1. Massive neutrinos Dirac vs. Majorana
Niels Martens
Supervisor: Dr. J.G. Messchendorp
8 okt 2010

2. Outline Introduction Theory Experiments 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
Vraag: What happens with helicity when m>0 en lorentz boost?
Als m>0, chirality zijn eigenstates van weak interaction.

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:
Parity is like a mirror.
P189 subatomic physics boek

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

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:
Dit is relativistische variant van kinetische term in schrodinger.
Om te voldoen aan klein gordon zijn het 2x2 matrices, pauli, en dus twee-component spinors.

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
Flavour oscillation: Marcel’s presentation  at least 2 flavors have mass (probably all three of them).
So, we need an extension of the SM. But how?
Helicity is not a good quantum number anymore.

9. Massive neutrinos – Dirac neutrino
Dirac mass term in Lagrangian
What other mass terms are possible?
When extending the SM, we should consider all possible extensions.
Psi-bar-c*psi-c, psi-bar*psi-c, psi-bar-c*psi. Psi-bar-c*psi-c is equivalent to dirac case above.

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.
What would happen if Mr=0 instead of Ml=0? Ans: we observe a really low mass.
Fi-2 is ~TeV, so at the scale of GUT, that’s why it is so popular (physics beyond the SM).
 Dark Matter

14. Related experiments Tritium β-decay Flavor oscillations
Neutrinoless double β-decay
Tritium: upper bound of 2eV. Geen uitsluitsel majorana/dirac nature.
Oscillations: only mass differences. Geen uitsluitsel majorana/dirac nature.

15. Neutrinoless double β-decay
Could any nucleus be used?
No: *
* Single β-decay must be forbidden 
Lets first look at double beta decay.
Beta-decay liftetime is much shorther than 2beta-decay lifetime.
Forbidden single beta-decay: ground state energy is lower than N(A,Z+1)+Me
Beta-min ipv beta-plus, omdat beta-plus-double decay kernen veel zeldzamer zijn, omdat de energieverschillen tussen initial
En final states nog groter moet zijn vanwege electron capture proces that single-beta-plus verval mogelijk maakt.
Teken een plaatje hierbij, van de drie levels (medium, hoog, laag).

16. Neutrinoless double β-decay
Semi-empirical mass/Weizsäcker formula:
SEMF: remember from subatomic physics

17. Neutrinoless double β-decay
35 naturally occurring isotopes which decay via 2β-, all even-even
So, can anyone explain why 2-beta-plus is much rarer?

18. Neutrinoless double β-decay
So how can 2β- show that the neutrino is a majorana particle?
Neutrinoless double beta decay X
What conservation law is violated? Lepton number!

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
So, if neutrinoless double beta decay occurs, the neutrino is a massive majorana particle.

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
For m < 50 meV, half-life is about 10^26 y, for 1 event/year, you need 100 kg.
Nuclear structure matrix element is uncertain by a factor 3.

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