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