Transcript Double-Beta Decay Valencia - uni

Double Beta Decay,
a Test for New
Physics
Amand Faessler
Tuebingen
„The Nuclear Matrix Elements for the
0nbb are as important as the Data
to extract the Neutrino Mass“ (and in general New
Physics).
(Frank Avignone in Erice, September 2005)
Amand Faessler,
Madrid, 8. June 2006
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Oνββ-Decay (forbidden)
P
P
Left
ν
Phase Space
Left
106 x 2νββ
n
n
only for Majorana Neutrinos
ν = νc
Amand Faessler,
Madrid, 8. June 2006
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GRAND UNIFICATION
Left-right Symmetric Models SO(10)
Majorana Mass:
Amand Faessler,
Madrid, 8. June 2006
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Theoretical Description:
Tübingen: Simkovic, Rodin, Benes, Vogel,
Bilenky, Salesh, Gutsche, Pacearescu, Haug,
Kovalenko, Vergados, Kosmas, Schwieger, Raduta,
Kaminski, Stoica, Suhonen, Civitarese, Tomoda,
Moya de Guerra, Sarriguren, Valle et al.
k
0+
k
k
1+
P
P
e1
ν
2-
n
e2
Ek
n
Ei
0+
0+
0νββ
Amand Faessler,
Madrid, 8. June 2006
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Neutrinoless Double BetaDecay Probability
+…
Amand Faessler,
Madrid, 8. June 2006
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The best choice:
Quasi-Particle-
Pairing
(a)
Quasi-Boson-Approx.:
(b)
Particle Number non-conserv.
(important near closed shells)
Unharmonicities
Proton-Neutron Pairing
(c)
(d)
Amand Faessler,
Madrid, 8. June 2006
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g(A)**4 = 1.25**4 = 2.44;
fit of gpp to 2nbb
Rodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063 and Nucl. Phys. A (2006)
Amand Faessler,
Madrid, 8. June 2006
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Overlap of the inert
Core of the initial and
final Nucleus due to
changes in
Deformation b, Pairing
and Hilbert Space.
Amand Faessler,
Madrid, 8. June 2006
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Proton and Neutron Number
conserved as <N> and <N2> and
improved spherical Overlap of the
inert Core due to different Pairing.
<NP> = Z; <NP2> = Z2
~20 % Reduction due
to (Pairing) Overlap
gA = 1.25
3 basis sets:~3 and 4 and 5 oscillator shells;
Amand Faessler,
Force: Bonn
Madrid, 8. June 2006
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2.76 (QRPA)
2.34 (RQRPA) Muto corrected
Amand Faessler,
Madrid, 8. June 2006
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M0ν (QRPA)
O. Civitarese, J. Suhonen,
NPA 729 (2003) 867
Nucleus
76Ge
100Mo
130Te
136Xe



their(QRPA, 1.254) our(QRPA, 1.25)
3.33
2.97
3.49
4.64
2.68(0.12)
1.30(0.10)
1.56(0.47)
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.
Short-range Brueckner Correlations not
included.
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Madrid, 8. June 2006
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Differences
1. Ajustment of gpp for the NN force to
.
the total 2nbb-decay probability
(Tuebingen) or to (Jyväskylä):
<0+ |Single b in second leg| 1+ >
1+
2β-
pn-1
1+
x
np-1
0+
x
100Mo
0+
This log ft value known in only
three double beta decay nuclei:
Amand Faessler,
100Mo, 116Cd, 128
Te
8. June 2006
Madrid,
28
2. leg: known only
in these three
nuclei
For the first leg
no agreement
Amand Faessler,
Madrid, 8. June 2006
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2. Uncorrelated and Correlated
Relative N-N-Wavefunction
in the N-N-Potential
Short Range Correlations
Amand Faessler,
Madrid, 8. June 2006
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Influence of Short Range
Correlations
(Parameters from Miller and Spencer, Ann. Phys 1976)
Amand Faessler,
Madrid, 8. June 2006
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Comparison of 2nbb
Half Lives with Shell model
Results from Strassburg-Madrid
For 0nbb one needs intermidiate negative Parity
States and higher Multipoles
Amand Faessler,
Madrid, 8. June 2006
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Contributions of different
Multipolarities for 0nbb
Negative Parity States not
described by Shell Model
N= 3 and 4 oscillator shells
76Ge
100Mo
N= 0 to 5 oscillator shells
76Ge
100Mo
Blue: Short Range Correlations and Higher Order Currents.
Red: Short Range Correlations, no Higher Order Currents
White: No Short range Correlations, no Higher order
Currents
Amand Faessler,
Madrid, 8. June 2006
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Summary:
Results from 0nbb


<m(n)>(0nbb Ge76, Exp. Klapdor) < 0.47 [eV]
Klapdor et al. from 0nbb Ge76 with R-QRPA
(no error of theory included): 0.15 to 0.72
[eV].

<M(heavy n)> > 1.2 [GeV]

<M(heavy Vector B)> > 5600 [GeV]

SUSY+R-Parity: l‘(1,1,1) < 1.1*10**(-4)

Mainz-Troisk, Triton Decay: m(n) < 2.2 [eV]

Astro Physics (SDSS): Sum{ m(n) } < ~0.5
to 2 [eV]
Do not take democratic
averaged matrixelements !!!
Amand Faessler,
Madrid, 8. June 2006
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Open Problems:
1.
Overlapping but slightly different Hilbert
spaces in intermediate Nucleus for
QRPA from intial and from final nucleus.
0+
pn-1
β-
1+
2-
np-1
0+
0+
2. BCS Pairing does not conserve Nucleon
number. Problem at closed shells.
Particle projection.
3. Deformed nuclei? (e.g.:
Amand Faessler,
Madrid, 8. June 2006
150Nd
)
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Open Problems:
4. Ajustment of gpp for the NN force
to the total 2nbb-decay
probability or to:
<0+ |Single b in second leg| 1+ >
0+
2β-
pn-1
1+
x
np-1
0+
100Mo
x
0+
Amand Faessler,
Madrid, 8. June 2006
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Open Problems:
5. What is the leading Mechanisme
for the Neutrinoless double BetaDecay ?
a) Light Majorana Neutrino exchange
b) Heavy Majorana Neutrino exchange
c) Right handed Current at one Vertex
d) Heavy Vector-boson at one Vertex
e) Minimal Supersymmetry with
R-parity Violation
And Others
0nbb to Excited States
Amand Faessler,
Madrid, 8. June 2006
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Open Problems: shell model
Contribution of Different Multipoles to the zero
Neutrino Matrixelements in QRPA
6. Shell model needs to enlarge the
single particle space to three
oscillator shells to include
negative parity states and five
shells to include deformations:
76 Ge
100 Mo
Different Multipoles
Blue: Short Range Correlations and Higher Order Currents.
Red: Short Range Correlations, no Higher Order Currents
White: No Short range Correlations, no Higher order
Currents
THE END
Amand Faessler,
Madrid, 8. June 2006
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