1. Neutrino Masses, Double Beta Decay and Nuclear Structure
ECT*(Trento), Doctoral Training Program on “Neutrinos in Nuclear, Particle- and Astrophysics”.
Amand Faessler,
University of Tuebingen,

2. CONTENTS: 0. History of the Neutrinos (Introduction)
1. Neutrino Properties
2. The See-Saw Model
3. The Single Beta Decay
4. The Neutrinoless Double Beta Decay
5. The Quasi-Particle Random Phase Approximation (QRPA)
6. Comparison of QRPA, Shell Model, Projected Hartree Fock Bogoliubov (PHBF), Interacting Boson Model 2
7. Can one measure with Charge Transfer Reactions the 0nbb-Matrix element?
8. Competing Mechanisms for the 0nbb
9. The Heidelberg-Moscow data and the Neutrino Mass
FAESSLER; Trento 2011

3. 0. History of the Neutrinos
1930 Pauli‘s invention of the neutrino
1955 Reines and Cowen detection of the electron neutrino ne
1962 Brookhaven; detection of muon neutrino nm
2000 Fermi Lab; detection of tau neutrino nt
1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2nbb decay
1986 Santa Barbara (Caldwell) detection of 2nbb.
20xx Detection of 0nbb decay ?
FAESSLER; Trento 2011

4. 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.
FAESSLER; Trento 2011

5. History of the Neutrinos
1930 Pauli‘s invention of the neutrino
1955 Reines and Cowen detection of the electron neutrino ne
1962 Brookhaven; detection of muon neutrino nm
2000 Fermi Lab; detection of tau neutrino nt
1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2nbb decay
1986 Santa Barbara detection of 2nbb decay
20xx Detection of 0nbb decay ?
FAESSLER; Trento 2011

6. Reines and Cowen at the Neutrino-Experiment (at Savannah River Reactor)
Fissions of Uranium143 produces neutron rich fragments. Beta decay: n  p + e- + nec
FAESSLER; Trento 2011

7. History of the Neutrinos
1930 Pauli‘s invention of the neutrino
1955 Reines and Cowen detection of the electron neutrino ne
1962 Brookhaven; detection of muon neutrino nm
p-  m- + ncm; ncm + p  n + m+ (no: e+)
2000 Fermi Lab; detection of tau neutrino nt
1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2nbb decay
1986 Santa Barbara: 2nbb decay by Caldwell
20xx Detection of 0nbb decay ?
FAESSLER; Trento 2011

8. 1. Neutrino properties: What is the Mass of the Neutrino ?
mne Mass measurement in the single beta decay
nm and nt ?
Si mni from cosmology
mne from the neutrinoless double beta decay
FAESSLER; Trento 2011

9. For the Triton Te [keV] (Te - Q) [eV] antineutrino
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10. Mass of the Electron Neutrino? Tritium decay (Mainz + Troitsk)
With:
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11. Upper Limit of the Neutrino Mass:
< (2.2 eV)2 ;
95% conf. limit
5 %
95 %
(2.2 eV)2
mnb2
FAESSLER; Trento 2011

12. A dinosaur on trip
KATRIN Spectrometer tank on the way from the Rhine to the FZ Karslsruhe
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13. Mass of nm (Paul Scherrer Institut 1996):
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14. Mass of tau Neutrino ARGUS (DESY Hamburg) e+ + e-  t+ + t-;
mnt < 28 MeV by ALEPH
mnt < 15 MeV together
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15. Neutrino Mass from Astrophysics:
Density Distribution of Matter in the Universe
(Power Spectrum of Matter Distribution)
Hubble law: v = H0 *Distance
= h*100 [km/(sec*Mpc)] *Distance [Mpc]
= 71[km/(sec*Mpc)]*Distance [Mpc]; h=0.71;
Hubble Constant: H0 = 71 [km/sec*Mpc]
FAESSLER; Trento 2011

16. k = 2p/l [(h=0.71)/ Mpc]
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17. W0 = WL= 0.66 Wb= 0.04 H0 = ns = 0.94 Wn = 0
0.01
FAESSLER; Trento 2011

18. W0 = WL= 0.66 Wb= 0.04 H0 = ns = 0.94 Wn = 0.05
0.01
FAESSLER; Trento 2011

19. W0 = WL= 0.66 Wb= 0.04 H0 = ns = 0.94 Wn = 0.25
0.01
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20. FAESSLER; Trento 2011

