Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

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Double Beta DecayandNeutrino MassesAmand
FaesslerTuebingen

• Neutrino Masses and the
• Neutrinoless Double
• Beta Decay Dirac versus
• Majorana Neutrinos
• Accuracy of the Nuclear Matrix Elements

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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

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P
n
n
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O?ßß-Decay (forbidden)

• only for Majorana Neutrinos
• ? ?c

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

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

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e-
?
?
e-
L/R
l/r
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n
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l/r
?
light ? heavy N Neutrinos
l/r
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Supersymmetry

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

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e-
Proton
Proton
u
u
u
u
d
d
Neutron
Neutron
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Theoretical Description

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

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k
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k
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Ek
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2-
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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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Only for Majorana ? possible.
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• gPP fixed to 2?ßß M(0nbb) MeV(-1)
• 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
Experiments
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Neutrino-Masses from the 0?bband Neutrino
Oscillations

• Solar Neutrinos (CL, Ga, Kamiokande, SNO)
• Atmospheric ? (Super-Kamiokande)
• 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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• ?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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Bilenky, Faessler, Simkovic P. R. D
70(2004)33003
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• (Bild)

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SummaryAccuracy of Neutrino Masses from 0nbb

• Fit the g(pp) by 2nbb in front of the
  proton-neutron Gamow-Teller NN matrixelement
  include exp. Error of 2nbb.
• Calculate with these g(pp) for three different
  forces (Bonn, Nijmegen, Argonne) and three
  different basis sets the 0nbb.
• Use QRPA and R-QRPA (Pauli principle)
• Use g(A) 1.25 and 1.00
• Error of matrixelement 20 to 50 (large errors
  from experim value of T(1/2, 2nbb)).

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SummaryResults from 0nbb

• ltm(n)gt(0nbb Ge76, Exp. Klapdor) lt 0.47 eV
• ltM(heavy n)gt gt 1.2 GeV
• ltM(heavy Vector B)gt gt 5600 GeV
• SUSYR-Parity l(1,1,1) lt 1.110(-4)
• Mainz-Troisk m(n) lt 2.2 eV
• Astro Physics (SDSS) Sum m(n) lt 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 END

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SummaryAccuracy of Neutrino Masses by the
Double Beta Decay

• Dirac versus Majorana Neutrinos
• Grand Unified Theories (GUTs), R-Parity
  violatingSupersymmetry ?Majorana-Neutrino
  Antineutrinos

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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

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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