1. Can one measure the Neutrino Mass in the Double Beta Decay ?
Fest-Colloquium for the 60. Birthday of Jochen Wambach.
Can one measure the Neutrino Mass in the Double Beta Decay ?
Amand Faessler,
University of Tuebingen

2. FAESSLER; GSI 16. November 2010
Preparation for the legendary Football Game in Jülich against Solar Energy ~1977
Müther
Baur
Meyer ter Vehn
Wambach
FAESSLER; GSI 16. November 2010

3. The successful Nuclear Physics Football Team in Jülich-Broich ~1975
Müther, Grümmer
Krewald
Wambach
Faessler
Meyer ter V.
K. W. Schmid
Baur
Osterfeld
FAESSLER; GSI 16. November 2010

4. FAESSLER; GSI 16. November 2010
Jochen Wambach * July
Studies at Univ. Bonn
Dipl. + Ph. D. in Jülich/Bonn
Stony Brook
Univ. Illinois 1990 Full Prof.
Univ. Bonn
+ Vice-Director Jülich
Full Prof. TU Darmstadt
Head Theory Group Hadrons +
QCD at GSI.
FAESSLER; GSI 16. November 2010

5. Honors and Service of Jochen Wambach
Fellow of American Phys. Soc.
Senat of DFG
Editor: European J. of Phys. A
Editor: Phys. Rev. Lett.
Member of many National and International Committees.
FAESSLER; GSI 16. November 2010

6. SPIRES: Famous Publication
„Famous paper“ with 436 citations with
R. Rapp:Chiral Symmetry Restoration
and Dileptons in Relativistic HI
Collisions. Published in Annals of Physics 2000.
1) Cooperstein, Wambach: Electron capture in Stellar Collaps ; Nucl. Phys. A420(1984)
2) Chanfray, Rapp, Wambach: Medium Modifications of the r Meson at SPS Energies; Phys. Rev. Lett. 76 (1996)
FAESSLER; GSI 16. November 2010

7. FAESSLER; GSI 16. November 2010
1) What triggers the presupernova stellar collaps? Wambach, Cooperstein. Nucl. P.A420(1984)
Electrons
Iron Core 26Fe30
Energy e-
Protons
Neutrons
g9/2
P1/2
f5/2
Fermi Surface
P3/2
f7/2
Bethe+Brown 1979: e- + p f7/2 n f5/2 + ne
Fuller soon blocked 1982: n f5/2 full
Wambach 1984: Thermal unblocking:
p g9/2  n g9/2 ; p g9/2  n g7/2
FAESSLER; GSI 16. November 2010

8. FAESSLER; GSI 16. November 2010
2) Propagation of the r-Meson in hot and dense Nuclear Matter (CERES Data) Wambach et al. Phys. Rev. Lett. 76 (1996)436
Model for r-Meson
Model for r-Meson
p-Meson
p-Meson
Pion propagation in hot and dense nuclear matter:
p-Meson
p-Meson
N N-1 ; D N-1 ; N D-1 ; D D-1
FAESSLER; GSI 16. November 2010

9. Explanation of the CERES-Dilepton-Data CERN PPE 1995
Vector Meson Dominance
r  g  e+ e-
Modified r
Bare r meson
Mass of modified r-Meson
FAESSLER; GSI 16. November 2010

10. Can one measure the Neutrino Mass in the 0n Double Beta Decay ?
Fest-Colloquium for the 60. Birthday of Jochen Wambach July
Amand Faessler,
University of Tuebingen

11. FAESSLER; GSI 16. November 2010
Sehr geehrte radioaktiven
Damen und Herren:
Invention of the Neutrino in a letter from Zuerich to Tuebingen on December 4th, 1930: Conservation of Energy and Angular Momentum in b-Decay.
FAESSLER; GSI 16. November 2010

12. FAESSLER; GSI 16. November 2010
Reines and Cowen and the Neutrino-Detection (1956 at Savanna River Reactor)
FAESSLER; GSI 16. November 2010

13. FAESSLER; GSI 16. November 2010
Detection of the
Neutrino
1955/56:
by Fred Reines
and Clyde Cowen
FAESSLER; GSI 16. November 2010

14. FAESSLER; GSI 16. November 20101)
Mainz + Troisk
Triton Beta-Decay
mn < 2.3 eV
FAESSLER; GSI 16. November 2010

15. 1)Mass of the Electron Neutrino? Tritium decay (Mainz + Troitsk)
Mainz + Troisk
Triton Beta-Decay
mn < 2.3 eV
FAESSLER; GSI 16. November 2010

