1. K. Zuber, University of Sussex Neutrinoless double beta decay SUSSP 61, St. Andrews, 9-23 Aug. 2006

2. References F. Boehm, P. Vogel, Physics of massive neutrinos, Cambridge Univ. Press 1992 K. Zuber, Neutrino Physics, IOP, 2004 M. Doi, T. Kotani, E. Takasugi, Prog. Theo. Phys. 69, 602 (1983), Prog. Theo. Phys. Suppl. 83,1 (1985) W. Haxton, G. Stephenson, Prog. Nucl. Part. Phys. 12, 409 (1984) J. Suhonen, O. Civitarese, Phys. Rep. 300, 123 (1998) A. Faessler, F. Simkovic, J. Phys. G 24,2139 (1998) H. Ejiri, Phys. Rep. 338, 265 (2000) S. Elliott, P. Vogel, Ann. Rev. Nucl. Part. Sci. 52, 115 (2002) S, Elliott, J. Engel, J. Phys. G 30, R183 (2004) K. Zuber, Contemp. Physics 45, 491 (2005) Several more....

3. Contents Lecture 1 General introduction What is measured in DBD ? Neutrino oscillations and DBD Other BSM physics and DBD Nuclear matrix elements Lecture 2 Experimental considerations Current status of experiments Future activities Outlook and summary

4. (A,Z)  (A,Z+1) + e - + e  -decay (A,Z)  (A,Z+2) + 2 e - 0  - Beta and double beta decay (A,Z)  (A,Z+2) +2 e - + 2 e 2  n  p + e - + e - - Double beta decay Beta decay changing Z by two units while leaving A constant

5. Requirements - I 2.) Single beta decay must be forbidden (m (A,Z) < m (A,Z+1)) or at least strongly suppressed (large change in angular momentum) 1.) m(A,Z) > m(A,Z+2)

6. Requirements- II Weizsäcker formula for A=const near minimum well approximated by Pairing energy  leads to splitting:  = 0 for even-odd, odd-even  = - 12 MeV/A 1/2 for even-even  = + 12 MeV/A 1/2 for odd-odd    O-O E-E A Even Z m ZoZo    There are 35  -  - isotopes in nature

7. Example - Ge76

8. History 1934: E. Fermi theory of weak interaction 1935: M. Goeppert-Mayer discussed 2  1937: E. Majorana two component neutrino 1937,39: G. Racah, W.H. Furry discussed 0  1949: First half-life limits (Fireman, Fremlin,...) 1967: First geochemical evidence for 2  1987: First laboratory evidence for 2  2002: First laboratory evidence for 0  ???

9. 2  All even-even ground state transitions are 0 +  0 + 2  : Fermi‘s Golden rule Only Gamow-Teller transitions No unknowns from particle physics

10. 2  Sum energy spectrum: S. Elliott et al., 1987 82 Se, 35 events Measured for about 10 isotopes Important for nuclear matrix elements

11. 0  Any ∆L=2 process can contribute to 0  R p violating SUSY V+A interactions Leptoquarks Double charged Higgs bosons Compositeness Heavy Majorana neutrino exchange Light Majorana neutrino exchange... 1 / T 1/2 = PS * NME 2 *  2

12. Schechter-Valle theorem

13. The standard lore Measured quantity Phase space integral calculable Nuclear transition matrix element Quantity of interest Effective Majorana neutrino mass 1 / T 1/2 = PS * NME 2 * ( / m e ) 2 Light Majorana neutrino exchange

14. (A,Z)  (A,Z+2) + 2 e - 0  New situation for nuclear matrix elements, higher multipoles contribute

15. Contents Lecture 1 General introduction What is measured in DBD ? Neutrino oscillations and DBD Other BSM physics and DBD Nuclear matrix elements Lecture 2 Experimental considerations Current status of experiments Future activities Outlook and summary

16. Oscillation evidences LSND Atmospheric Solar + reactors sin 2 2  = 10 -1 -10 -3,  m 2 = 0.1-6 eV 2 sin 2 2  = 1.00,  m 2 = 2.5  10 -3 eV 2 sin 2 2  = 0.81,  m 2 = 8.0  10 -5 eV 2 If all three are correct... we need more (sterile ones) depends onNo absolute mass measurement

