Amand Faessler, GERDA, 11. November Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines the Error of the Majorana Neutrino Mass extracted

Amand Faessler, GERDA, 11. November Neutrinoless Double Beta Decay The Double Beta Decay: β-β β-β- e-e- e-e- E>2m e

Amand Faessler, GERDA, 11. November νββ -Decay (in SM allowed) Thesis Maria Goeppert-Mayer 1935 Goettingen PP nn

Amand Faessler, GERDA, 11. November 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, GERDA, 11. November GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

Amand Faessler, GERDA, 11. November P P ν ν nn e-e- e-e- L/R l/r

Amand Faessler, GERDA, 11. November l/r P ν P n n light ν heavy N Neutrinos l/r L/R

Amand Faessler, GERDA, 11. November Supersymmetry Bosons ↔ Fermions Neutralinos PP e-e- e-e- nn u u u u dd Proton Neutron

Amand Faessler, GERDA, 11. November Theoretical Description: Simkovic, Rodin, Benes, Vogel, Bilenky, Salesh, Gutsche, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Stoica, Suhonen, Civitarese, Tomoda et al k k k e1e1 e2e2 P P ν EkEk EiEi n n 0 νββ

Amand Faessler, GERDA, 11. November Neutrinoless Double Beta- Decay Probability

Amand Faessler, GERDA, 11. November Effective Majorana Neutrino-Mass for the 0  Decay CP Tranformation from Mass to Flavor Eigenstates

Amand Faessler, GERDA, 11. November 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:

Amand Faessler, GERDA, 11. November ν 1, ν 2, ν 3 Mass States ν e, ν μ, ν τ Flavor States Theta 12 = 32.6 degrees Solar + KamLand Theta 13 < 13 degrees Chooz Theta 23 = 45 degrees S-Kamiokande  m 2 12 (solar  8  eV   m 2 23  atmospheric  eV 

Amand Faessler, GERDA, 11. November 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

Amand Faessler, GERDA, 11. November BilenkyBilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/ FaesslerSimkovic

Amand Faessler, GERDA, 11. November (Bild) Bilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/ Bilenky FaesslerSimkovic

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

Amand Faessler, GERDA, 11. November

Amand Faessler, GERDA, 11. November 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] > > > > > > > > > > > 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.

Amand Faessler, GERDA, 11. November Contribution of Different Multipoles to M(0 )

Amand Faessler, GERDA, 11. November g(A)**4 = 1.25**4 = 2.44 fit to 2  RodinRodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/ FaesslerSimkovicVogel

Amand Faessler, GERDA, 11. November Overlap of Wave Functions of the not involved core of the initial and final nuclei. Benes, Faessler, Simkovic Benesch, Faessler, Simkovic Preliminary (July 2005) Ge76

Amand Faessler, GERDA, 11. November Overlap of the core added to the 0  decay and new 2  -decay data (NEMO).

Amand Faessler, GERDA, 11. November R-QRPA-0  -Decay Nuclear Matrix Elements with Lipkin-Nogami and and Overlap of the Core. No experimental error included Closed Shells involved Benesch, Faessler, Simkovic (July 2005) Preliminary 20; 50; 82

Amand Faessler, GERDA, 11. November Renormalized QRPA with Lipkin-Nogami including the experimental error of the 2  decay

Amand Faessler, GERDA, 11. November Relation of M(0 ) on M(2 ) independent on Size of Basis ( 21 and 9 or 13 levels) Ratio M(0 )/M(2 ) with g(pp) fixed to M(2 ) independent of basis size

Amand Faessler, GERDA, 11. November (QRPA) 2.34 (RQRPA) Muto corrected

Amand Faessler, GERDA, 11. November 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. What is the basis and the dependence on the size of the basis? Short-range Brueckner Correlations not included. But finite size effects included. We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)!

Amand Faessler, GERDA, 11. November Neutrinoless Double Beta Decay The Double Beta Decay: β-β β-β- e-e- e-e- E>2m e x xxx Gamov-Teller single beta decay in the second leg fitted with g(pp) by Suhonen et al.. Underestimates the first leg. We fit the full 2  decay by adjusting g(pp).

Amand Faessler, GERDA, 11. November Fit of g(pp) to the single beta (2. leg) and the 2 double beta decay (small and large basis). Fit to 2  Fit to 1+ to 0+

Amand Faessler, GERDA, 11. November

Amand Faessler, GERDA, 11. November Uncorrelated and Correlated Relative N-N-Wavefunction in the N-N-Potential Short Range Correlations

Amand Faessler, GERDA, 11. November Jastrow-Function multiplying the relative N-N wavefunction (Parameters from Miller and Spencer, Ann. Phys 1976)

Amand Faessler, GERDA, 11. November Influence of Short Range Correlations (Parameters from Miller and Spencer, Ann. Phys 1976)

Amand Faessler, GERDA, 11. November Contribution of Different Multipoles to the zero Neutrino Matrixelements in QRPA s.r.c. = short range correlations h.o.t. = higher order currents Different Multipoles a) 76 Ge small model space ( 9 levels) b) 76 Ge large model space (21 levels) C) 100 Mo small model space ( 13 levels) d) 100 Mo large model space ( 21 levels)

Amand Faessler, GERDA, 11. November Comparison of 2  Half Lives with Shell model Results from Strassburg

Amand Faessler, GERDA, 11. November  Decay Matrix Elements in R-QRPA and the Strassburg Shell Model

Amand Faessler, GERDA, 11. November Contribution of GT 1+ States and the Sum of all other States to M(0 )

Amand Faessler, GERDA, 11. November Multipole Decomposition of M(0 ) in QRPA

Amand Faessler, GERDA, 11. November

Amand Faessler, GERDA, 11. November

Amand Faessler, GERDA, 11. November M0ν (R-QRPA; 1.25) S. Stoica, H.V. Klapdor- Kleingrothaus, NPA 694 (2001) 269 A similar procedure of fixing g(pp) to the two neutrino decay in one basis (?). Higher order terms of nucleon current not considered Nucleus l.m.s s.m.s our 76Ge 1.87 (l=12) 3.74 (s=9) 2.40(.12) 100Mo (.15) 130Te (.46) 136Xe (.23) Model space dependence ? Disagreement also between his tables and figures for R-QRPA and S-QRPA!

