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Neutrino Physics Caren Hagner Universität Hamburg Part 3: Absolute neutrino mass Introduction beta decay double beta decay Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Nature of Neutrino Mass I Neutrino fields v(x) with mass m are described by the Dirac equation: (i m)v( x) 0 4 component spinor The left-handed and right-handed components are: 1 5 vR ( x ) v( x ) 2 15 vL ( x ) v( x ) 2 2 components each This leads to a system of two coupled equations: i vL mvR 0 i vR mvL 0 With m=0 one obtains the decoupled Weyl equations: i vL,R 0 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. Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg 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: LD mvRvL h.c. m vR vL 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 Graduiertenkolleg Bullay 12.9.2005 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): c for a Majorana particle: M M c C T But what about experiments? vveLe 3737Cl Cl 3737Ar Aree-37 37 -37 37 v Cl Ar e Anti-neutrinos(reactor): veR e Cl Ar e 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! Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Majorana Mass Term Note that and Let’s try (vR )c (vc )L (vL )c (vc )R LM L is a left-handed field is a right-handed field mL c c ( vL ) vL vL ( vL ) 2 ok! mL (vL )c right handed field LM R vL left handed field mR c c ( vR ) vR vR ( vR ) 2 Graduiertenkolleg Bullay 12.9.2005 Lepton number violation! works too! Caren Hagner, Uni Hamburg Dirac-Majorana Mass Term mass term for each flavor: 2 LDM mD (vL )c h.c. mR vR m c L vL , (vR ) mD mass matrix M In order to obtain the mass eigenstates one must diagonalize M: find unitary U with cos U sin sin cos m1 0 ~ M U MU 0 m2 with with the mass eigenstates: vL v1L U c v2 L ( vR ) Graduiertenkolleg Bullay 12.9.2005 2mD tan2 mR mL and mass eigenvalues: m1, 2 1 (mR mL ) (mL mR )2 4mD2 2 Caren Hagner, Uni Hamburg What if… 1. mL = mR = 0: pure Dirac case θ = 45, m1=m2=mD. 2 degenerate Majorana states can be combined to form 1 Dirac state. 2. mD = 0: pure Majorana case θ = 0, m1=mL m2=mR 3. mR≫ mD, mL= 0: seesaw model θ = mD/mR≪ 1 mD2 m1 , mR m1 mR 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! Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Lower Limit of Neutrino Mass Super-K (atmospheric neutrinos): m2atm = 2.5 × 10-3 eV2 m(νi) ≥ 0.05 eV This sets the energy scale for mass search! Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Which mass hierarchy? - Lightest neutrino mass not known v1 v2 v3 - Δm2atm < 0 or >0 ? v3 v2 v1 Δmsolar 0.05 eV ≲ 2 eV Δmatm Δmatm Δmsolar v2 v1 v3 ? 0 normal hierarchy inverted hierarchy 0 quasi-degenerate Tritium β-Decay: Mainz/Troitsk 3 H He e e 3 - E0 = 18.6 keV dN/dE = K × F(E,Z) × p × Etot × (E0-Ee) × [ (E0-Ee)2 – m2 ]1/2 m Graduiertenkolleg Bullay 12.9.2005 Uei m 2 2 2 i i Caren Hagner, Uni Hamburg 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: Bmax = 6 T Bmin = 3×10-4 T energy analysis by static retarding E-field with varying strength: high pass filter with integral transmission for E>qU Results from the MAINZ Experiment Mainz Data (1998,1999,2001) m2 1.2 2.2 2.1 eV2 m 2.2eV 95%CL The KArlsruhe TRItium Neutrino Experiment KATRIN Ziel: m 0.20 eV Double-beta decay 0 - decay 2 - decay u d d e- W W u u d e W e W e- d e e e e- u Lepton number violation ΔL = 2 Summenenergie der Elektronen (E/Q) Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Neutrinoless Double Beta Decay 0 1 1/ 2 0 [T ] G ( E0 , Z ) M Phase space factor 0 GT 2 V 2 A g M F0 g 2 mv 2 Effective neutrino mass Transition matrix element Effective neutrino mass in 0νββ-decay: m 3 mU i 2 ei i 1 Compare to β-decay: m Graduiertenkolleg Bullay 12.9.2005 2 m U ei 2 i 2 i Caren Hagner, Uni Hamburg 0v Doppel-Beta Experimente: Ergebnisse m 0.35 eV (90% CL) 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 0.85 – 2.1 all 90%CL Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Jedoch: ein Teil der HdM Kollaboration veröffentlicht Evidenz für 0v Doppel-Beta Zerfall! ? (Q = 2039 keV für 76Ge Doppel-Beta Zerfall) Zukunft: Heidelberg Ge Initiative (MPIK Heidelberg) Phase I: 20kg angereichertes (86%) 76Ge, vgl. HDM Phase II: 100 kgJahre, 0.1 – 0.3 eV Phase III: O(1t) angereichertes 76Ge, 10meV Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg CUORICINO @ Gran Sasso (Start 2003) 2v Doppelbeta mit 130Te (Q=2529 keV) 18 crystals 3x3x6 cm3 + 44 crystals 5x5x5 cm3 40.7 kg of TeO2 Suche nach 0v Doppelbeta: T 1/2 0v (130Te) > 7.5 x 1023 y <mv> < 0.3 - 1. 6 eV 2 modules, 9 detector each, crystal dimension 3x3x6 cm3 crystal mass 330 g 9 x 2 x 0.33 = 5.94 kg of TeO2 Graduiertenkolleg Bullay 12.9.2005 11 modules, 4 detector each, crystal dimension 5x5x5 cm3 crystal mass 790 g 4 x 11 x 0.79 = 34.76 kg of TeO2 Caren Hagner, Uni Hamburg End part 3 Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Boris Kayser: (at v2002) Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg LM L LM R mL ( vL ) c vL vL ( vL ) c 2 mR ( vR ) c vR vR ( vR ) c 2 Construct the Majorana fields: c v ( v ) 1 vL (vL ) 2 R R 1,2 (1,2 )c c 2LM L mL11 2LMR mR22 Eigenstates of the interaction: vL and vR Mass eigenstates: Φ1 (mass mL), Φ2 (mass mR)