Transcript Folie 1 - uni-tuebingen.de

Double Beta Decay
and
Neutrino Masses
Amand Faessler
Tuebingen
1.
Solution of the Solar Neutrino Problem
by SNO.
2.
Neutrino Masses and the Neutrinoless Double
Beta Decay: Dirac versus Majorana Neutrinos
3.
Neutrino Masses and Supersymmetry
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(1) Solar Neutrino Problem
Reaction Network:
Oscillations:
Fewer νe on Earth detected
than produced in the Sun.

Oscillations depend on:
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Sudburry Neutrino Observatory
Creighton Mine
Ontario / Canada
(Zink Mine)
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THE SNO CHERENKOV DETECTOR
WITH HEAVY WATER
9456 Photomultipliers Ø 20 cm 55 % of 4π
Cherenkow radiation of eTrigger ≥ 23 PMT
Eν (Threshold) = 6.75 MeV
Ø 17 m; view from below
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Cherenkov - Detectors:
(ES) Elastic Neutrino Scattering:
e- (fast)
νe
+
W+
νe
Z0
νx
e-
6
e- (fast)
νx
:
e- forward scattering
S-KAMIOKANDE + SNO
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e-
1:1:1
Charged Current (CC):
P
e-
P
W+
νe
Deuteron
(p + n)
e- backward
SNO
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(NC) Neutral Current:
n
P
νx
Z0
νx
Deuteron
SNO
n-capture in salt NaCl (n, γ)
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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
Φ(ν-Bahcall) = 5.14*106
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(CC)
(CC+ES)
(NC)
ν1, ν2, ν3
νe, νμ, ντ
Mass States
Flavor States
Theta(1,2) = 32.6 degrees Solar + KamLand
Theta(1,3) < 13 degrees
Chooz
Theta(2,3) = 45 degrees
S-Kamiokande
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(Bild)
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(2) Neutrinoless Double
Beta Decay
The Double Beta Decay:
0+
1+
β0+
2e-
eE>2me
β-
0+
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2νββ-Decay (in SM allowed)
P
n
P
n
Thesis Maria Goeppert-Mayer
1935 Goettingen
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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
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GRAND UNIFICATION
Left-right Symmetric Models SO(10)
Majorana Mass:
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P
P
ν
e-
L/R
n
ν
l/r
n
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e-
P
P
l/r
ν
light ν
heavy N
l/r
Neutrinos
n
n
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Theoretical Description:
Simkovic, Rodin, Haug, Kovalenko, Vergados,
Kosmas, Schwieger, Raduta, Kaminski,
Gutsche, Bilenky, Vogel et al.
0+
k
k
1+
P
P
e1
ν
k
e2
Ek
2n
0+
0+
0νββ
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n
Ei
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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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Majorana;
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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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Nucleus
48Ca
76Ge
82Se
96Zr
100Mo
116Cd
128Te
130Te
134Xe
136Xe
150Nd
T1/2 (exp)
[years]
>9.5
1021
>1.9
1025
>1.4
1022
>1.0
1021
>5.5
1022
>7.0
1022
>8.6
1022
>1.4
1022
>5.8
1022
>7.0
1023
>1.7
1021
Ref.:
You
Klapdor
Elliott
Arn.
Ejiri
Danevich
Ales.
Ales.
Ber.
Stau
dt
Klime
nk.
<m>[eV]
<22.
<0.47
<8.7
<40.
<2.8
<3.8
<17.
<3.2
<27.
<3.8
<7.2
η~m(p)/M(n)
<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.
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gPP fixed to 2νββ
Each point: (3 basis sets) x (3 forces) = 9 values
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Neutrinoless Double Beta Decay and the
Sensitivity to the Neutrino Mass
of planed Experiments
x from R-QRPA; m(n) = x/T(1/2)
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Neutrino-Masses for the
Double 0νβ-Decay and
Neutrino Oscillations
Solar Neutrinos
Atmospheric ν
Reactor ν (Chooz; KamLand)
with CP-Invariance:
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Solar Neutrinos (+KamLand):
(KamLand)
Atmospheric Neutrinos:
(Super-Kamiok.)
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Reactor Neutrinos (Chooz):
CP
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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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Normal:
Inverted:
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
(Bild)
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Summary:
Neutrinos Oscillations, Neutrino Masses
and
the Double beta Decay
1. Solution of the Solar Neutrino Problem by
theSudburry-Neutrino-Observatory (SNO):
Elastic Scattering (S-KAMIOKANDE):
e-
νx
e-
νc
Z0
W+
νx
νc
e-
e-
Heavy Water (SNO: Charged Currents):
νx
e-
P
P
W+
νc
P
Z0
P
n
n
νx
d
P
n
d
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2. Neutrinoless Double
Beta Decay
Dirac versus Majorana Neutrinos
Grand Unified Theories (GUT‘s),
R-Parity violating Supersymmetry →
Majorana-Neutrinos = Antineutrinos
P
P
P
u
u
P
u
d
n
n
u
u
dd
d u
n
n
Direct measurement in the Tritium Beta Decay in Mainz
and Troisk
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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:
X
X
Figure 0.1: quark-squark 1-loop contribution to mv
Majorana
Neutrino
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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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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) 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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How to calculate λ‘i33 (and λi33) from
λ‘333?
U(1) charge conserved!
1,2,3 = families
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