21. 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; Trento 2011

22. Page 1
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23. 2. The See-Saw Model
Diagonalise the matrix:
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24. 3. The Single Beta Decay W- p e nc p e n n n -1/( MW2 )d(r12)
1/(q2 – MW2 ) n n n
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25. Page 17
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26. 4. Neutrino Mass from Neutrinoless Double Beta Decay
The neutrinoless Double Beta Decay is forbidden in the Standard Model. Allowed in GUT‘s and SUSY. It determines the absolute mass of Majorana Neutrinos.
Matrix elements as important as the data.
Practically all Grand Unified Theories and
Supersymmetry request massive Majorana Neutrinos
FAESSLER; Trento 2011

27. Oνββ-Decay (forbidden in Standard Model)
only for massive Majorana Neutrinos
ν = νc P P
Left ν
Phase Space
106 x 2νββ
Left n n
FAESSLER; Trento 2011

28. GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:
FAESSLER; Trento 2011

29. P P ν e- e- ν
L/R
l/r
2*2*2 = 8 posibilities n n
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30. 8x8x2 = 128 contributions light ν heavy N Neutrinos p p e- e- n n l/rW n n P
light ν
heavy N
Neutrinos P ν
l/r n
l/r
8x8x2 = 128 contributions n
FAESSLER; Trento 2011

31. Theoretical Description of Nuclei: Vadim Rodin, Fedor Simkovic, Amand Faessler, Saleh Yousef, D.-L. Fang k 0+ P P e2 k 1+ e1 k 2- ν Ek n n Ei 0+ 0+
0νββ
FAESSLER; Trento 2011

32. Neutrinoless Double Beta-
Decay Probability
FAESSLER; Trento 2011

33. 5. The best choice: Quasi-Particle Random Phase Approximation (QRPA) and Shell Model
QRPA starts with Pairing:
FAESSLER; Trento 2011

34. Effective Majorana Neutrino-Mass for the 0nbb-Decay
Tranformation from Mass
to Flavor Eigenstates CP
Time reversal
CPT = I
FAESSLER; Trento 2011

35. FAESSLER; Trento 2011

36. Page 25b
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37. 2011
FAESSLER; Trento 2011

38. From Dirac to Majorana Neutrinos
DIRAC NEUTRINOS:
Majorana Neutrinos:
FAESSLER; Trento 2011

39. Neutrino Masses Depends on Cosmological models (Hannestad)
Single Beta Decay (Mainz, Troisk)
Double Beta Decay Majorana Mass (Tübingen):
Astophysics: S = m1 + m2 + m3 < 0.17 to 2.0 [eV]
Depends on Cosmological models (Hannestad)
< 2.2 [eV]
< 0.27 [eV]
FAESSLER; Trento 2011

40. Page 26
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41. FAESSLER; Trento 2011

42. PMNS-Matrix Parameters 2011
Pontecorvo-Maki-Nakagawa-Sakata
Solar:
Atmospheric:
Reactor
FAESSLER; Trento 2011

43. Results from Oscillations: No Hierarchy, no absolute Mass Scale
(Bild)
Fogli, Lisi, Marrone, Palazzo: Prog. Part. Nucl. Phys. 57(2006)742; Data 2011
Sequence 1-2 fixed by oscillations in the sun and in vacuum. No oscillations 13 for solar neutrinos observed,

44. Effective Majorana Neutrino-Mass for the 0nbb-Decay
Tranformation from Mass
to Flavor Eigenstates CP
Time reversal
CPT = I
CP = T= K
FAESSLER; Trento 2011

45. Normal Hierarchy: Double Beta Decay Majorana Mass mbb versus lowest mass m1

46. Inverted Hierarchy: Double Beta Decay Majorana Mass mbb versus lowest mass m3
FAESSLER; Trento 2011

47. Amand Faessler, Tuebingen
6. Different Methods for the 0nbb-Matrix Elements for the Light Majorana Neutrino Exchange. A. Escuderos, A. Faessler, V. Rodin, F. Simkovic, J. Phys. G37 (2010) ; arXiv: [nucl-th]
Quasi-Particle Random Phase Approximation (QRPA; Tübingen).
Shell Model (Strasbourg-Madrid).
Angular Momentum Projected Hartee-Fock-Bogoliubov (Tuebingen; P. K. Rath et al.).
Interacting Boson Model (Barea and Iachello).
Amand Faessler, Tuebingen

48. Neutrinoless Double Beta-
Decay Probability
FAESSLER; Trento 2011

49. Amand Faessler, Tuebingen
QRPA all the Ring diagrams: Ground State (Exercise IV.5): 0, 4, 8, 12 , … quasi- particles (seniority)
b) The Shell Model
Ground state: 0, 4, 6, 8, ….
Problem for SM: Size of the Single Particle Basis.
Amand Faessler, Tuebingen

