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Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen. Neutrino Masses and the Neutrinoless Double Beta Decay: Dirac versus Majorana Neutrinos Accuracy of the Nuclear Matrix Elements. Neutrinoless Double Beta Decay. The Double Beta Decay:. 0 +. - PowerPoint PPT Presentation
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Amand Faessler, Tuebingen
1
Double Beta Decayand
Neutrino Masses
Amand FaesslerTuebingen
Neutrino Masses and the Neutrinoless Double Beta Decay: Dirac versus Majorana NeutrinosAccuracy of the Nuclear Matrix
Elements
Amand Faessler, Tuebingen
2
Neutrinoless Double Beta Decay
The Double Beta Decay:
0+
0+
0+
β-
1+
2-
β-
e- e-
E>2me
Amand Faessler, Tuebingen
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2νββ-Decay (in SM allowed)
Thesis Maria Goeppert-Mayer1935 Goettingen
P P
n n
Amand Faessler, Tuebingen
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Oνββ-Decay (forbidden)
only for Majorana Neutrinos ν = νc
P
P
n n
Left
Leftν
Phase Space
106 x 2νββ
Amand Faessler, Tuebingen
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GRAND UNIFICATION
Left-right Symmetric Models SO(10)
Majorana Mass:
Amand Faessler, Tuebingen
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P P
νν
n n
e-
e-
L/R l/r
Amand Faessler, Tuebingen
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l/r
P
ν
P
l/r
n n
light ν
heavy N
Neutrinos
Amand Faessler, Tuebingen
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Supersymmetry
Bosons ↔ Fermions--------------------------------------------------------------------
---
Neutralinos
P P
e- e-
n n
u
u u
ud d
Proton Proton
Neutron Neutron
Amand Faessler, Tuebingen
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Theoretical Description:
Simkovic, Rodin, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel et al.
0+
0+
0+
1+
2-
k
k
ke1
e2PP
ν Ek
Ein n
0νββ
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Amand Faessler, Tuebingen
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The best choice:
Quasi-Particle-
(a) Quasi-Boson-Approx.:
(b) Particle Number non-conserv.(important near closed shells)
(c) Unharmonicities(d) Proton-Neutron Pairing
Pairing
Amand Faessler, Tuebingen
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Amand Faessler, Tuebingen
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Nucleus 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 134Xe 136Xe
150Nd
T1/2 (exp)[years]
>9.51021
>1.91025
>1.41022
>1.01021
>5.51022
>7.01022
>8.61022
>1.41022
>5.81022
>7.01023
>1.71021
Ref.: You Klap-dor
Elli-ott
Arn. Ejiri Dane-vich
Ales.
Ales. Ber. Staudt
Klimenk.
<m>[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.
Amand Faessler, Tuebingen
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gPP fixed to 2νββ; M(0) [MeV**(-1)]
Each point: (3 basis sets) x (3 forces) = 9 values
Amand Faessler, Tuebingen
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Amand Faessler, Tuebingen
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Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass
of planed Experiments
Amand Faessler, Tuebingen
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Neutrino-Masses from the 0ν
and Neutrino Oscillations
Solar Neutrinos (CL, Ga, Kamiokande, SNO)Atmospheric ν (Super-Kamiokande)Reactor ν (Chooz; KamLand)
with CP-Invariance:
Amand Faessler, Tuebingen
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Solar Neutrinos (+KamLand):
(KamLand)
Atmospheric Neutrinos: (Super-Kamiok.)
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Reactor Neutrinos (Chooz):
CP
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ν1, ν2, ν3 Mass States
νe, νμ, ντ Flavor States
Theta(1,2) = 32.6 degrees Solar + KamLandTheta(1,3) < 13 degrees ChoozTheta(2,3) = 45 degrees S-Kamiokande
Amand Faessler, Tuebingen
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OSCILLATIONS AND DOUBLE BETA DECAY
Hierarchies: mν
Normal
m3
m2
m1
m1<<m2<<m3
Inverted m2
m1
m3
m3<<m1<<m2
Bilenky, Faessler, Simkovic P. R. D 70(2004)33003
Amand Faessler, Tuebingen
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(Bild)
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Summary:Accuracy of Neutrino
Masses from 0
Fit the g(pp) by in front of the proton-neutron Gamow-Teller NN matrixelement include exp. Error of .
Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets the
Use QRPA and R-QRPA (Pauli principle)
Use: g(A) = 1.25 and 1.00
Error of matrixelement 20 to 50 % (large errors from experim value of T(1/2, 2))
Amand Faessler, Tuebingen
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Summary:Results from
<m()>(GeExp. Klapdor) 0.47 [eV]
<M(heavy >[GeV]
<M(heavy Vector B)> > 5600 [GeV]
SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4)
Mainz-Troisk: m(2.2 [eV]
Astro Physics (SDSS): Sum{ m() } < 1 to 2 [eV]
Klapdor et al. from Ge76 with R-QRPA (no error of theory included):
0.15 to 0.72 [eV], if confirmed.
THE END
THE END 25
Summary:Accuracy of Neutrino
Masses by the Double Beta Decay
Dirac versus Majorana NeutrinosGrand 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.: <mββ> = 0.1 – 0.9 [eV] ; R-QRPA: 0.15 – 0.72 [eV]
n n
nn
PP
P P
d
d
d
d
u u
u
u u
u
Amand Faessler, Tuebingen
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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 <mββ> = 0.009 - 0.045 [eV]
ββ Experiment: <mββ> < 0.47 [eV]
Klapdor et al.: <mββ> = 0.1 – 0.9 [eV]
Tritium (Otten, Weinheimer, Lobashow) <m> < 2.2 [eV]
THE END
Amand Faessler, Tuebingen
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ν-Mass-Matrix by Mixing with:
Diagrams on the Tree level:
Majorana Neutrinos:
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Loop Diagrams:
Figure 0.1: quark-squark 1-loop contribution to mv
X
X
Majorana
Neutrino
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Figure 0.2: lepton-slepton 1-loop contribution to mv
(7x7) Mass-Matrix:
X
X
Block
Diagonalis.
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7 x 7 Neutrino-Massmatrix:
Basis: Eliminate Neutralinos in 2. Order:
separabel
{ Mass Eigenstate
Vector in
flavor space
for 2 independent
and possible
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Super-K:
Amand Faessler, Tuebingen
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Horizontal U(1) Symmetry
U(1) FieldU(1) chargeR-Parity breaking terms must be without U(1) charge change (U(1) charge
conservat.)Symmetry Breaking:
Amand Faessler, Tuebingen
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How to calculate λ‘i33 (and λi33) from λ‘333?
U(1) charge conserved!
1,2,3 = families