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

Nature of Neutrino Mass I Neutrino fields v(x) with mass m are described by the Dirac equation: 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: 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.

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: Dirac mass term m 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

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!

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

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

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 mR m1 3. mR≫ mD, mL= 0: seesaw model θ = mD/mR≪ 1 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!

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!

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

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 Super-erlaubt, E0 = 18.6 keV, T1/2 = 12.3a

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

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

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

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

Neutrinoless Double Beta Decay Transition matrix element Phase space factor Effective neutrino mass Effective neutrino mass in 0νββ-decay: Beide Verfahren liefern komplemaentaere Info Eine Majorana Phase kann bestimmt werden Da im solaren Bereich keine max. Mischung -> keine vollstaendige Ausloeschung moeglich! Compare to β-decay:

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

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

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 11 modules, 4 detector each, crystal dimension 5x5x5 cm3 crystal mass 790 g 4 x 11 x 0.79 = 34.76 kg of TeO2

End part 3

Boris Kayser: (at v2002)

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