Massive neutrinos Dirac vs. Majorana

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Massive neutrinosDirac vs. Majorana

• Niels Martens
• Supervisor Dr. J.G. Messchendorp

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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

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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

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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

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Parity violation in weak interactions
P

• Only lefthanded photons observed ? only
  lefthanded neutrinos
• Later experiments only righthanded
  anti-neutrinos

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Neutrinos in the Standard Model

• Fermion spin-½
• Massless
• only lefthanded neutrinos, righthanded
  anti-neutrinos

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Neutrinos in the standard model

• Massless spin-½ particles are described by the
  Dirac eqation for massless particles

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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

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Massive neutrinos Dirac neutrino

• Dirac mass term in Lagrangian
• What other mass terms are possible?

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Massive neutrinos Majorana neutrino

• (2) Majorana mass
• Neutrino is chargeless, so it can be its own
  antiparticle
• ? mM couples particle and antiparticle

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General case Dirac-Majorana-mass

• (3) Dirac-Majorana mass term
• Diagonalizing M gives two mass eigenvalues

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Different scenarios

• (a)
  pure Dirac case
• ? (Dirac field)
• pure
  Majorana case
• ?

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Different scenarios

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

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Related experiments

• Tritium ß-decay
• Flavor oscillations
• Neutrinoless double ß-decay

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Neutrinoless double ß-decay

• ßdecay
• Double ß--decay
• Could any nucleus be used?
• No
• Single ß-decay must be forbidden
• ?

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Neutrinoless double ß-decay

• Semi-empirical mass/Weizsäcker formula

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Neutrinoless double ß-decay

• 35 naturally occurring isotopes which decay via
  2ß-, all even-even

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Neutrinoless double ß-decay

• So how can 2ß- show that the neutrino is a
  majorana particle?

Neutrinoless double beta decay
X
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Neutrinoless double ß-decay

• 2 necessary conditions
• Particle-antiparticle matching
• ?
• Helicity matching
• ?
• If neutrinoless double ß-decay occurs, the
  neutrino is a massive majorana particle.

Virtual neutrino line
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Neutrinoless double ß-decay

• Experimental signatures
• Two e- from same place at same time
• Daughter nucleus (Z2,A)
• Neutrinoless case sharp defined kinetic energy
  of electrons, instead of continuous spectrum

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Neutrinoless double ß-decay

• Theoretical uncertainty (76Ge) 1.5 lt M lt 4.6
• Half-lives
• ß from seconds to 105 y
• 2?ßß 1020 y
• 0 ?ßß gt 1025 y
• m? 50 meV ? 100 kg needed for 1 event/y

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Neutrinoless double ß-decay

• Experimental difficulties
• Count rate How to measure T1/2 beyond 1025 y!?
• Source strength expensive!
• Background Cosmic rays, 2?ßß, natural
  radioactive decay
• Energy resolution

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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)
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Heidelberg-Moscow experiment
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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 0?ßß observations would prove that the
  neutrino is a Majorana particle and give the
  neutrino mass, but at the moment 0?ßß-experiments
  face many difficulties.

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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) 198212