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Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

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Presentation on theme: "Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines."— Presentation transcript:

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2 Amand Faessler, GERDA, 11. November 20051 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

3 Amand Faessler, GERDA, 11. November 20052 Neutrinoless Double Beta Decay The Double Beta Decay: 0+0+ 0+0+ 0+0+ β-β- 1+1+ 2-2- β-β- e-e- e-e- E>2m e

4 Amand Faessler, GERDA, 11. November 20053 2 νββ -Decay (in SM allowed) Thesis Maria Goeppert-Mayer 1935 Goettingen PP nn

5 Amand Faessler, GERDA, 11. November 20054 O νββ -Decay (forbidden) only for Majorana Neutrinos ν = ν c P P nn Left ν Phase Space 10 6 x 2 νββ

6 Amand Faessler, GERDA, 11. November 20055 GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

7 Amand Faessler, GERDA, 11. November 20056 P P ν ν nn e-e- e-e- L/R l/r

8 Amand Faessler, GERDA, 11. November 20057 l/r P ν P n n light ν heavy N Neutrinos l/r L/R

9 Amand Faessler, GERDA, 11. November 20058 Supersymmetry Bosons ↔ Fermions ----------------------------------------------------------------------- Neutralinos PP e-e- e-e- nn u u u u dd Proton Neutron

10 Amand Faessler, GERDA, 11. November 20059 Theoretical Description: Simkovic, Rodin, Benes, Vogel, Bilenky, Salesh, Gutsche, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Stoica, Suhonen, Civitarese, Tomoda et al. 0+0+ 0+0+ 0+0+ 1+1+ 2-2- k k k e1e1 e2e2 P P ν EkEk EiEi n n 0 νββ

11 Amand Faessler, GERDA, 11. November 200510 Neutrinoless Double Beta- Decay Probability

12 Amand Faessler, GERDA, 11. November 200511 Effective Majorana Neutrino-Mass for the 0  Decay CP Tranformation from Mass to Flavor Eigenstates

13 Amand Faessler, GERDA, 11. November 200512 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:

14 Amand Faessler, GERDA, 11. November 200513 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 

15 Amand Faessler, GERDA, 11. November 200514 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

16 Amand Faessler, GERDA, 11. November 200515 BilenkyBilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250 FaesslerSimkovic

17 Amand Faessler, GERDA, 11. November 200516 (Bild) Bilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250 Bilenky FaesslerSimkovic

18 Amand Faessler, GERDA, 11. November 200517 The best choice: Quasi-Particle-  Quasi-Boson-Approx.:  Particle Number non-conserv. (important near closed shells)  Unharmonicities  Proton-Neutron Pairing Pairing

19 Amand Faessler, GERDA, 11. November 200518

20 Amand Faessler, GERDA, 11. November 200519 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] >9.5 10 21 >1.9 10 25 >1.4 10 22 >1.0 10 21 >5.5 10 22 >7.0 10 22 >8.6 10 22 >1.4 10 22 >5.8 10 22 >7.0 10 23 >1.7 10 21 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.

21 Amand Faessler, GERDA, 11. November 200520 Contribution of Different Multipoles to M(0 )

22 Amand Faessler, GERDA, 11. November 200521 g(A)**4 = 1.25**4 = 2.44 fit to 2  RodinRodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063FaesslerSimkovicVogel

23 Amand Faessler, GERDA, 11. November 200522 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

24 Amand Faessler, GERDA, 11. November 200523 Overlap of the core added to the 0  decay and new 2  -decay data (NEMO).

25 Amand Faessler, GERDA, 11. November 200524 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

26 Amand Faessler, GERDA, 11. November 200525 Renormalized QRPA with Lipkin-Nogami including the experimental error of the 2  decay

27 Amand Faessler, GERDA, 11. November 200526 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

28 Amand Faessler, GERDA, 11. November 200527 2.76 (QRPA) 2.34 (RQRPA) Muto corrected

29 Amand Faessler, GERDA, 11. November 200528 M0ν (QRPA) O. Civitarese, J. Suhonen, NPA 729 (2003) 867 Nucleus their(QRPA, 1.254) our(QRPA, 1.25) 76Ge 3.33 2.68(0.12) 100Mo 2.97 1.30(0.10) 130Te 3.49 1.56(0.47) 136Xe 4.64 0.90(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, …)!

30 Amand Faessler, GERDA, 11. November 200529 Neutrinoless Double Beta Decay The Double Beta Decay: 0+0+ 0+0+ 0+0+ β-β- 1+1+ 2-2- 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).

