Amand Faessler, GERDA, 11. November 2005
1
Double Beta Decayand
Neutrino MassesAmand Faessler
Tuebingen
Accuracy of the Nuclear Matrix Elements.
It determines the Error of the Majorana Neutrino Mass extracted
Amand Faessler, GERDA, 11. November 2005
4
Oνββ-Decay (forbidden)
only for Majorana Neutrinos ν = νc
PP
n nLeft
Leftν
Phase Space106 x 2νββ
Amand Faessler, GERDA, 11. November 2005
5
GRAND UNIFICATION
Left-right Symmetric Models SO(10)
Majorana Mass:
Amand Faessler, GERDA, 11. November 2005
6
P Pνν
n n
e-e-
L/R l/r
Amand Faessler, GERDA, 11. November 2005
7
l/r
P
ν
P
l/r
n n
light νheavy NNeutrinos
l/r L/R
Amand Faessler, GERDA, 11. November 2005
8
SupersymmetryBosons ↔ Fermions---------------------------------------------------------------------
--
Neutralinos
Neutralinos
P P
e- e-
n n
u
u u
ud d
Proton Proton
Neutron Neutron
Amand Faessler, GERDA, 11. November 2005
9
Theoretical Description:Simkovic, Rodin, Benes, Vogel, Bilenky,
Salesh, Gutsche, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger,
Raduta, Kaminski, Stoica, Suhonen, Civitarese, Tomoda et al.
0+
0+
0+
1+
2-
kkk
e1
e2PP
ν Ek
Ein n
0νββ
Amand Faessler, GERDA, 11. November 2005
10
Neutrinoless Double Beta-
Decay Probability
Amand Faessler, GERDA, 11. November 2005
11
Effective Majorana Neutrino-Mass
for the 0Decay
CP
Tranformation from Mass to Flavor Eigenstates
Amand Faessler, GERDA, 11. November 2005
12
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, GERDA, 11. November 2005
13
ν1, ν2, ν3 Mass Statesνe, νμ, ντ Flavor States
Theta12 = 32.6 degrees Solar + KamLandTheta13 < 13 degrees ChoozTheta23 = 45 degrees S-Kamiokande
m 212(solar
8eV
m223atmosphericeV
Amand Faessler, GERDA, 11. November 2005
14
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, GERDA, 11. November 2005
15
Bilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250
Amand Faessler, GERDA, 11. November 2005
17
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, GERDA, 11. November 2005
18
Amand Faessler, GERDA, 11. November 2005
20
Contribution of Different Multipoles to M(0)
Amand Faessler, GERDA, 11. November 2005
21
g(A)**4 = 1.25**4 = 2.44 fit to 2
Rodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063
Amand Faessler, GERDA, 11. November 2005
27
2.76 (QRPA) 2.34 (RQRPA) Muto corrected
Amand Faessler, GERDA, 11. November 2005
28
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)
g(pp) fitted differently
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?
Short-range Brueckner Correlations not included. But finite size effects included.
We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)!
Amand Faessler, GERDA, 11. November 2005
29
Neutrinoless Double Beta Decay
The Double Beta Decay:
0+
0+
0+
β-
1+
2-
β-
e- e-
E>2me
x x x
xxx Gamov-Teller single beta decay in the second leg fitted with g(pp) by Suhonen et al.. Underestimates the first leg.
We fit the full 2decay by adjusting g(pp).
Amand Faessler, GERDA, 11. November 2005
30
Fit of g(pp) to the single beta (2. leg) and the 2 double beta decay (small and large basis).
Fit to 2
Fit to 1+ to 0+
Amand Faessler, GERDA, 11. November 2005
32
Uncorrelated and Correlated Relative N-N-
Wavefunctionin the N-N-Potential
Short Range Correlations
Amand Faessler, GERDA, 11. November 2005
33
Jastrow-Function multiplying the relative
N-N wavefunction
(Parameters from Miller and Spencer, Ann. Phys 1976)
Amand Faessler, GERDA, 11. November 2005
34
Influence of Short Range Correlations
(Parameters from Miller and Spencer, Ann. Phys 1976)
Amand Faessler, GERDA, 11. November 2005
35
Contribution of Different Multipoles to the zero Neutrino
Matrixelements in QRPAs.r.c. = short range correlations
h.o.t. = higher order currents
Different Multipoles
a) 76Ge small model space ( 9 levels) b) 76Ge large model space (21 levels)
C) 100Mo small model space ( 13 levels) d) 100Mo large model space ( 21 levels)
Amand Faessler, GERDA, 11. November 2005
36
Comparison of 2Half Lives with Shell model Results from Strassburg
Amand Faessler, GERDA, 11. November 2005
46
Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass
of planed Experiments
expt. T1/2
[y]<mv>[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
GERDA II(76Ge)
1 X 1026 0.16
CANDLES (48Ca)
1 X 1026 0.2
MOON (100Mo)
1 X 1027 0.058
Amand Faessler, GERDA, 11. November 2005
47
Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass
of planed Experiments
expt. T1/2
[y]<mv>[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
Amand Faessler, GERDA, 11. November 2005
54
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))
Core overlap reduction by ~0.85 (preliminary)
Amand Faessler, GERDA, 11. November 2005
55
Summary:Results from
<m()>(GeExp. Klapdor) 0.47 [eV]
Klapdor et al. from Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV].
<M(heavy >[GeV]
<M(heavy Vector B)> > 5600 [GeV]
SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4)
Mainz-Troisk, Triton Decay: m(2.2 [eV]
Astro Physics (SDSS): Sum{ m() } < ~0.5 to 2 [eV]
Do not take democratic averaged matrix elements !!!
THE END
Amand Faessler, GERDA, 11. November 2005
56
Open Problems:1. Overlapping but slightly different
Hilbert space in intermediate Nucleus for QRPA from intial and from final nucleus.
2. Pairing does not conserve Nucleon
number. Problem at closed shells. Particle projection. Lipkin-Nogami <N>, <N2>
3. Deformed nuclei?
Top Related