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?ßßDecay (in SM allowed)
 Thesis Maria GoeppertMayer
 1935 Goettingen
P
P
n
n
4O?ßßDecay (forbidden)
 only for Majorana Neutrinos
 ? ?c
P
P
Left
?
Phase Space 106 x 2?ßß
Left
n
n
5GRAND UNIFICATION
 Leftright 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
 QuasiParticle
 QuasiBosonApprox.
 Particle Number nonconserv.
 (important near closed shells)
 Unharmonicities
 ProtonNeutron 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 Elliott Arn. Ejiri Danevich 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)104 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 2neutrino 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? (RQRPA 1.25) S. Stoica,
H.V. KlapdorKleingrothaus, 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 RQRPA and SQRPA!
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
22NeutrinoMasses from the 0?bband Neutrino
Oscillations
 Solar Neutrinos (CL, Ga, Kamiokande, SNO)
 Atmospheric ? (SuperKamiokande)
 Reactor ? (Chooz KamLand)
 with CPInvariance
23Solar Neutrinos (KamLand)
 (KamLand)
 Atmospheric Neutrinos

(SuperKamiok.)
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 SKamiokande
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
particleparticle 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 RQRPA (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
 SUSYRParity l(1,1,1) lt 1.110(4)
 MainzTroisk m(n) lt 2.2 eV
 Astro Physics (SDSS) Sum m(n) lt 1 to 2 eV
 Klapdor et al. from 0nbb Ge76 with RQRPA (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), RParity
violatingSupersymmetry ?MajoranaNeutrino
Antineutrinos 


P
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u
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u
u
P
P
d
d
d
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u
u
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313. Neutrino Masses and Supersymmetry
 RParity violating Supersymmetry mixes Neutrinos
with Neutrinalinos (Photinos, Zinos, Higgsinos)
and TauSusytauLoops, BottomSusybottomLoops ?
MajoranaNeutrinos (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
 0Neutrino 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 ?MassMatrix by Mixing with
 Diagrams on the Tree level
 Majorana Neutrinos
33Loop Diagrams
 Figure 0.1 quarksquark 1loop contribution to mv
X
X
Majorana Neutrino
34 Figure 0.2 leptonslepton 1loop contribution to
mv  (7x7) MassMatrix
X
Block Diagonalis.
X
357 x 7 NeutrinoMassmatrix
 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
 RParity 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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