Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

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Double Beta DecayandNeutrino MassesAmand
FaesslerTuebingen

• 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 ?e 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 4p
• Cherenkow radiation of e-
• Trigger 23 PMT
• E? (Threshold) 6.75 MeV
• Ø 17 m view from below

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Cherenkov - Detectors

• (ES) Elastic Neutrino Scattering
• e- forward scattering
• S-KAMIOKANDE SNO

e- (fast)
e- (fast)
?x
?e

W
Z0
?e
e-
e-
?x
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111
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Charged Current (CC)

• e- backward
• SNO

P
e-
P
W
Deuteron (p n)
?e
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(NC) Neutral Current

• n-capture in salt NaCl (n, ?)

P
n
?x
Z0
?x
Deuteron SNO
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• Assuming only Electron Neutrinos
• (ES) 2.35106 F
• (CC) 1.76106 F
• (NC) 5.09106 F
• Including Muon and Tauon ?

F(?e) 1.76106 (CC)
F(?µ?t) 3.41106 (CCES)
F(?e?µ?t) 5.09106 (NC)
F(?-Bahcall) 5.14106
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• ?1, ?2, ?3 Mass States
• ?e, ?µ, ?t Flavor States
• Theta(1,2) 32.6 degrees Solar KamLand
• Theta(1,3) lt 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
2-
ß-
ß-
e-
e-
0
Egt2me
0
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2?ßß-Decay (in SM allowed)

• Thesis Maria Goeppert-Mayer
• 1935 Goettingen

P
P
n
n
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O?ßß-Decay (forbidden)

• only for Majorana Neutrinos
• ? ?c

P
P
Left
?
Phase Space 106 x 2?ßß
Left
n
n
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GRAND UNIFICATION

• Left-right Symmetric Models SO(10)
• Majorana Mass

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P
P
e-
?
?
e-
L/R
l/r
n
n
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P
P
l/r
?
light ? heavy N Neutrinos
l/r
n
n
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Theoretical Description

• Simkovic, Rodin, Haug, Kovalenko, Vergados,
  Kosmas, Schwieger, Raduta, Kaminski, Gutsche,
  Bilenky, Vogel et al.

P
k
0
e2
P
k
e1
k
?
Ek
1
2-
n
Ei
n
0
0
0?ßß
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Supersymmetry

• Bosons ? Fermions
• --------------------------------------------------
  ---------------------
• Neutralinos

P
P
e-
e-
Proton
Proton
u
u
u
u
d
d
Neutron
Neutron
n
n
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• Majorana

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The best choice

• Quasi-Particle-
• Quasi-Boson-Approx.
• Particle Number non-conserv.
• (important near closed shells)
• Unharmonicities
• Proton-Neutron Pairing

Pairing
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Nucleus 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 134Xe 136Xe 150Nd
T1/2 (exp) years gt9.5 1021 gt1.9 1025 gt1.4 1022 gt1.0 1021 gt5.5 1022 gt7.0 1022 gt8.6 1022 gt1.4 1022 gt5.8 1022 gt7.0 1023 gt1.7 1021
Ref. You Klap- dor Elli-ott Arn. Ejiri Dane-vich Ales. Ales. Ber. Staudt Klimenk.
ltmgteV lt22. lt0.47 lt8.7 lt40. lt2.8 lt3.8 lt17. lt3.2 lt27. lt3.8 lt7.2
?m(p)/M(n) lt200. lt0.79 lt15. lt79. lt6.0 lt7.0 lt27. lt4.9 lt38. lt3.5 lt13.
?(111)10-4 lt8.9 lt1.1 lt5.0 lt9.4 lt2.8 lt3.4 lt5.8 lt2.4 lt6.8 lt2.1 lt3.8
Only for Majorana ? possible.
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• gPP fixed to 2?ßß
• Each point (3 basis sets) x (3 forces) 9
  values

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Neutrinoless Double Beta Decay and the
Sensitivity to the Neutrino Massof planed
Experimentsx from R-QRPA m(n) x/T(1/2)
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Neutrino-Masses for the Double 0?ß-Decay and
Neutrino Oscillations

• Solar Neutrinos
• Atmospheric ?
• Reactor ? (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 Hierarchies m? OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies m?
Normal m3 m2 m1 m1ltltm2ltltm3 Inverted m2 m1 m3 m3ltltm1ltltm2
Bilenky, Faessler, Simkovic P. R. D
70(2004)33003
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• Normal
• Inverted

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• (Bild)

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SummaryNeutrinos Oscillations, Neutrino Masses
andthe Double beta Decay

• 1. Solution of the Solar Neutrino Problem by
  theSudburry-Neutrino-Observatory (SNO)
• Elastic Scattering (S-KAMIOKANDE)
• Heavy Water (SNO Charged Currents)

e-
e-
?x
?c
Z0
W
?x
e-
e-
?c
?x
e-
n
P
P
P
W
Z0
P
P
n
n
?c
?x
d
d
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2. Neutrinoless Double Beta Decay

• Dirac versus Majorana Neutrinos
• Grand Unified Theories (GUTs),
• R-Parity violating Supersymmetry ?
• Majorana-Neutrinos Antineutrinos
• Direct measurement in the Tritium Beta Decay in
  Mainz
• and Troisk

P
P
u
u
u
u
P
P
d
d
d
u
u
n
n
d
n
n
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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
• ltmßßgt 0.009 - 0.045 eV
• ßß Experiment ltmßßgt lt 0.47 eV
• Klapdor et al. ltmßßgt 0.1 0.9 eV
• Tritium (Otten, Weinheimer, Lobashow)
• ltmgt lt 2.2 eV
• THE END

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• ?-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

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Block Diagonalis.
X
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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 ?i33 (and ?i33) from ?333?

• U(1) charge conserved!
• 1,2,3 families