1. Neutrinoless Double Beta Decay and the Majorana Neutrino
By Andrew Eberhardt

2. History: Pauli and Weyl
[3]
Pauli observes continuous beta decay spectrum (1930)
Energy conservation problem
Solution is neutrino
Weyl Fermion
Only two states
Speed is c

3. History: Goldhaber Eu152 sample in a magnetic field
[4]
Eu152 sample in a magnetic field
decays via electron capture
Photon an neutrino have opposite helicity
Photon emission angle is related to neutrino helicity
All photons exit in the same direction
All neutrinos must be left helicity
No implications for Weyl neutrinos

4. History: Neutrino Mass
[5]
Neutrinos are not massless
The Weyl model must be wrong
Uniform helicity of neutrinos is now concerning

5. Majorana v Dirac: wavefunctions
[3]
Majorana:
Are their own anti particle
Combination of a handed and anti other handed Weyl fermion
left handed particle state and right handed antiparticle state
Dirac:
Have distinct anti-particles
Combination of independent left and right handed Weyl fermions
Interacting left handed particle state and right handed antiparticle state and sterile right handed particle state and left handed antiparticle state
[7]

6. Majorana v Dirac: Autobahn Helicity Paradox
[2]
Massive particles are subluminal
All neutrinos are left helicity
What would happen if we boosted past the neutrino?
Theoretically we could test using accelerator
Majorana:
As the neutrino is overtaken the helicity flips and the neutrino reacts as an anti-neutrino
Dirac:
As the neutrino is overtaken the helicity left neutrino is sterilized and the helicity right neutrino is desterilized
[2]
[2]

7. Majorana v Dirac: Feynman Rules
[3]
Majorana:
Particles incoming are equivalent to anti particles outgoing or anti particles incoming with a phase shift and vice versa
Dirac:
Particles incoming are equivalent to antiparticles outgoing and vice versa
[3]
[6]

8. Experiments: Neutrinoless Double Beta Decay
[1]
neutrinoless double beta decay
no neutrinos are emitted
The electrons carry away all the energy

9. Experiments: How do they work?
A large amount of an isotope that can decay via double beta decay (e.g. Ca-48, Cd-116, Ge-76, Mo-100, Nd-150, Xe-136)
Measure beta energies
Analyze the end of the spectrum
This peak puts limits on the mass mixing terms (<mee>)
Currently limiting lifetime of neutrinoless double beta decay

10. Experiments: What is planned?
[1]
Experiment
Isotope
AMoRE
Mo-100
CANDLES
Ca-48
COBRA
Cd-116, Te-130
DCBA
Se-82, Nd-150
EXO
Xe-136
GERDA
Ge-76
KamLAND-Zen
LUCIFER
Se-82, Mo-100, Nd-150
MAJORANA
MOON
NEXT
SNO+
Nd-150
SuperNEMO
XMASS

11. Implications: Mass Heiarchy
[1]
Informs the neutrino mass hierarchy
Measurements of neutrinoless double beta decay put vertical constraints on this graph
Measurements of the lightest neutrino mass put horizontal constraints on this graph

12. Implications: New Physics
[1]
Indication of physics beyond the Standard Model
Majorana Fermions
See-saw mechanism

13. Implications: Leptogensis
[7]
Neutrinoless double beta decay does not conserve lepton number
This could help explain the matter-anitmatter asymmetry
Leptogenesis may also be able to be linked to baryogenesis

14. Bibliography
Rodejohann W., “Neutrinoless double-beta decay and neutrino physics”, Journal of Physics G: Nuclear and Particle Physics, November 2012
Jentschura U., Wundt B., “Neutrino helicity reversal and fundamental symmetries”, Journal of Physics G: Nuclear and Particle Physics, April 2014
Pal P., “Dirac, Majorana, and Weyl fermions”, American Journal of Physics No. 79 pg. 485, 2011
Goldhaber M., Grodzins L., Sunyar A., “Helicity of Neutinos”, December 1957