Title: Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen
1Double Beta DecayandNeutrino MassesAmand
FaesslerTuebingen
- Accuracy of the Nuclear Matrix Elements.
- It determines the Error of the Majorana Neutrino
Mass extracted
2Neutrinoless Double Beta Decay
0
1
2-
ß-
ß-
e-
e-
0
Egt2me
0
32?ßß-Decay (in SM allowed)
- Thesis Maria Goeppert-Mayer
- 1935 Goettingen
P
P
n
n
4O?ßß-Decay (forbidden)
- only for Majorana Neutrinos
- ? ?c
P
P
Left
?
Phase Space 106 x 2?ßß
Left
n
n
5GRAND UNIFICATION
- Left-right Symmetric Models SO(10)
- Majorana Mass
6P
P
e-
?
?
e-
L/R
l/r
n
n
7P
P
l/r
?
light ? heavy N Neutrinos
l/r
n
n
8Supersymmetry
- Bosons ? Fermions
- --------------------------------------------------
--------------------- - Neutralinos
P
P
e-
e-
Proton
Proton
u
u
u
u
d
d
Neutron
Neutron
n
n
9Theoretical DescriptionSimkovic, Rodin,
Pacearescu, Haug, Kovalenko, Vergados, Kosmas,
Schwieger, Raduta, Kaminski, Gutsche, Bilenky,
Vogel, Stoica, Suhonen, Civitarese, Tomoda et
al.
P
k
0
e2
P
k
e1
k
?
Ek
1
2-
n
Ei
n
0
0
0?ßß
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11The best choice
- Quasi-Particle-
- Quasi-Boson-Approx.
- Particle Number non-conserv.
- (important near closed shells)
- Unharmonicities
- Proton-Neutron Pairing
Pairing
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13Nucleus 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 134Xe 136Xe 150Nd
T1/2 (exp) years gt9.5 1021 gt1.9 1025 gt1.4 1022 gt1.0 1021 gt5.5 1022 gt7.0 1022 gt8.6 1022 gt1.4 1022 gt5.8 1022 gt7.0 1023 gt1.7 1021
Ref. You Klap- dor Elli-ott Arn. Ejiri Dane-vich Ales. Ales. Ber. Staudt Klimenk.
ltmgteV lt22. lt0.47 lt8.7 lt40. lt2.8 lt3.8 lt17. lt3.2 lt27. lt3.8 lt7.2
?m(p)/M(n) lt200. lt0.79 lt15. lt79. lt6.0 lt7.0 lt27. lt4.9 lt38. lt3.5 lt13.
?(111)10-4 lt8.9 lt1.1 lt5.0 lt9.4 lt2.8 lt3.4 lt5.8 lt2.4 lt6.8 lt2.1 lt3.8
Only for Majorana ? possible.
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16 M0? (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) - 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, )!
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19 M0? (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 (l12) 3.74 (s9)
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!
20Neutrinoless Double Beta Decay and the
Sensitivity to the Neutrino Massof planed
Experiments
expt. T1/2 y ltmvgt eV
DAMA (136Xe) 1.2 X 1024 2.3
MAJORANA (76Ge) 3 X 1027 0.044
EXO 10t (136Xe) 4 X 1028 0.012
GEM (76Ge) 7 X 1027 0.028
GENIUS (76Ge) 1 X 1028 0.023
CANDLES (48Ca) 1 X 1026 0.2
MOON (100Mo) 1 X 1027 0.058
21Neutrinoless Double Beta Decay and the
Sensitivity to the Neutrino Massof planed
Experiments
expt. T1/2 y ltmvgt eV
XMASS (136Xe) 3 X 1026 0.10
CUORE (130Te) 2 X 1026 0.10
COBRA (116Cd) 1 X 1024 1
DCBA (100Mo) 2 X 1026 0.07
DCBA (82Se) 3 X 1026 0.04
CAMEO (116Cd) 1 X 1027 0.02
DCBA (150Nd) 1 X 1026 0.02
22Neutrino-Masses from the 0?bband Neutrino
Oscillations
- Solar Neutrinos (CL, Ga, Kamiokande, SNO)
- Atmospheric ? (Super-Kamiokande)
- Reactor ? (Chooz KamLand)
- with CP-Invariance
23Solar Neutrinos (KamLand)
- (KamLand)
- Atmospheric Neutrinos
-
(Super-Kamiok.)
24Reactor Neutrinos (Chooz)
CP
25- ?1, ?2, ?3 Mass States
- ?e, ?µ, ?t Flavor States
- Theta(1,2) 32.6 degrees Solar KamLand
- Theta(1,3) lt 13 degrees Chooz
- Theta(2,3) 45 degrees S-Kamiokande
26OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies m? OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies m?
Normal m3 m2 m1 m1ltltm2ltltm3 Inverted m2 m1 m3 m3ltltm1ltltm2
Bilenky, Faessler, Simkovic P. R. D
70(2004)33003
27 28SummaryAccuracy of Neutrino Masses from 0nbb
- Fit the g(pp) by 2nbb in front of the
particle-particle NN matrixelement include exp.
Error of 2nbb. - 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
0nbb. - 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,
2nbb)).
29SummaryResults from 0nbb
- ltm(n)gt(0nbb Ge76, Exp. Klapdor) lt 0.47 eV
- ltM(heavy n)gt gt 1.2 GeV
- ltM(heavy Vector B)gt gt 5600 GeV
- SUSYR-Parity l(1,1,1) lt 1.110(-4)
- Mainz-Troisk m(n) lt 2.2 eV
- Astro Physics (SDSS) Sum m(n) lt 1 to 2 eV
- Klapdor et al. from 0nbb 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.
30SummaryAccuracy of Neutrino Masses by the
Double Beta Decay
- Dirac versus Majorana Neutrinos
- Grand Unified Theories (GUTs), R-Parity
violatingSupersymmetry ?Majorana-Neutrino
Antineutrinos -
-
-
P
P
u
u
u
u
P
P
d
d
d
d
u
u
n
n
n
n
313. 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
- ltmßßgt 0.009 - 0.045 eV
- ßß Experiment ltmßßgt lt 0.47 eV
- Klapdor et al. ltmßßgt 0.1 0.9 eV
- Tritium (Otten, Weinheimer, Lobashow)
- ltmgt lt 2.2 eV
- THE END
32- ?-Mass-Matrix by Mixing with
- Diagrams on the Tree level
- Majorana Neutrinos
33Loop Diagrams
- Figure 0.1 quark-squark 1-loop contribution to mv
X
X
Majorana Neutrino
34- Figure 0.2 lepton-slepton 1-loop contribution to
mv - (7x7) Mass-Matrix
X
Block Diagonalis.
X
357 x 7 Neutrino-Massmatrix
- Basis
- Eliminate Neutralinos in 2. Order
separabel
Mass Eigenstate
Vector in flavor space
for 2 independent and possible
36 37Horizontal 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
38How to calculate ?i33 (and ?i33) from ?333?
- U(1) charge conserved!
- 1,2,3 families
39- gPP fixed to 2?ßß M(0nbb) MeV(-1)
- Each point (3 basis sets) x (3 forces) 9
values
40- Assuming only Electron Neutrinos
- (ES) 2.35106 F
- (CC) 1.76106 F
- (NC) 5.09106 F
- Including Muon and Tauon ?
F(?e) 1.76106 (CC)
F(?µ?t) 3.41106 (CCES)
F(?e?µ?t) 5.09106 (NC)
F(?-Bahcall) 5.14106
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