50. Amand Faessler, Tuebingen
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
Amand Faessler, Tuebingen

51. Basis Size Effect for 82Se82Kr on the Neutrinoless Double Beta Decay.
4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2
4levels: Ikeda Sum rule 50 %; 5 levels: 60 %
6levels: 0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2
9levels:0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2
Amand Faessler, Tuebingen

52. GT Contrib. of different Angular Momenta Neutron Pairs to the 0nbb Decay.
A Comparison QRPA (TUE) and Shell Model (Madrid) with the same Basis.
82Se;
2p3/2, 1f5/2, 2p1/2, 1g9/2
130Te;
1g7/2, 2d5/2, 2d3/2, 3s1/2,1h11/2
Amand Faessler, Tuebingen

53. Amand Faessler, Tuebingen
Contributions of different Angular Momentum and Parity Neutron Pairs to the Matrix Elements of 0nbb Decay in QRPA
for 76Ge, 100Mo
and 130Te.
QRPA
QRPA
Amand Faessler, Tuebingen

54. Contribution of Higher Angular Momentum Pairs in Projected HFB.
HFB 0bbn
Only even Angular Momentum Pairs with Positive Parity can contribute.
IBM: = 0+ and 2+ Pairs
Amand Faessler, Tuebingen

55. IBM: Lowest Order Mapping (LO).
Ap(j) and Bp(j, j‘) by equating matrix elements in Fermion and Boson representation.(Tabulated by Barea and Iachello table XVII Phys. Rev. C79 (2009)

56. Next to Lowest Order Mapping (NLO)
Fermions  Bosons
76Ge  76Se
Lowest Order is enough

57. Neutrinoless Double Beta-
Decay Probability
FAESSLER; Trento 2011

58. QRPA (TUE), Shell Model IBM2, PHFB, PHFB+GCM(b)
QRPA; RQRPA; 3 Basis Sets; gA=1.00 1.25;
Bonn+Argonne; 2 Short Range Correlations
Amand Faessler, Tuebingen

59. Fermi and Gamow-Teller 0nbb Transition Operator with Closure
7. Can one measure with Charge Transfer Reactions the 0nbb Fermi Matrix Element? (V. Rodin and A. Faessler, Phys.Rev. C80(2009)041302; Prog. Part. Nucl. Phys. 66 (2011) 441)
Fermi and Gamow-Teller 0nbb Transition Operator with Closure
FAESSLER; Trento 2011

60. Fermi and Gamow-Teller 0nbb Transition Operator with Closure
0nbb Transition Matrix Element
with Closure Relation:
Amand Faessler, Tuebingen

61. Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS>
|DIAS> = |T, T-2> |IAS> = |T, T-1> |g.s.i>=|0i+> |g.s.f>=|T-2,T-2>
Isotensor force needed: T  T-2; Coulomb Interaction 0+ T- 0+ T- T-
+e|DIAS>

62. Gamow Teller Strength not concentrated in one State broad Resonance.
Fermi Transition: narrow Gamow-Teller: Main Contrib. Neutron Pairs: T =1, L=0  S=0 Gamow-Teller: gA (s*s) |S=0> = - gA 3|S=0> Fermi (no spin dep.): gV |S=0> = 1 |S=0> Shell Model for Fermi ~ (1/5) of QRPA
Amand Faessler, Tuebingen

63. Fermi 0nbb Transition Operator (Vadim Rodin)
Amand Faessler, Tuebingen

64. Page 38
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65. Transition Matrix Elements for Fermi Transitions:
|IAS> = |T, T-1> 0+ |g.s.i> =|T, T> |g.s.f> = |T-2,T-2> + e|DIAS>
First Leg
Second Leg 0+ T-
Exp. (d,2He): Frekers; Sakai; Zegers T-

66. 8. How to find the Leading Mechanism for the onbb ?
Light left handed Majorana n Exchange
Heavy left handed Majorana n Exchange
Heavy right handed Majorana n Exchange
SUSY Lepton Number Violating Mechanism.
F. Simkovic, J. Vergados, A. Faessler,
Phys. Rev. D82, (2010)
A. Faessler, A. Meroni, Petcov, Simkovic, Vergados, Phs. Rev.D; arXive:
Amand Faessler, Tuebingen

67. GUT: Light and Heavy left handed Majorana Neutrino ExchangeWL e-
Unek=1,2,3
nkM mass
NkL mass
UNek=4,5,6
Page 41 e- WL u d
Amand Faessler, Tuebingen

