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Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Neutrino Physics Caren Hagner Universität Hamburg Caren Hagner Universität Hamburg Part 3:

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Präsentation zum Thema: "Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Neutrino Physics Caren Hagner Universität Hamburg Caren Hagner Universität Hamburg Part 3:"—  Präsentation transkript:

1 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Neutrino Physics Caren Hagner Universität Hamburg Caren Hagner Universität Hamburg Part 3: Absolute neutrino mass Introduction beta decay double beta decay

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

3 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Dirac mass term Dirac Mass Term The neutrino mass term in L could have exactly the same form as the mass term of the quarks and charged leptons: m Must add v R (right handed SU(2) singlets) to standard model! Problem: When the mechanism is the same, why are the masses so small? m t = ± 5.1 GeV; m b = ( ) GeV; m τ = ± 0.29 MeV; m 3 < 2eV Lepton number is conserved!

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

5 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Majorana Mass Term Note that is a left-handed field and is a right-handed field Lets try vLvL left handed field (v L ) c right handed field mLmL ok! works too! Lepton number violation!

6 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Dirac-Majorana Mass Term mass matrix M mass term for each flavor: In order to obtain the mass eigenstates one must diagonalize M: find unitary U with with with the mass eigenstates:and mass eigenvalues:

7 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg What if… 1. m L = m R = 0: pure Dirac case θ = 45, m 1 =m 2 =m D. 2 degenerate Majorana states can be combined to form 1 Dirac state. 2. m D = 0: pure Majorana case θ = 0, m 1 =m L m 2 =m R 3. m R m D, m L = 0: seesaw model θ = m D /m R 1 per neutrino flavor: one very light Majorana neutrino v 1L = v L one very heavy Majorana neutrino v 2L = (v R ) c m D of the order of lepton masses, m R reflects scale of new physics explains small neutrino masses! mRmR m1m1

8 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Lower Limit of Neutrino Mass Super-K (atmospheric neutrinos): m 2 atm = 2.5 × eV 2 m(ν i ) 0.05 eV This sets the energy scale for mass search!

9 Which mass hierarchy? v1v1 v2v2 Δm solar v3v3 Δm atm inverted hierarchy v3v3 v1v1 v2v2 Δm solar Δm atm normal hierarchy 0.05 eV - Lightest neutrino mass not known - Δm 2 atm 0 ? ? 0 v3v3 v1v1 v2v2 2 eV quasi-degenerate 0

10 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Tritium β-Decay: Mainz/Troitsk E 0 = 18.6 keV dN/dE = K × F(E,Z) × p × E tot × (E 0 -E e ) × [ (E 0 -E e ) 2 – m 2 ] 1/2

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

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

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

14 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Double-beta decay 2 - decay u e - d d e - W u e e W 0 - decay e - e - d d u u W W e e Lepton number violation ΔL = 2 Summenenergie der Elektronen (E/Q)

15 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Neutrinoless Double Beta Decay Effective neutrino mass in 0νββ-decay: Compare to β-decay: Phase space factor Transition matrix element Effective neutrino mass

16 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg 0v Doppel-Beta Experimente: Ergebnisse Heidelberg-Moskau Collaboration, Eur.Phys.J. A12 (2001) 147 IGEX Collaboration, hep-ex/ , Phys. Rev. C59 (1999) × – 2.1 all 90%CL HM-K IGEX

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

18 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Zukunft: Heidelberg Ge Initiative (MPIK Heidelberg) Phase I: 20kg angereichertes (86%) 76 Ge, vgl. HDM Phase II: 100 kgJahre, 0.1 – 0.3 eV Phase III: O(1t) angereichertes 76 Ge, 10meV

19 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg Gran Sasso (Start 2003) 11 modules, 4 detector each, crystal dimension 5x5x5 cm 3 crystal mass 790 g 4 x 11 x 0.79 = kg of TeO 2 2 modules, 9 detector each, crystal dimension 3x3x6 cm 3 crystal mass 330 g 9 x 2 x 0.33 = 5.94 kg of TeO 2 2v Doppelbeta mit 130 Te (Q=2529 keV) 18 crystals 3x3x6 cm crystals 5x5x5 cm kg of TeO 2 Suche nach 0v Doppelbeta: T 1/2 0v ( 130 Te) > 7.5 x y < eV

20 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg End part 3

21 Boris Kayser: (at v2002)

22 Graduiertenkolleg Bullay Caren Hagner, Uni Hamburg

23 Construct the Majorana fields: Eigenstates of the interaction: v L and v R Mass eigenstates: Φ 1 (mass m L ), Φ 2 (mass m R )


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