1. -Nucleus Interactions Double-beta Decay and Cristina VOLPE Institut de Physique Nucléaire Orsay, France

2. 2b-Decay: Status and Future PLANPLAN Intense -sources -Nucleus: Link to 2  -decay Conclusions and Pespectives

3. : Majorana or Dirac particles?  Dirac Majorana = ? How do we search for the -nature? Beyond the Standard Model (e.g. exchange of massive Majorana neutrinos) 2  0  : 2n  2p + 2e - Lepton-violating process 2  2  : 2n  2p + 2e - + 2 e 2  0  : 2n  2p + 2e - Within the Standard Model (V-A theory) 76 Ge 76 As 76 Se  (0 ) Haxton and Stevenson, Prog. Part. Nucl. Phys., 1984; Suhonen and Civitarese, Phys. Rep., 1998; Faessler and Simkovic, J. Phys. G, 1998; Elliott and Vogel, Ann. Rev. Nucl. Part. Sci. 2002; H. Ejiri, Phys. Rep.; Elliott and Engel, J. Phys. G, 2004;….

4. Klapdor et al., 2001 > 1.9 10 25 y (90% C.L.) < 0.3 – 1.0 eV 2  0  : 2n  2p + 2e - The present best limit (Heidelberg-Moscow,IGEX ). 76 Ge 76 As 76 Se  (0 ) The experimental search 2  2  : 2n  2p + 2e - + 2 e Observed in various nuclei: 48 Ca, 76 Ge, 82 Se, 96 Zr, 100 Mo, 116 Cd, 128 Te, 130 Te, 136 Xe, 150 Nd. The half-lives vary in the range: T 1/2 ( 150 Nd) = 4.2 10 19 y to T 1/2 ( 128 Te) = 7.2 10 24 y A RECENT CLAIM for EVIDENCE by KLAPDOR et al., PLB (2004).

5. Present and Future The only presently running experiment is NEMO3 (Modane, France). T 1/2 = 7.3 ±0.0025(stat)±0.7(syst)  10 18 y 100 Mo CUORE and GERDA will confirm or refute Klapdor’s claim. A large number of experiments (Majorana, MOON, COBRA, XMASS, SuperNEMO, etc…) are now under investigation. The aim is to reach about 50meV sensitivity.

6. Theoretical Aspects  : phase space factor M : nuclear matrix elements : effective neutrino mass  ( ) M 2 2 Q5Q5  1 = This has important implications: e.g. _ it translates in an uncertainty on the -mass; _ it can prevent getting the hierarchy; _ it renders difficult to choose the best candidate. REDUCING THE UNCERTAINTIES: A MAJOR CHALLENGE. Several efforts to understand the sensitivity of the calculations ( e.g. interaction, spaces ) and to better constrain the predictions. Theoretical predictions (mainly performed within Shell Model and QRPA) exhibit significant variations of the neutrinoless double-beta decay half-lives for the same candidate emitter. ex: Rodin, Faessler, Simkovic, Vogel, PRC68 (2003).

7. The 2  (2 ) T 1/2 2  2  : 2n  2p + 2e - + 2 e GAMOW-TELLER STATES CONTRIBUTE. Using second-order perturbation theory and j  (H) 1. , 

8. The 2  half-life 2  0  : 2n  2p + 2e - 76 Ge Bobyk,Kaminski,Simkovic,PRC2001 MANY STATES ARE INVOLVED. Exchange of a massive Majorana neutrino e- n n p p Little experimental information on such states.

9. Several processes have been considered to constrain the nuclear matrix elements, in particular beta-decay, muon capture, 2  (2 ), charge-exchange reactions. 48 Ti 48 Ca 48 Sc  (0 )    Constraints e e C.Volpe, hep-ph/0501233. What about using neutrino-nucleus interactions ?  : only a few energy levels Muto,Bender,Klapdor, Z.Phys.A 1989; Aunola, Suhonen, 1996; Civitarese, Suhonen; … charge-exchange reactions : a very good tool, high resolution Bernabeu et al., 1988; Akimune et al., 1997; Ejiri, Phys. Rep.; S. Rakers et al, PRC 2004; …  capture : states up to 100 MeV, only one branch Kortelainen and Suhonen, Europhys. Lett. 2002; Phys. Atom. 2004.  : only 1 + (GT) states Muto, Bender, Klapdor, 1993; Faessler et al., 1987; Rodin et al. PRC 2003; …

