Amand Faessler, Tuebingen 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

Amand Faessler, Tuebingen (1) Solar Neutrino Problem Reaction Network: Oscillations: Fewer ν e on Earth detected than produced in the Sun. Oscillations depend on:

Amand Faessler, Tuebingen Sudburry Neutrino Observatory Creighton Mine Ontario / Canada (Zink Mine)

Amand Faessler, Tuebingen THE SNO CHERENKOV DETECTOR WITH HEAVY WATER 9456 Photomultipliers Ø 20 cm 55 % of 4 π Cherenkow radiation of e - Trigger ≥ 23 PMT E ν (Threshold) = 6.75 MeV Ø 17 m; view from below

Amand Faessler, Tuebingen Cherenkov - Detectors: (ES) Elastic Neutrino Scattering: e- forward scattering S-KAMIOKANDE + SNO e - (fast) νeνe W+W+ νeνe e-e- e-e- νxνx νxνx Z0Z0 + 6:1:1:1

Amand Faessler, Tuebingen Charged Current (CC): e- backward SNO e-e- νeνe W+W+ P P Deuteron (p + n)

Amand Faessler, Tuebingen (NC) Neutral Current: n-capture in salt NaCl (n, γ) νxνx νxνx Z0Z0 Pn Deuteron SNO

Amand Faessler, Tuebingen Assuming only Electron Neutrinos: (ES) 2.35*10 6 [ Φ ] (CC) 1.76*10 6 [ Φ ] (NC) 5.09*10 6 [ Φ ] Including Muon and Tauon ν : Φ ( ν e)=1.76*10 6 (CC) Φ ( νμ + ν τ)=3.41*10 6 (CC+ES) Φ ( ν e+ νμ + ν τ)=5.09*10 6 (NC) Φ ( ν -Bahcall)=5.14*10 6

Amand Faessler, Tuebingen ν 1, ν 2, ν 3 Mass States ν e, ν μ, ν τ Flavor States Theta(1,2) = 32.6 degrees Solar + KamLand Theta(1,3) < 13 degrees Chooz Theta(2,3) = 45 degrees S-Kamiokande

Amand Faessler, Tuebingen (Bild)

Amand Faessler, Tuebingen (2) Neutrinoless Double Beta Decay The Double Beta Decay: β-β β-β- e-e- e-e- E>2m e

Amand Faessler, Tuebingen 2 νββ -Decay (in SM allowed) Thesis Maria Goeppert-Mayer 1935 Goettingen PP nn

Amand Faessler, Tuebingen O νββ -Decay (forbidden) only for Majorana Neutrinos ν = ν c P P nn Left ν Phase Space 10 6 x 2 νββ

Amand Faessler, Tuebingen GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

Amand Faessler, Tuebingen P P ν ν nn e-e- e-e- L/R l/r

Amand Faessler, Tuebingen l/r P ν P n n light ν heavy N Neutrinos

Amand Faessler, Tuebingen Theoretical Description: Simkovic, Rodin, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel et al k k k e1e1 e2e2 P P ν EkEk EiEi n n 0 νββ

Amand Faessler, Tuebingen

Supersymmetry Bosons ↔ Fermions Neutralinos PP e-e- e-e- nn u u u u dd Proton Neutron

Amand Faessler, Tuebingen Majorana;

Amand Faessler, Tuebingen The best choice: Quasi-Particle-  Quasi-Boson-Approx.:  Particle Number non-conserv. (important near closed shells)  Unharmonicities  Proton-Neutron Pairing Pairing

Amand Faessler, Tuebingen

Nucleus 48 Ca 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 128 Te 130 Te 134 Xe 136 Xe 150 Nd T1/2 (exp) [years] > > > > > > > > > > > Ref.:YouKlap- dor Elli- ott Arn.EjiriDane- vich Ales. Ber.Stau dt Klime nk. [eV]<22.<0.47<8.7<40.<2.8<3.8<17.<3.2<27.<3.8<7.2 η ~m(p)/M(  <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.

Amand Faessler, Tuebingen g PP fixed to 2 νββ Each point: (3 basis sets) x (3 forces) = 9 values

Amand Faessler, Tuebingen

Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass of planed Experiments  from R-QRPA; m  ) =  )

Amand Faessler, Tuebingen Neutrino-Masses for the Double 0 νβ- Decay and Neutrino Oscillations Solar Neutrinos Atmospheric ν Reactor ν (Chooz; KamLand) with CP-Invariance:

Amand Faessler, Tuebingen Solar Neutrinos (+KamLand): (KamLand) Atmospheric Neutrinos: (Super-Kamiok.)

Amand Faessler, Tuebingen Reactor Neutrinos (Chooz): CP

Amand Faessler, Tuebingen OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies: m ν Normal m 3 m 2 m 1 m 1 <<m 2 <<m 3 Inverted m 2 m 1 m 3 m 3 <<m 1 <<m 2 Bilenky, Faessler, Simkovic P. R. D 70(2004)33003

Amand Faessler, Tuebingen Normal: Inverted:

Amand Faessler, Tuebingen (Bild)

Amand Faessler, Tuebingen

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): Heavy Water (SNO: Charged Currents): νxνx νxνx Z0Z0 e-e- e-e- e-e- e-e- νcνc νcνc W+W+ νcνc d d e-e- W+W+ PP P n n n P P νxνx νxνx Z0Z0

Amand Faessler, Tuebingen 2. Neutrinoless Double Beta Decay Dirac versus Majorana Neutrinos Grand Unified Theories (GUT‘s), R-Parity violating Supersymmetry → Majorana-Neutrinos = Antineutrinos Direct measurement in the Tritium Beta Decay in Mainz and Troisk nn nn P P PP d d d d u u u u u u

Amand Faessler, Tuebingen 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) = – 0.04 [eV] m(neutrino3) = 0.03 – 1.03 [eV] 0-Neutrino Double Beta decay = [eV] ββ Experiment: < 0.47 [eV] Klapdor et al.: = 0.1 – 0.9 [eV] Tritium (Otten, Weinheimer, Lobashow) < 2.2 [eV] THE END

Amand Faessler, Tuebingen ν -Mass-Matrix by Mixing with: Diagrams on the Tree level: Majorana Neutrinos:

Amand Faessler, Tuebingen Loop Diagrams: Figure 0.1: quark-squark 1-loop contribution to m v X X Majorana Neutrino

Amand Faessler, Tuebingen Figure 0.2: lepton-slepton 1-loop contribution to m v (7x7) Mass-Matrix: X X Block Diagonalis.

Amand Faessler, Tuebingen 7 x 7 Neutrino-Massmatrix: Basis: Eliminate Neutralinos in 2. Order: separabel { Mass Eigenstate Vector in flavor space for 2 independent and possible

Amand Faessler, Tuebingen Super-K:

Amand Faessler, Tuebingen 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:

Amand Faessler, Tuebingen How to calculate λ ‘ i33 (and λ i33 ) from λ ‘ 333 ? U(1) charge conserved! 1,2,3 = families