31 Amand Faessler, GERDA, 11. November 200530 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+

32 Amand Faessler, GERDA, 11. November 200531

33 Amand Faessler, GERDA, 11. November 200532 Uncorrelated and Correlated Relative N-N-Wavefunction in the N-N-Potential Short Range Correlations

34 Amand Faessler, GERDA, 11. November 200533 Jastrow-Function multiplying the relative N-N wavefunction (Parameters from Miller and Spencer, Ann. Phys 1976)

35 Amand Faessler, GERDA, 11. November 200534 Influence of Short Range Correlations (Parameters from Miller and Spencer, Ann. Phys 1976)

36 Amand Faessler, GERDA, 11. November 200535 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)

37 Amand Faessler, GERDA, 11. November 200536 Comparison of 2  Half Lives with Shell model Results from Strassburg

38 Amand Faessler, GERDA, 11. November 200537 0  Decay Matrix Elements in R-QRPA and the Strassburg Shell Model

39 Amand Faessler, GERDA, 11. November 200538 Contribution of GT 1+ States and the Sum of all other States to M(0 )

40 Amand Faessler, GERDA, 11. November 200539 Multipole Decomposition of M(0 ) in QRPA

41 Amand Faessler, GERDA, 11. November 200540

42 Amand Faessler, GERDA, 11. November 200541

43 Amand Faessler, GERDA, 11. November 200542 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 3.40 4.36 1.20(.15) 130Te 3.00 4.55 1.46(.46) 136Xe 1.02 1.57 0.85(.23) Model space dependence ? Disagreement also between his tables and figures for R-QRPA and S-QRPA!

44 Amand Faessler, GERDA, 11. November 200543 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.

45 Amand Faessler, GERDA, 11. November 200544 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.

46 Amand Faessler, GERDA, 11. November 200545 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.

47 Amand Faessler, GERDA, 11. November 200546 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 10 24 2.3 MAJORANA ( 76 Ge) 3 X 10 27 0.044 EXO 10t ( 136 Xe) 4 X 10 28 0.012 GEM ( 76 Ge)7 X 10 27 0.028 GERDA II ( 76 Ge) 1 X 10 26 0.16 CANDLES ( 48 Ca) 1 X 10 26 0.2 MOON ( 100 Mo) 1 X 10 27 0.058

48 Amand Faessler, GERDA, 11. November 200547 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 10 26 0.10 CUORE ( 130 Te) 2 X 10 26 0.10 COBRA ( 116 Cd) 1 X 10 24 1 DCBA ( 100 Mo) 2 X 10 26 0.07 DCBA ( 82 Se)3 X 10 26 0.04 CAMEO ( 116 Cd) 1 X 10 27 0.02 DCBA ( 150 Nd) 1 X 10 26 0.02

49 Amand Faessler, GERDA, 11. November 200548 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:

50 Amand Faessler, GERDA, 11. November 200549 Solar Neutrinos (+KamLand): (KamLand) Atmospheric Neutrinos: (Super-Kamiok.)

51 Amand Faessler, GERDA, 11. November 200550 Reactor Neutrinos (Chooz): CP

52 Amand Faessler, GERDA, 11. November 200551 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

53 Amand Faessler, GERDA, 11. November 200552 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

54 Amand Faessler, GERDA, 11. November 200553 (Bild)

55 Amand Faessler, GERDA, 11. November 200554 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)

56 Amand Faessler, GERDA, 11. November 200555 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

57 Amand Faessler, GERDA, 11. November 200556 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?

58 Amand Faessler, GERDA, 11. November 200557 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

59 Amand Faessler, GERDA, 11. November 200558 3. 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) = 0.002 – 0.04 [eV] m(neutrino3) = 0.03 – 1.03 [eV] 0-Neutrino Double Beta decay = 0.009 - 0.045 [eV] ββ Experiment: < 0.47 [eV] Klapdor et al.: = 0.1 – 0.9 [eV] Tritium (Otten, Weinheimer, Lobashow) < 2.2 [eV] THE END

60 Amand Faessler, GERDA, 11. November 200559 ν -Mass-Matrix by Mixing with: Diagrams on the Tree level: Majorana Neutrinos:

61 Amand Faessler, GERDA, 11. November 200560 Loop Diagrams: Figure 0.1: quark-squark 1-loop contribution to m v X X Majorana Neutrino

62 Amand Faessler, GERDA, 11. November 200561 Figure 0.2: lepton-slepton 1-loop contribution to m v (7x7) Mass-Matrix: X X Block Diagonalis.

63 Amand Faessler, GERDA, 11. November 200562 7 x 7 Neutrino-Massmatrix: Basis: Eliminate Neutralinos in 2. Order: separabel { Mass Eigenstate Vector in flavor space for 2 independent and possible

64 Amand Faessler, GERDA, 11. November 200563 Super-K:

65 Amand Faessler, GERDA, 11. November 200564 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:

66 Amand Faessler, GERDA, 11. November 200565 How to calculate λ ‘ i33 (and λ i33 ) from λ ‘ 333 ? U(1) charge conserved! 1,2,3 = families

67 Amand Faessler, GERDA, 11. November 200566 g PP fixed to 2 νββ; M(0  ) [MeV**(-1)] Each point: (3 basis sets) x (3 forces) = 9 values

68 Amand Faessler, GERDA, 11. November 200567 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

69 Amand Faessler, GERDA, 11. November 200568

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