17. 3 Flavour oscillations (PMNS) solar If sin  13  0  CP-violation atmospheric U= U PMNS diag(1,e i  1,e i  2 )Majorana:

18. Neutrino mass schemes normalinverted almost degenerate neutrinos m 1 ≈ m 2 ≈ m 3 hierarchical neutrino mass schemes

19. Physical quantities Experimental observable: Half-life Double beta decay: Effective Majorana neutrino mass Beta decay m =  |U ek | 2 m k CP-invariance: Measurements are complementary

20. Contents Lecture 1 General introduction What is measured in DBD ? Neutrino oscillations and DBD Other BSM physics and DBD Nuclear matrix elements Lecture 2 Experimental considerations Current status of experiments Future activities Outlook and summary

21. Oscillations and 0  General: Rough estimate:

22. 0  - Normal hierarchy

23. Neutrino mass schemes and 0  M. Hirsch Neutrino 2006 Best fit values

24. Neutrino mass schemes and 0  Adding errors

25. Effect of  13 in normal hierarchy

26. 0  -Inverted mass scheme

27. 0  - Inverted hierarchy

28. Normal + inverted scheme

29. Comments Uncertainties in nuclear matrix elements not included Difference between normal and inverted tiny, might be swamped by NME Benchmark number of 50 meV neutrino mass, in case of inverted hierarchy should lead to an observation Eff. Majorana mass should be plotted against other observables (beta, decay, cosmology) Claimed evidence

30. Contents Lecture 1 General introduction What is measured in DBD ? Neutrino oscillations and DBD Other BSM physics and DBD Nuclear matrix elements Lecture 2 Experimental considerations Current status of experiments Future activities Outlook and summary

31. Right handed weak currents Add a (V+A) weak interaction (left-right symmetric theories)

32. Neutrino mass vs. right handed currents (eV) Possible evidence M. Hirsch et al., Z. Phys. A 347,151 (1994) EC/ß +

33.  +  + - modes (A,Z)  (A,Z-2) + 2 e + (+2 e )  +  + e - + (A,Z)  (A,Z-2) + e + (+2 e )  +/EC 2 e - + (A,Z)  (A,Z-2) (+2 e ) EC/EC Important to reveal mechanism if 0  is discovered Enhanced sensitivity to right handed weak currents (V+A) n n p p e e In general: Q-4m e c 2 Q-2m e c 2 Q Double charged higgs bosons, R-parity violating SUSY couplings, leptoquarks...

34. More on V+A interactions Transitions to excited 2 + states dominated by V+A 0+0+ 1+1+ 0+0+ (A,Z) (A,Z+1) (A,Z+2) 2+2+ Nice signal: Coincidence of electron and gamma Angular correlation coefficient  Single electron spectra

35. Supersymmetry Each known particle gets a supersymmetric partner MSSM: Conserves R-parity = (-1) 3B+L+2S

36. R p violating SUSY Double beta probes

37.  L=2 Processes 3.5 10 -10 1.7 (8.2) 10 -2 8.4 10 3 5008.7 10 3 2.0 10 4 In general 9 mass terms limits on (in GeV) W. Rodejohann, K. Zuber, Phys. Rev. D 62, 094017 (2000)  e-conversion on nuclei M. Flanz, W. Rodejohann, K. Zuber, Eur. Phys. J. C 16, 453 (2001) K. Zuber, Phys. Lett. B 479,33 (2000) M. Flanz, W. Rodejohann, K. Zuber, Phys. Lett. B 473, 324 (2000) W. Rodejohann, K. Zuber, Phys. Rev. D 63, 054031 (2001)

38. Candidate events NOMAD trimuon eventH1 charged current event

39. Majoron modes Majoron = Goldstone boson of spontaneously broken global (B-L) symmetry n=1,3,7 (depending on transformation under weak isospin) Triplet and pure doublet ruled out by Z-width Current bounds around 10 -4 Sum energy spectrum of electrons Observable: