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Double Beta Decayand
Neutrino MassesAmand Faessler
Tuebingen
Accuracy of the Nuclear Matrix Elements.
It determines the Error of the Majorana Neutrino Mass extracted
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Oνββ-Decay (forbidden)
only for Majorana Neutrinos ν = νc
P
P
n n
Left
Leftν
Phase Space
106 x 2νββ
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GRAND UNIFICATION
Left-right Symmetric Models SO(10)
Majorana Mass:
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P P
νν
n n
e-
e-
L/R l/r
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l/r
P
ν
P
l/r
n n
light ν
heavy N
Neutrinos
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Supersymmetry
Bosons ↔ Fermions--------------------------------------------------------------------
---
Neutralinos
P P
e- e-
n n
u
u u
ud d
Proton Proton
Neutron Neutron
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Theoretical Description:Simkovic, Rodin, Pacearescu, Haug,
Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel, Stoica, Suhonen, Civitarese, Tomoda et al.
0+
0+
0+
1+
2-
k
k
ke1
e2PP
ν Ek
Ein n
0νββ
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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
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M0ν (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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M0ν (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 (l=12) 3.74 (s=9) 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!
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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:
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Reactor Neutrinos (Chooz):
CP
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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
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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 particle-particle NN matrixelement include exp. Error of .
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
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, 2))
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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 Theory Groups must check their Results against each other.
THE END
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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
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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
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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:
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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:
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How to calculate λ‘i33 (and λi33) from λ‘333?
U(1) charge conserved!
1,2,3 = families
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gPP fixed to 2νββ; M(0) [MeV**(-1)]
Each point: (3 basis sets) x (3 forces) = 9 values
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Assuming only Electron Neutrinos:(ES) 2.35*106 [Φ](CC) 1.76*106 [Φ](NC) 5.09*106 [Φ]
Including Muon and Tauon ν:
Φ(νe) = 1.76*106 (CC)
Φ(νμ+ντ) = 3.41*106 (CC+ES)
Φ(νe+νμ+ντ) = 5.09*106 (NC)
Φ(ν-Bahcall) = 5.14*106
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