10. Neutrinoless Double-beta Decay e- n n p p Using second-order perturbation theory, the matrix elements involved in the half-lives are of the type : j  (H) 1. ,  The excited states are called isospin (Fermi) and spin-isospin modes (Gamow-Teller).  f|O 12 |i>= where O 12 is a two-body operator and V(|r 1 -r 2 |) is the neutrino propagator which describes the exchange of the neutrino between the two decay vertices («neutrino potential»). By making a multipole expansion of the neutrino potential : V(|r 1 -r 2 |)~dqq 2 v(q)[j L (qr 1 )Y L (r 1 )][j L (qr 2 )Y L (r 2 )] and inserting a number of intermediate states :  m 2+2+ 48 Ti 48 Ca 48 Sc  (0 ) 1-1- 1+1+ 3-3- -Nucleus : a new constraint for 2  (0 )? C.Volpe, hep-ph/0501233.

11. The effective V-A interaction Hamiltonian : The nuclear transition probabilities are the key quantities : THE SAME STATES AS IN ( 0 ) 2  ARE EXCITED. Applying the Foldy-Wouthuysen transformation and using perturbation theory : -Nucleus Interactions C N e e C.Volpe, hep-ph/0501233.

12. e + 48 Ca 48 Sc + e - = 60 MeV An example 48 Ti 48 Ca 48 Sc  (0 ) e 1-1- 1+1+ 2+2+ 3-3- e Results of a microscopic calculation (QRPA). C.Volpe, hep-ph/0501233. = 30 MeV e + 48 Ca 48 Sc + e -

13. e + 48 Ti 48 Sc + e + = 60 MeV An example 48 Ti 48 Ca 48 Sc  (0 ) e 1-1- 1+1+ 2+2+ 3-3- e Results of a microscopic calculation (QRPA). C.Volpe, hep-ph/0501233. THESE STUDIES COULD GIVE A SUPPLEMENTARY CONSTRAIN TO 2  (0 ) DECAY PREDICTIONS. = 30 MeV e + 48 Ti 48 Sc + e + Future intense -sources : conventional & low-energy beta-beams.

14. INTENSE -SOURCES Neutrino beams can be produced with:    e  e SnS, Oak Ridge (USA), JHP (Japan), Multi-MW proton driver (Europe) THE BETA-BEAM CONCEPT : Zucchelli, PLB 2002 Lorentz boost  1/ high  Low-Energy BETA-BEAMS 6 He CONVENTIONAL METHODS : 6 He 6 Li + e - + e Pure neutrino beams produced by boosting ions which decay through beta-decay. H.Ejiri NIMA, 503, 278(2003).

15. THE PROPOSAL C. Volpe, Journ. Phys. G. 30 (2004), hep-ph/0303222. Neutrino properties, like the magnetic moment. Low-energy Beta-beams To exploit the beta-beam concept to produce intense and pure low energy neutrino beams. A BETA-BEAM FACILITY FOR LOW ENERGY NEUTRINOS. PHYSICS POTENTIAL Neutrino-nucleus interaction studies. boost 6 He 6 He …

16. close detector PS SPS EURISOLEURISOL Beta-beam baseline at CERN Storage Ring …or at one of the laboratories that will produce intense radioactive beams in the future (need of ion acceleration to GeV energy and of a storage ring). Neutrino-nucleus measurements TWO POSSIBLE SCENARIOS. d length of the straight sections L total length Two options studied : - Large ring - Small Ring Serreau and Volpe, hep-ph/0403293, PRC70 (2004). POSSIBLE SITES

17. -Nucleus Interaction Rates INTERESTING INTERACTION RATES CAN BE OBTAINED. Neutrino Fluxes  <E  ~2  Q  /2 The unique feature that the -energy can be easily varied. Serreau and Volpe, hep-ph/0403293, PRC70 (2004). Small Ring : d = 150 m, L= 450m Large Ring :d = 2.5 km, L =7.5 km Small RingLarge Ring 257791956 e + D Events per year 194 2494 m=35 tons 1802363

18. Conclusions and Perspectives The search for the neutrinoless double-beta decay is crucial. Future experiments will reach the tens of meV sensitivity. Conventional sources and low-energy beta-beams could offer the opportunity to perform such studies. Neutrino-nucleus interactions : a new constraint for the calculation of the half-lives. Constraining the theoretical predictions represents a major challenge.