68. Different Mechanisms for the 0nbb
FAESSLER; Trento 2011

69. Coefficients for the different Mechanisms
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70. SUSY: R-Parity Breaking Lepton Number-Violating
Minimal Supersymmetric Model
Super-fields:
Amand Faessler, Tuebingen

71. Gluino Exchange; Strong Interaction;
Gluinos couple to Quarks and SUSY-Quarks.
l‘ijk LLi QLj DRk
FAESSLER; Trento 2011

72. Amand Faessler, Tuebingen
Transition Probability prop to Inverse Half Life; SUSY Contribution l‘111.
Dominance of Gluino echange in short range part assumed.
Similar expression for Dominance of Neutralino exchange.
Amand Faessler, Tuebingen

73. Two leading non-interfering Mechanisms: Light Majorana and Heavy R Neutrino
i = different nuclei, e.g. 76Ge, 100Mo, 130Te;
|h|2 > 0 and our matrix element for gA = 1.25
Due to ratios only minimal changes for gA=1.00
Amand Faessler, Tuebingen

74. Two interfering Mechanisms: Light Majorana and Heavy Left Neutrino
Light Majorana-Neutrino and
Gluino or Neutralino exchange.
Three different transitions needed, e.g. 76Ge, 100Mo, 130Te, to determine the three parameters.
Amand Faessler, Tuebingen

75. 9. HD claim for Detection of 0n DBD
hep-ph/
Klapdor and coworkers in Heidelberg claim, they have detected 0nbb of 76Ge
Source = Detector
10.9 kg - ( 86% from 8% nat.) 76Ge
Gran Sasso Laboratory (Italy)
Spectrum with 71.7 kg•y
FAESSLER; Trento 2011

76. Amand Faessler, Tuebingen
Neutrino Mass from 0nbb
Experiment Klapdor et al. 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]
Amand Faessler, Tuebingen

77. Amand Faessler, Tuebingen
1) Summary
Comparing four different approaches for the 0nbb matrix elements:
Shell model only small basis; violates the Ikeda sum rule by 50 to 60%.
Interacting boson Model: only s (0+) and d (2+) pairs.
Projected Hartee Fock Bogoliubov: Only 0+ pairs.
QRPA large basis; fulfills Ikeda sum rule; realistic forces.
Amand Faessler, Tuebingen

78. Amand Faessler, Tuebingen
2) Summary
Search for the Leading Mechanism
One Leading Mechanism: Determine the h1(mn ?) in two systems. Is it the same?
Two leading non-interfering mechanisms: Determine h1 and h2 in three systems
Two interfering mechanisms: Determine h1, h2 and the relative phase theta in three nuclei and verify it in three nuclei with at least one other.
THE END
Amand Faessler, Tuebingen

79. Fermi and Gamow-Teller 0nbb Transition Operator with Closure
7. Can one measure with Charge Transfer Reactions the 0nbb Fermi Matrix Element? (V. Rodin and A. Faessler, Phys.Rev. C80(2009)041302; Prog. Part. Nucl. Phys. 66 (2011) 441)
Fermi and Gamow-Teller 0nbb Transition Operator with Closure
FAESSLER; Trento 2011

80. Fermi and Gamow-Teller 0nbb Transition Operator with Closure
0nbb Transition Matrix Element
with Closure Relation:
Amand Faessler, Tuebingen

81. Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS>
|DIAS> = |T, T-2> |IAS> = |T, T-1> |g.s.i>=|0i+> |g.s.f>=|T-2,T-2>
Isotensor force needed: T  T-2; Coulomb Interaction 0+ T- 0+ T- T-
+e|DIAS>

82. Gamow Teller Strength not concentrated in one State broad Resonance.
Fermi Transition: narrow Gamow-Teller: Main Contrib. Neutron Pairs: T =1, L=0  S=0 Gamow-Teller: gA (s*s) |S=0> = - gA 3|S=0> Fermi (no spin dep.): gV |S=0> = 1 |S=0> Shell Model for Fermi ~ (1/5) of QRPA
Amand Faessler, Tuebingen

83. Fermi 0nbb Transition Operator (Vadim Rodin)
Amand Faessler, Tuebingen

84. Transition Matrix Elements for Fermi Transitions:
|IAS> = |T, T-1> 0+ |g.s.i> =|T, T> |g.s.f> = |T-2,T-2> + e|DIAS>
First Leg
Second Leg 0+ T-
Exp. (d,2He): Frekers; Sakai; Zegers T-