16. Upper limit of Neutrino mass from the Mainz( Troisk) Experiment
Results with Gaussian error
95 % confidence limit
<m n> < 2.3 eV 5%
<m neff>2 [eV2]
-0.6
(2.3 eV)2
FAESSLER; GSI 16. November 2010

17. Tranformation from Mass to Flavor Eigenstates
FAESSLER; GSI 16. November 2010

18. FAESSLER; GSI 16. November 2010
A dinosaur on trip
KATRIN Spectrometer tank on the way from the Rhine to the FZ Karslsruhe
FAESSLER; GSI 16. November 2010

19. 2) Neutrino Mass from Astrophysics:
Density Distribution of Matter in the Universe
(Power Spectrum of Matter Distribution)
h = 0.71
FAESSLER; GSI 16. November 2010

20. FAESSLER; GSI 16. November 2010
k = 2p/l [(h=0.71)/ Mpc]
FAESSLER; GSI 16. November 2010

21. FAESSLER; GSI 16. November 2010
W0 = WL= Wb= H0 = 72[km/(sec*Mpc] ns = Wn = 0
Cosmic Background Radiation
0.01
FAESSLER; GSI 16. November 2010

22. FAESSLER; GSI 16. November 2010
W0 = WL= 0.66 Wb= 0.04 H0 = ns = 0.94 Wn = 0.05
0.01
FAESSLER; GSI 16. November 2010

23. FAESSLER; GSI 16. November 2010
W0 = WL= 0.66 Wb= 0.04 H0 = ns = 0.94 Wn = 0.1
0.01
FAESSLER; GSI 16. November 2010

24. FAESSLER; GSI 16. November 2010
W0 = WL= 0.66 Wb= 0.04 H0 = ns = 0.94 Wn = 0.25
0.01
FAESSLER; GSI 16. November 2010

25. FAESSLER; GSI 16. November 2010

26. FAESSLER; GSI 16. November 2010
WMAP = Wilkinson Microwave
Anisotropy Probe.
ACBAR = Arcminute Cosmology
Bolometer Array Receiver (Berkeley)
CBI = Cosmic Background Imager
(CALTEC)
2dFGRS = 2 degree Field Galaxy
Redshift Survey
FAESSLER; GSI 16. November 2010

27. 3) Neutrino mass from Oνββ-Decay (forbidden in Standard Model)P e1 P
Left ν
Phase Space
106 x 2νββ
Left n n
n = nc Majorana Neutrino
Neutrino must have a Mass
FAESSLER; GSI 16. November 2010

28. FAESSLER; GSI 16. November 2010
GRAND UNIFICATION
Left-right Symmetric Models SO(10)
Majorana Mass:
FAESSLER; GSI 16. November 2010

29. Grand Unified left-right Symmetry
Proton
Proton
Neutron
Neutron
Neutron
Proton
Neutron
Proton
Proton
Neutron
First and Third Diagram ~ Neutrino Mass
Neutron
Proton
FAESSLER; GSI 16. November 2010

30. Supersymmetric Diagrams for the Neutrinoless Double Beta decay.
Neutron
Proton
l‘111
Lightest SUSY Particle (LSP) c
g~, h1~; h2~; W~
LSP c + g~
l‘111
Neutron
Proton
l‘111
FAESSLER; GSI 16. November 2010

31. FAESSLER; GSI 16. November 2010
Theoretical Description of Nuclei: Vadim Rodin, Fedor Simkovic, Amand Faessler, Saleh Yousef k 0+ P P e2 k 1+ e1 k 2- ν Ek n n Ei 0+ 0+
0νββ
FAESSLER; GSI 16. November 2010

32. V. Rodin, F. Simkovic, S. Yousef, D. L. Fang, A. Escuderos
The best choice: Quasi-Particle Random Phase Approximation (QRPA) and Shell Model
QRPA starts with Pairing:
V. Rodin, F. Simkovic, S. Yousef,
D. L. Fang, A. Escuderos
FAESSLER; GSI 16. November 2010

33. Neutrinoless Double Beta- Decay Probability
FAESSLER; GSI 16. November 2010

34. Effective Majorana Neutrino-Mass for the 0nbb-Decay
Tranformation from Mass
to Flavor Eigenstates CP
Time reversal
CPT
FAESSLER; GSI 16. November 2010

