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Neutrino Physics

Neutrino Physics. Part 3: Absolute neutrino mass Introduction beta decay double beta decay. Caren Hagner Universität Hamburg. 4 component spinor. The left-handed and right-handed components are:. 2 components each. This leads to a system of two coupled equations:.

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Neutrino Physics

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  1. Neutrino Physics Part 3: Absolute neutrino mass Introduction beta decay double beta decay Caren Hagner Universität Hamburg

  2. 4 component spinor The left-handed and right-handed components are: 2 components each This leads to a system of two coupled equations: With m=0 one obtains the decoupled Weyl equations: Nature of Neutrino Mass I Neutrino fields v(x) with mass m are described by the Dirac equation: From Goldhaber experiment one knows that vL is realized.With m=0 there is no need to have vR. Therefore there were no vR in the Standard Model.

  3. m Dirac Mass Term The neutrino mass term in L could have exactly the same formas the mass term of the quarks and charged leptons: Dirac mass term Lepton number is conserved! Must add vR (right handed SU(2) singlets) to standard model! Problem: When the mechanism is the same, why are the masses so small? mt = 174.3 ± 5.1 GeV; mb = (4.0-4.5) GeV;mτ= 1776.99 ± 0.29 MeV; m3 < 2eV

  4. particle anti-particle (charge conjugate field): for a Majorana particle: observed! Neutrinos (solar): not observed! Anti-neutrinos(reactor): Majorana Particles Because neutrinos carry no electric charge(and no color charge), there is the possibility: particle ≡ anti-particle Majorana particle But what about experiments? There are two different states per flavorbut the difference could be due to left-handed and right-handed states!

  5. mL vL (vL)c right handed field left handed field Majorana Mass Term is a left-handed field Note that is a right-handed field and ok! Let’s try Lepton number violation! works too!

  6. Dirac-Majorana Mass Term with with the mass eigenstates: and mass eigenvalues: mass term for each flavor: mass matrix M In order to obtain the mass eigenstates one must diagonalize M: find unitary U with

  7. What if… m1 mR 3. mR≫ mD, mL= 0: seesaw modelθ = mD/mR≪ 1 1. mL = mR = 0: pure Dirac caseθ = 45, m1=m2=mD. 2 degenerate Majorana states can be combined to form 1 Dirac state. 2. mD = 0: pure Majorana caseθ = 0, m1=mL m2=mR per neutrino flavor: one very light Majorana neutrino v1L = vL one very heavy Majorana neutrino v2L = (vR)c mD of the order of lepton masses, mR reflects scale of new physics⇒ explains small neutrino masses!

  8. Lower Limit of Neutrino Mass Super-K (atmospheric neutrinos): m2atm = 2.5 × 10-3 eV2  m(νi) ≥ 0.05 eV This sets the energy scalefor mass search!

  9. v1 v2 v3 v2 Δmsolar v1 ≲ 2 eV Δmatm v3 0 quasi-degenerate inverted hierarchy Which mass hierarchy? • Lightest neutrino mass not known • Δm2atm < 0 or >0 ? v3 Δmatm 0.05 eV v2 Δmsolar v1 ? 0 normal hierarchy

  10. Tritium β-Decay: Mainz/Troitsk E0 = 18.6 keV dN/dE = K × F(E,Z) × p × Etot × (E0-Ee) × [ (E0-Ee)2 – mn2]1/2

  11. principle of an electrostatic filter with magnetic adiabatic collimation (MAC-E) adiabatic magnetic guiding of b´s along field lines in stray B-field of s.c. solenoids: Bmax = 6 T Bmin = 3×10-4 T energy analysis by static retarding E-field with varying strength: high pass filter with integral b transmission for E>qU

  12. Results from the MAINZ Experiment Mainz Data (1998,1999,2001)

  13. Ziel: TheKArlsruhe TRItium Neutrino Experiment KATRIN ~70 m beamline, 40 s.c. solenoids

  14. - - e - e u e 0n - bb decay 2n - bb decay d W u W d W d n e u d n e W - e u n n e e Summenenergie der Elektronen (E/Q) Double-beta decay Lepton number violation ΔL = 2

  15. Phase space factor Effective neutrino mass Transition matrix element Effective neutrino mass in 0νββ-decay: Compare to β-decay: Neutrinoless Double Beta Decay

  16. Heidelberg-Moskau Collaboration, Eur.Phys.J. A12 (2001) 147 IGEX Collaboration, hep-ex/0202026, Phys. Rev. C59 (1999) 2108 HM-K IGEX 2.1 × 1023 all 90%CL 0.85 – 2.1 0v Doppel-Beta Experimente: Ergebnisse

  17. Jedoch: ein Teil der HdM Kollaboration veröffentlicht Evidenz für 0v Doppel-Beta Zerfall! ? (Q = 2039 keV für 76Ge Doppel-Beta Zerfall)

  18. Zukunft: Heidelberg Ge Initiative (MPIK Heidelberg) Phase I: 20kg angereichertes (86%) 76Ge, vgl. HDMPhase II: 100 kgJahre, 0.1 – 0.3 eVPhase III: O(1t) angereichertes 76Ge, 10meV

  19. 2v Doppelbeta mit 130Te (Q=2529 keV) 18 crystals 3x3x6 cm3 + 44 crystals 5x5x5 cm340.7 kg of TeO2 Suche nach 0v Doppelbeta:T 1/20v (130Te) > 7.5 x 1023 y <mv> < 0.3 - 1. 6 eV CUORICINO @ Gran Sasso (Start 2003) 11 modules, 4 detector each, crystal dimension 5x5x5 cm3 crystal mass 790 g 4 x 11 x 0.79 = 34.76 kg of TeO2 2 modules, 9 detector each, crystal dimension 3x3x6 cm3 crystal mass 330 g 9 x 2 x 0.33 = 5.94 kg of TeO2

  20. End part 3

  21. Boris Kayser:(at v2002)

  22. Construct the Majorana fields: Eigenstates of the interaction: vL and vR Mass eigenstates: Φ1 (mass mL), Φ2 (mass mR)

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