Amand Faessler, 22. Oct 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, 22. Oct Neutrinoless Double Beta Decay The Double Beta Decay: β-β β-β- e-e- e-e- E>2m e

Amand Faessler, 22. Oct νββ -Decay (in SM allowed) Thesis Maria Goeppert-Mayer 1935 Goettingen PP nn

Amand Faessler, 22. Oct 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, 22. Oct GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

Amand Faessler, 22. Oct P P ν ν nn e-e- e-e- L/R l/r

Amand Faessler, 22. Oct l/r P ν P n n light ν heavy N Neutrinos

Amand Faessler, 22. Oct Supersymmetry Bosons ↔ Fermions Neutralinos PP e-e- e-e- nn u u u u dd Proton Neutron

Amand Faessler, 22. Oct Theoretical Description: Simkovic, Rodin, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel, Stoica, Suhonen, Civitarese, Tomoda et al k k k e1e1 e2e2 P P ν EkEk EiEi n n 0 νββ

Amand Faessler, 22. Oct

Amand Faessler, 22. Oct The best choice: Quasi-Particle-  Quasi-Boson-Approx.:  Particle Number non-conserv. (important near closed shells)  Unharmonicities  Proton-Neutron Pairing Pairing

Amand Faessler, 22. Oct

Amand Faessler, 22. Oct 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, 22. Oct

Amand Faessler, 22. Oct

Amand Faessler, 22. Oct 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) A different procedure of fixing gpp to single beta decays. What is their g(pp) with error? How well is the 2-neutrino decay reproduced? 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? We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)!

Amand Faessler, 22. Oct

Amand Faessler, 22. Oct

Amand Faessler, 22. Oct M0ν (R-QRPA; 1.25) S. Stoica, H.V. Klapdor- Kleingrothaus, NPA 694 (2001) 269 The same procedure of fixing g(pp) 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, 22. Oct 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 GENIUS ( 76 Ge) 1 X CANDLES ( 48 Ca) 1 X MOON ( 100 Mo) 1 X

Amand Faessler, 22. Oct 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, 22. Oct 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, 22. Oct Solar Neutrinos (+KamLand): (KamLand) Atmospheric Neutrinos: (Super-Kamiok.)

Amand Faessler, 22. Oct Reactor Neutrinos (Chooz): CP

Amand Faessler, 22. Oct 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, 22. Oct 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, 22. Oct (Bild)

Amand Faessler, 22. Oct 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, 22. Oct Summary: Results from  (  Ge  Exp. Klapdor)  0.47 [eV]  [GeV] > 5600 [GeV] SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4) Mainz-Troisk: m(  2.2 [eV] Astro Physics (SDSS): Sum{ m( ) } < 1 to 2 [eV] Klapdor et al. from  Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV], if confirmed. The Theory Groups must check their Results against each other. THE END 

Amand Faessler, 22. Oct 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, 22. Oct 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, 22. Oct ν -Mass-Matrix by Mixing with: Diagrams on the Tree level: Majorana Neutrinos:

Amand Faessler, 22. Oct Loop Diagrams: Figure 0.1: quark-squark 1-loop contribution to m v X X Majorana Neutrino

Amand Faessler, 22. Oct Figure 0.2: lepton-slepton 1-loop contribution to m v (7x7) Mass-Matrix: X X Block Diagonalis.

Amand Faessler, 22. Oct x 7 Neutrino-Massmatrix: Basis: Eliminate Neutralinos in 2. Order: separabel { Mass Eigenstate Vector in flavor space for 2 independent and possible

Amand Faessler, 22. Oct Super-K:

Amand Faessler, 22. Oct 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, 22. Oct How to calculate λ ‘ i33 (and λ i33 ) from λ ‘ 333 ? U(1) charge conserved! 1,2,3 = families

Amand Faessler, 22. Oct g PP fixed to 2 νββ; M(0  ) [MeV**(-1)] Each point: (3 basis sets) x (3 forces) = 9 values

Amand Faessler, 22. Oct 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, 22. Oct