Amand Faessler, Madrid, 8. June Double Beta Decay, a Test for New Physics Amand Faessler Tuebingen „The Nuclear Matrix Elements for the  are as important as the Data to extract the Neutrino Mass“ (and in general New Physics). (Frank Avignone in Erice, September 2005)

Amand Faessler, Madrid, 8. June O νββ -Decay (forbidden) only for Majorana Neutrinos ν = ν c P P nn Left ν Phase Space 10 6 x 2 νββ

Amand Faessler, Madrid, 8. June GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

Amand Faessler, Madrid, 8. June P P ν ν nn e-e- e-e- L/R l/r

Amand Faessler, Madrid, 8. June l/r P ν P n n light ν heavy N Neutrinos l/r L/R p p n n e-e- vcvc vcvc e-e- W W

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

Amand Faessler, Madrid, 8. June Theoretical Description: Tübingen: Simkovic, Rodin, Benes, Vogel, Bilenky, Salesh, Gutsche, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Stoica, Suhonen, Civitarese, Tomoda, Moya de Guerra, Sarriguren, Valle et al k k k e1e1 e2e2 P P ν EkEk EiEi n n 0 νββ

Amand Faessler, Madrid, 8. June Neutrinoless Double Beta- Decay Probability + …

Amand Faessler, Madrid, 8. June Effective Majorana Neutrino-Mass for the 0  Decay CP Tranformation from Mass to Flavor Eigenstates

Amand Faessler, Madrid, 8. June BilenkyBilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/ FaesslerSimkovic

Amand Faessler, Madrid, 8. June The best choice: Quasi-Particle-  Quasi-Boson-Approx.:  Particle Number non-conserv. (important near closed shells)  Unharmonicities  Proton-Neutron Pairing Pairing

Amand Faessler, Madrid, 8. June g(A)**4 = 1.25**4 = 2.44; fit of g pp to 2  RodinRodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/ and Nucl. Phys. A (2006)FaesslerSimkovicVogel

Amand Faessler, Madrid, 8. June Quasi-Particle Random Phase (QRPA), Renormalized QRPA (RRPA) and Selfconsistent QRPA (SRPA)for three Basis Sizes and three Forces g pp fixed to 2  No experimental error g A = 1.25

Amand Faessler, Madrid, 8. June Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass of planed Experiments expt.T 1/2 [y] [eV] DAMA ( 136 Xe) 1.2 X MAJORANA ( 76 Ge) 3 X EXO 10t ( 136 Xe) 4 X GEM ( 76 Ge)7 X GERDA II ( 76 Ge) 2 X CANDLES ( 48 Ca) 1 X MOON ( 100 Mo) 1 X

Amand Faessler, Madrid, 8. June Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass of planed Experiments expt.T 1/2 [y] [eV] XMASS ( 136 Xe) 3 X CUORE ( 130 Te) 2 X COBRA ( 116 Cd) 1 X DCBA ( 100 Mo) 2 X DCBA ( 82 Se)3 X CAMEO ( 116 Cd) 1 X DCBA ( 150 Nd) 1 X

Amand Faessler, Madrid, 8. June Overlap of the inert Core of the initial and final Nucleus due to changes in Deformation  Pairing and Hilbert Space.

Amand Faessler, Madrid, 8. June Proton and Neutron Number conserved as and and improved spherical Overlap of the inert Core due to different Pairing. = Z; = Z 2 ~20 % Reduction due to (Pairing) Overlap g A = basis sets:~3 and 4 and 5 oscillator shells; Force: Bonn

Amand Faessler, Madrid, 8. June Dependence of 0  on the size of the Basis after Fit of g pp to 2 

Amand Faessler, Madrid, 8. June

Amand Faessler, Madrid, 8. June  Matrix Elements depending on the initial and final Deformation Beta

Amand Faessler, Madrid, 8. June Phenomenological NN-Force for differen Particle-Particle Strength kappa   adjusted to log ft in 1. leg

Amand Faessler, Madrid, 8. June new standard

Amand Faessler, Madrid, 8. June new standard

Amand Faessler, Madrid, 8. June

Amand Faessler, Madrid, 8. June

Amand Faessler, Madrid, 8. June (QRPA) 2.34 (RQRPA) Muto corrected

Amand Faessler, Madrid, 8. June M0ν (QRPA) O. Civitarese, J. Suhonen, NPA 729 (2003) 867 Nucleus their(QRPA, 1.254) our(QRPA, 1.25) 76Ge (0.12) 100Mo (0.10) 130Te (0.47) 136Xe (0.20) g(pp) fitted differently Higher order terms of nucleon Current included differently with Gaussian form factors based on a special quark model ( Kadkhikar, Suhonen, Faessler, Nucl. Phys. A29(1991)727). Does neglect pseudoscalar coupling (see eq. (19a)), which is an effect of 30%. We: Higher order currents from Towner and Hardy. Short-range Brueckner Correlations not included.

