Double Beta Decay
and
Neutrino Masses
Amand Faessler
Tuebingen
Accuracy of the Nuclear Matrix Elements.
It determines the Error of the Majorana
Neutrino Mass extracted
Amand Faessler,
22. Oct. 2004
1
Oνββ-Decay (forbidden)
P
P
Left
ν
Phase Space
Left
106 x 2νββ
n
n
only for Majorana Neutrinos
ν = νc
Amand Faessler,
22. Oct. 2004
4
GRAND UNIFICATION
Left-right Symmetric Models SO(10)
Majorana Mass:
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22. Oct. 2004
5
P
P
ν
e-
L/R
n
e-
ν
l/r
n
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22. Oct. 2004
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P
P
l/r
ν
light ν
heavy N
l/r
Neutrinos
n
n
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22. Oct. 2004
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Supersymmetry
Bosons ↔ Fermions
----------------------------------------------------------------------P
P
e-
e-
Proton
u
u
u
d
d
Proton
u
Neutron
Neutron
n
n
Neutralinos
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22. Oct. 2004
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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+
k
k
1+
P
P
e1
ν
k
e2
Ek
2n
n
Ei
0+
0+
0νββ
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22. Oct. 2004
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22. Oct. 2004
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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)
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22. Oct. 2004
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22. Oct. 2004
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22. Oct. 2004
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22. Oct. 2004
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M0ν (QRPA)
O. Civitarese, J. Suhonen,
NPA 729 (2003) 867
Nucleus
76Ge
100Mo
130Te
136Xe




their(QRPA, 1.254)
3.33
2.97
3.49
4.64
our(QRPA, 1.25)
2.68(0.12)
1.30(0.10)
1.56(0.47)
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,
…)!
Amand Faessler,
22. Oct. 2004
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M0ν (R-QRPA; 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
76Ge
100Mo
130Te
136Xe
l.m.s
s.m.s
1.87 (l=12) 3.74 (s=9)
3.40
4.36
3.00
4.55
1.02
1.57
our
2.40(.12)
1.20(.15)
1.46(.46)
0.85(.23)

Model space dependence ?

Disagreement also between his tables and
figures for R-QRPA and S-QRPA!
Amand Faessler,
22. Oct. 2004
19
Neutrino-Masses from the 0νbb
and Neutrino Oscillations
Solar Neutrinos (CL, Ga, Kamiokande, SNO)
Atmospheric ν (Super-Kamiokande)
Reactor ν (Chooz; KamLand)
with CP-Invariance:
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22. Oct. 2004
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Reactor Neutrinos (Chooz):
CP
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22. Oct. 2004
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OSCILLATIONS AND
DOUBLE BETA DECAY
Bilenky, Faessler, Simkovic P. R. D 70(2004)33003
Hierarchies: mν
Normal
Inverted
m2
m1
m3
m2
m1
m1<<m2<<m3
m3
m3<<m1<<m2
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22. Oct. 2004
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
(Bild)
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22. Oct. 2004
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Summary:
Accuracy 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 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, 2nbb)).
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22. Oct. 2004
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Summary:
Results from 0nbb

<m(n)>(0nbb Ge76, Exp. Klapdor) < 0.47 [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: m(n) < 2.2 [eV]

Astro Physics (SDSS): Sum{ m(n) } < 1 to 2 [eV]

Klapdor et al. from 0nbb 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
Amand Faessler,
22. Oct. 2004
29
Summary:
Accuracy of Neutrino Masses
by the Double Beta Decay
Dirac versus Majorana Neutrinos
Grand Unified Theories (GUT‘s), R-Parity violatingSupersymmetry →MajoranaNeutrino = Antineutrinos
P
P
P
P
u
d
n
n
d
d
u
n
<m(n)> < 0.47 eV;
u
u
u
d
u
n
l‘ < 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]
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22. Oct. 2004
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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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22. Oct. 2004
31
ν-Mass-Matrix by Mixing with:
Diagrams on the Tree level:
Majorana Neutrinos:
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22. Oct. 2004
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Loop Diagrams:
X
X
Figure 0.1: quark-squark 1-loop contribution to mv
Majorana
Neutrino
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22. Oct. 2004
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X
Block
Diagonalis.
X
Figure 0.2: lepton-slepton 1-loop contribution to mv
(7x7) Mass-Matrix:
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22. Oct. 2004
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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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22. Oct. 2004
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Super-K:
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22. Oct. 2004
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Horizontal U(1) Symmetry
U(1) Field
U(1) charge
R-Parity breaking terms must be without
U(1) charge change (U(1) charge conservat.)
Symmetry Breaking:
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22. Oct. 2004
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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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22. Oct. 2004
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gPP fixed to 2νββ; M(0nbb) [MeV**(-1)]
Each point: (3 basis sets) x (3 forces) = 9 values
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22. Oct. 2004
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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
Φ(νμ+ντ) = 3.41*106
Φ(νe+νμ+ντ) = 5.09*106
(CC)
(CC+ES)
(NC)
Φ(ν-Bahcall) = 5.14*106
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22. Oct. 2004
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22. Oct. 2004
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