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Massive neutrinos Dirac vs. Majorana

Massive neutrinos Dirac vs. Majorana. Niels Martens Supervisor: Dr. J.G. Messchendorp. Outline. Introduction Helicity Chirality Parity violation in weak interactions Theory SM: massless lefthanded neutrinos Massive neutrinos Dirac mass Majorana mass Dirac-Majorana mass terms

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Massive neutrinos Dirac vs. Majorana

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  1. Massive neutrinosDirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

  2. Outline • Introduction • Helicity • Chirality • Parity violation in weak interactions • Theory • SM: massless lefthanded neutrinos • Massive neutrinos • Dirac mass • Majorana mass • Dirac-Majorana mass terms • Possible scenarios • Experiments • Neutrinoless double beta decay • Results Heidelberg-Moscow cooperation

  3. Helicity & Chirality • Helicity: projection of spin in the direction of momentum • Ill-defined when m≠0 (Lorentz transformation)  Chirality states (eigenstates of weak interaction): superposition of helicity states

  4. Parity violation in weak interactions • Parity operation: x  -x • V  -V • A  A • Goldhaber experiment (1957): measuring neutrino helicity • Electron capture in 152Eu • Two co-linear events of opposite parity expected:

  5. Parity violation in weak interactions • Only lefthanded photons observed  only lefthanded neutrinos • Later experiments: only righthanded anti-neutrinos P

  6. Neutrinos in the Standard Model • Fermion; spin-½ • Massless • only lefthanded neutrinos, righthanded anti-neutrinos

  7. Neutrinos in the standard model • Massless spin-½ particles are described by the Dirac eqation for massless particles:

  8. Massive neutrinos – Dirac neutrino • Flavour oscillations  (small) neutrino mass!! • How to incorporate this in SM/ extend SM? • Dirac mass • Boost can change handedness • coupling between two helicity states • A single four-component spinor

  9. Massive neutrinos – Dirac neutrino • Dirac mass term in Lagrangian • What other mass terms are possible?

  10. Massive neutrinos – Majorana neutrino (2) Majorana mass • Neutrino is chargeless, so it can be its own antiparticle  mM couples particle and antiparticle

  11. General case: Dirac-Majorana-mass (3) Dirac-Majorana mass term • Diagonalizing M gives two mass eigenvalues:

  12. Different scenarios (a) : pure Dirac case  (Dirac field) • : pure Majorana case 

  13. Different scenarios (c) Seesaw model • Explains: • light mass of neutrinos • the experimental fact that only lefthanded neutrinos couple to the weak interaction.

  14. Related experiments • Tritium β-decay • Flavor oscillations • Neutrinoless double β-decay

  15. Neutrinoless double β-decay • β—decay: • Double β--decay: • Could any nucleus be used? No: * * Single β-decay must be forbidden 

  16. Neutrinoless double β-decay • Semi-empirical mass/Weizsäcker formula:

  17. Neutrinoless double β-decay • 35 naturally occurring isotopes which decay via 2β-, all even-even

  18. Neutrinoless double β-decay • So how can 2β- show that the neutrino is a majorana particle? Neutrinoless double beta decay X

  19. Neutrinoless double β-decay • 2 necessary conditions: • Particle-antiparticle matching  • Helicity matching  • If neutrinoless double β-decay occurs, the neutrino is a massive majorana particle. Virtual neutrino line

  20. Neutrinoless double β-decay • Experimental signatures: • Two e- from same place at same time • Daughter nucleus (Z+2,A) • Neutrinoless case: sharp defined kinetic energy of electrons, instead of continuous spectrum

  21. Neutrinoless double β-decay • Theoretical uncertainty (76Ge): 1.5 < |M| < 4.6 • Half-lives • β : from seconds to 105 y • 2νββ: ~1020 y • 0 νββ: > 1025 y • mν ~ 50 meV  100 kg needed for 1 event/y

  22. Neutrinoless double β-decay • Experimental difficulties: • Count rate: How to measure T1/2 beyond 1025 y!? • Source strength: expensive! • Background: Cosmic rays, 2νββ, natural radioactive decay • Energy resolution

  23. Heidelberg-Moscow Experiment Source strength  11,0 kg enriched 76Ge: Source = detector Background  find a mountain and dig a hole Enormous half-lives  experiment run from 1990 till 2003 (but, stability then becomes a problem)

  24. Heidelberg-Moscow experiment

  25. Conclusions • None… yet • Since neutrinos do have mass, the SM has to be extended. • Theoretically, massive neutrinos can have a Dirac and/or Majorana nature. • Reliable 0νββ observations would prove that the neutrino is a Majorana particle and give the neutrino mass, but at the moment 0νββ-experiments face many difficulties.

  26. Bibliography • C. Giunti & C.W. Kim, Fundamentals of neutrino physics and astrophycis, Oxford University Press, 2007 • K. Zuber, Neutrino Physics, IOP Publishing, 2004 • H.V. Klapdor-Kleingrothaus et al. / Physics Letters B 586 (2004) 198–212

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