Amand Faessler, Madrid, 8. June Differences 1.. Ajustment of g pp for the NN force to the total 2  decay probability (Tuebingen) or to (Jyväskylä): β-β pn -1 np -1 x x   This log ft value known in only three double beta decay nuclei: 100 Mo, 116 Cd, 128 Te

Amand Faessler, Madrid, 8. June Different ways for Determening the g pp 2. Leg: Log ft only known in 100 Mo, 116 Cd, 128 Te. 1. leg 2 

Amand Faessler, Madrid, 8. June leg: known only in these three nuclei For the first leg no agreement

Amand Faessler, Madrid, 8. June Uncorrelated and Correlated Relative N-N-Wavefunction in the N-N-Potential Short Range Correlations

Amand Faessler, Madrid, 8. June Influence of Short Range Correlations (Parameters from Miller and Spencer, Ann. Phys 1976)

Amand Faessler, Madrid, 8. June Grey Area: Uncertainty due to Deformation; Dashed: Spherical

Amand Faessler, Madrid, 8. June Comparison of 2  Half Lives with Shell model Results from Strassburg-Madrid For 0  one needs intermidiate negative Parity States and higher Multipoles

Amand Faessler, Madrid, 8. June Contributions of different Multipolarities for 0  Negative Parity States not described by  Shell Model Blue: Short Range Correlations and Higher Order Currents. Red: Short Range Correlations, no Higher Order Currents White: No Short range Correlations, no Higher order Currents 76 Ge    and  oscillator shells  to  oscillator shells 76 Ge  

Amand Faessler, Madrid, 8. June Summary: Accuracy of Neutrino Masses from 0  Fit the g(pp) by  in front of the particle- particle NN matrixelement include exp. Error of . Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets (small about 2 shells, intermediate 3 shells and large 5 shells) the  Use QRPA and R-QRPA (Pauli principle) Use: g(A) = 1.25 and 1.00 Error of matrixelement 20 to 40 % (96Zr larger; largest errors from experim. values of T(1/2, 2  )) 

Amand Faessler, Madrid, 8. June Summary: Results from  (  Ge  Exp. Klapdor)  0.47 [eV] Klapdor et al. from  Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV].  [GeV] > 5600 [GeV] SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4) Mainz-Troisk, Triton Decay: m(  2.2 [eV] Astro Physics (SDSS): Sum{ m( ) } < ~0.5 to 2 [eV] Do not take democratic averaged matrixelements !!!

Amand Faessler, Madrid, 8. June Open Problems: 1. Overlapping but slightly different Hilbert spaces in intermediate Nucleus for QRPA from intial and from final nucleus. 2. BCS Pairing does not conserve Nucleon number. Problem at closed shells. Particle projection. 3. Deformed nuclei? (e.g.: 150 Nd ) β-β pn -1 np -1

Amand Faessler, Madrid, 8. June Open Problems: 4. Ajustment of g pp for the NN force to the total 2  decay probability or to: β-β pn -1 np -1 x x  

Amand Faessler, Madrid, 8. June Open Problems: 5. What is the leading Mechanisme for the Neutrinoless double Beta- Decay ? a) Light Majorana Neutrino exchange b) Heavy Majorana Neutrino exchange c) Right handed Current at one Vertex d) Heavy Vector-boson at one Vertex e) Minimal Supersymmetry with R-parity Violation And Others 0  to Excited States

Amand Faessler, Madrid, 8. June Open Problems: shell model Contribution of Different Multipoles to the zero Neutrino Matrixelements in QRPA 6. Shell model needs to enlarge the single particle space to three oscillator shells to include negative parity states and five shells to include deformations: Different Multipoles Blue: Short Range Correlations and Higher Order Currents. Red: Short Range Correlations, no Higher Order Currents White: No Short range Correlations, no Higher order Currents THE END 76 Ge 100 Mo