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8 okt 2010
Massive neutrinosDirac vs. Majorana
Niels MartensSupervisor: Dr. J.G. Messchendorp
2
IntroductionIntroduction
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
IntroductionIntroduction
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
IntroductionIntroduction
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:
eSmEue 152152
5
IntroductionIntroduction
Parity violation in weak interactions
• Only lefthanded photons observed only lefthanded neutrinos
• Later experiments: only righthanded anti-neutrinos
P
6
Theory
Neutrinos in the Standard Model
• Fermion; spin-½
• Massless
• only lefthanded neutrinos, righthanded anti-neutrinos
7
Theory
Neutrinos in the standard model
• Massless spin-½ particles are described by the Dirac eqation for massless particles:
0 i
0 Li
0 Ri
LRLRp
p,,
8
Theory
Massive neutrinos – Dirac neutrino
• Flavour oscillations (small) neutrino mass!!• How to incorporate this in SM/ extend SM?(1) Dirac mass
Boost can change handedness coupling between two helicity states A single four-component spinor
0)(
DmiRL mi
LR mi
9
Theory
Massive neutrinos – Dirac neutrino
• Dirac mass term in Lagrangian
• What other mass terms are possible?
))(( RLRLDDMass mmL
)( LRRLDm
10
Theory
Massive neutrinos – Majorana neutrino
(2) Majorana mass
• Neutrino is chargeless, so it can be its own antiparticle mM couples particle and antiparticle
)(2
1L
c
RcRLL
LMass mL )(
2
1 cLRR
c
LRRMass mL
11
Theory
General case: Dirac-Majorana-mass
(3) Dirac-Majorana mass term
• Diagonalizing M gives two mass eigenvalues:
..)(2 chmmmL R
c
LRcRLL
cR
c
LRLD
.., chmm
mm
R
cR
RD
DLc
LL
222,1 4)()(
2
1DRLRL mmmmmm
12
Theory
Different scenarios
(a) : pure Dirac case
(Dirac field)
(b) : pure Majorana case
DRL mmmm 2,10
222,1 4)()(
2
1DRLRL mmmmmm
RLD mmm ,2,10
cLR
cRL 21 ,
13
Theory
Different scenarios
(c) Seesaw model
• Explains:– light mass of neutrinos– the experimental fact that only lefthanded neutrinos couple to
the weak interaction.
RR
DR
R
D
LDR
mm
mmm
m
mm
mmm
2
2
2
2
1 1;
0;
RcL
cRL 21 ,
14
Experiments
Related experiments
• Tritium β-decay
• Flavor oscillations
• Neutrinoless double β-decay
15
Experiments
Neutrinoless double β-decay
• β—decay:
• Double β--decay:
• Could any nucleus be used?
No: * * Single β-decay must be forbidden
emmMM
eZANZAN 22)2,(),(
eeZAZA 22)2,(),(
eZANZAN mMM )1,(),(
eepn
16
Experiments
Neutrinoless double β-decay
• Semi-empirical mass/Weizsäcker formula:
17
Experiments
Neutrinoless double β-decay
• 35 naturally occurring isotopes which decay via 2β-, all even-even
18
Experiments
Neutrinoless double β-decay
• So how can 2β- show that the neutrino is a majorana particle?
eeZAZA 22)2,(),(
Neutrinoless double beta decay
X
19
Experiments
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
0e
m
)(2
1)(
2
1R
c
LcLRRL
c
RcRLL
MMass mmL
20
Experiments
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
Experiments
Neutrinoless double β-decay
22
2/1
1mM
T
• 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
Experiments
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
Experiments
Heidelberg-Moscow Experiment
Background find a mountain and dig a hole
Source strength 11,0 kg enriched 76Ge: Source = detector
Enormous half-lives experiment run from 1990 till 2003 (but, stability then
becomes a problem)
24
Experiments
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