35. Neutrinoless Double Beta- Decay Probability
FAESSLER; GSI 16. November 2010

36. QRPA (TUE), Shell Model (Madrid-Strasburg), IBM2, PHFB
Different axial charges; gA
Forces; Bonn CD; Argonne V18
Different Basis Sizes
Short Range Correlations:
Jastrow
Fermi Hypernetted
Unitary Correlator Operator Metod
Brueckner
QRPA and Renormalized-QRPA
P-HFB-GCM
PHFB+GCM

37. FAESSLER; GSI 16. November 2010
Rodriguez, Martinez-Pinedo: projected-HFB, Gogny force, GCM; arXiv ; beta(Nd) = 0.35; beta(Sm) = 0.21
Fang, Faessler, Rodin, Simkovic:
Phys. Rev. C82, (2010)
150Nd b=0.24  150Sm: b= 0.15
<BCSi|BCSf> = 0.52; M0nbb = 3.16
FAESSLER; GSI 16. November 2010

38. FAESSLER; GSI 16. November 2010
Rodriguez, Martinez-Pinedo Energy Density functional + Generator Coordinate Method
FAESSLER; GSI 16. November 2010

39. FAESSLER; GSI 16. November 2010
Quasi-Particle Random Phase Approach (QRPA; Tübingen).
Shell Model Caurier et al.
Angular Momentum Projected Hartee-Fock-Bogoliubov (Tübingen; P. K. Rath et al.; Rodriguez & Martinez-Pinedo+GCMb).
Interacting Boson Model (Barea+Iachello)
Which Angular Momentum Jp Neutron Pairs contribute to the Neutrinoless Double Beta decay?
FAESSLER; GSI 16. November 2010

40. FAESSLER; GSI 16. November 2010
QRPA all the Ring digrams:
Ground State: 0, 4, 8, 12 , … quasi- particles (seniority) 4 8
b) The Shell Model
Ground state: 0, 4, 6, 8, …. 6
Problem for SM: Size of the Single Particle Basis.
FAESSLER; GSI 16. November 2010

41. FAESSLER; GSI 16. November 2010
Additive Contributions of 0, 4, 6, … Quasi-Particle States in the SM (Poves et al.).
128Te
Not in QRPA
82Se
Increasing Admixtures
in the Ground State
FAESSLER; GSI 16. November 2010

42. Basis Size Effect for 82Se on the Neutrinoless Double Beta Decay.
4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2
4levels: Ikeda Sum rule 50 %
6levels: 0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2; Ikeda 100%
9levels:0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2
FAESSLER; GSI 16. November 2010

43. FAESSLER; GSI 16. November 2010
Contribution of Higher Angular Momentum Pairs in Projected HFB (Tübingen).
HFB 0bbn
Particle number and angular momentum projection before
the variation; Gogny force;
Axial symmetric deformation;
No parity mixing; real coefficients of the Bogoliubov transformation
IBM: = 0+ and 2+ Pairs
FAESSLER; GSI 16. November 2010

44. FAESSLER; GSI 16. November 2010
QRPA (TUE), Shell Model (Madrid-Strassburg), IBM2 (Iachello), PHFB (P. Rath)
FAESSLER; GSI 16. November 2010

45. FAESSLER; GSI 16. November 2010
HD claim for Detection of 0n DBD
hep-ph/
Exp.Heidelberg-Moscow: Klapdor and coworkers in Heidelberg claim, they have detected 0nbb of 76Ge
Source = Detector
10.9 kg 86% enriched 76Ge
from 8 % natGe in Russia
Spectrum with
71.7 kg•y
Q(0nbb) =
2038 keV
FAESSLER; GSI 16. November 2010

46. FAESSLER; GSI 16. November 2010
Neutrino Mass from 0nbb
Experiment Heidelberg-Moskau:
Klapdor‘s et al. Claim
76Ge Mod. Phys. Lett. A21,1547(2006) ;
T(1/2; 0nbb) = ( ) x 1025 years; 6s
Matrix Elements: QRPA Tuebingen
<m(n)> = [eV]
(exp+-0.02; theor+-0.01) [eV]
FAESSLER; GSI 16. November 2010

47. FAESSLER; GSI 16. November 2010
Summary
QRPA seems presently a reliable method
Shell Model: to small basis IKEDA sum rule violated by 50%
Projected Hartree Fock Bogoliubov: Pairing +Quadrupole and Gogny force; mainly 0+ neutron pairs change in proton pairs.
Interacting Boson Model: Changes only s(0+) and d(2+) neutron pairs into protons pairs.
To prove the mass mechanism is leading, one needs to measure several nuclear systems. Only if proved, the neutrino mass can be measured in the neutrinoless Double BetaDecay.
THE END
FAESSLER; GSI 16. November 2010