Amand Faessler, GERDA, 11. November Neutrinoless Double Beta Decay Matrix Elements EVZ-88 = Engel, Vogel, Zirnbauer; MBK-89 = Muto. Bender, Klapdor; T-91 Tomoda; SKF-91 = Suhonen, Khadkikar, Faessler; PSVF-96 = Pantis, Simkovic, Vergados, Faessler; AS-98 = Aunola, Suhonen; SPVF-99 = Simkovic, Pantis, Vergados, Faessler; SK-01 = Stoica, Klapdor; CS-03= Civitarese, Suhonen.

Amand Faessler, GERDA, 11. November Neutrinoless Double Beta Decay Matrix Elements EVZ-88 = Engel, Vogel, Zirnbauer; MBK-89 = Muto. Bender, Klapdor; T-91 Tomoda; SKF-91 = Suhonen, Khadkikar, Faessler; PSVF-96 = Pantis, Simkovic, Vergados, Faessler; AS-98 = Aunola, Suhonen; SPVF-99 = Simkovic, Pantis, Vergados, Faessler; SK-01 = Stoica, Klapdor; CS-03= Civitarese, Suhonen.

Amand Faessler, GERDA, 11. November Neutrinoless Double Beta Decay Matrix Elements EVZ-88 = Engel, Vogel, Zirnbauer; MBK-89 = Muto. Bender, Klapdor; T-91 Tomoda; SKF-91 = Suhonen, Khadkikar, Faessler; PSVF-96 = Pantis, Simkovic, Vergados, Faessler; AS-98 = Aunola, Suhonen; SPVF-99 = Simkovic, Pantis, Vergados, Faessler; SK-01 = Stoica, Klapdor; CS-03= Civitarese, Suhonen.

Amand Faessler, GERDA, 11. November 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) 1 X CANDLES ( 48 Ca) 1 X MOON ( 100 Mo) 1 X

Amand Faessler, GERDA, 11. November 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, GERDA, 11. November 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:

Amand Faessler, GERDA, 11. November Solar Neutrinos (+KamLand): (KamLand) Atmospheric Neutrinos: (Super-Kamiok.)

Amand Faessler, GERDA, 11. November Reactor Neutrinos (Chooz): CP

Amand Faessler, GERDA, 11. November 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

Amand Faessler, GERDA, 11. November 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

Amand Faessler, GERDA, 11. November (Bild)

Amand Faessler, GERDA, 11. November 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  ))  Core overlap reduction by ~0.85 (preliminary)

Amand Faessler, GERDA, 11. November 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 matrix elements !!! THE END

Amand Faessler, GERDA, 11. November Open Problems: 1. Overlapping but slightly different Hilbert space in intermediate Nucleus for QRPA from intial and from final nucleus. 2. Pairing does not conserve Nucleon number. Problem at closed shells. Particle projection. Lipkin-Nogami, 3. Deformed nuclei?

Amand Faessler, GERDA, 11. November 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

Amand Faessler, GERDA, 11. November 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) = – 0.04 [eV] m(neutrino3) = 0.03 – 1.03 [eV] 0-Neutrino Double Beta decay = [eV] ββ Experiment: < 0.47 [eV] Klapdor et al.: = 0.1 – 0.9 [eV] Tritium (Otten, Weinheimer, Lobashow) < 2.2 [eV] THE END

Amand Faessler, GERDA, 11. November ν -Mass-Matrix by Mixing with: Diagrams on the Tree level: Majorana Neutrinos:

Amand Faessler, GERDA, 11. November Loop Diagrams: Figure 0.1: quark-squark 1-loop contribution to m v X X Majorana Neutrino

Amand Faessler, GERDA, 11. November Figure 0.2: lepton-slepton 1-loop contribution to m v (7x7) Mass-Matrix: X X Block Diagonalis.

Amand Faessler, GERDA, 11. November x 7 Neutrino-Massmatrix: Basis: Eliminate Neutralinos in 2. Order: separabel { Mass Eigenstate Vector in flavor space for 2 independent and possible

Amand Faessler, GERDA, 11. November Super-K:

Amand Faessler, GERDA, 11. November 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:

Amand Faessler, GERDA, 11. November How to calculate λ ‘ i33 (and λ i33 ) from λ ‘ 333 ? U(1) charge conserved! 1,2,3 = families

Amand Faessler, GERDA, 11. November g PP fixed to 2 νββ; M(0  ) [MeV**(-1)] Each point: (3 basis sets) x (3 forces) = 9 values

Amand Faessler, GERDA, 11. November 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(νe)Φ(νe)=1.76*10 6 (CC) Φ(νμ+ντ)Φ(νμ+ντ)=3.41*10 6 (CC+ES) Φ(νe+νμ+ντ)Φ(νe+νμ+ντ)=5.09*10 6 (NC) Φ ( ν -Bahcall)=5.14*10 6

Amand Faessler, GERDA, 11. November