Massive neutrinos
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Transcript Massive neutrinos
Massive neutrinos
Dirac vs. Majorana
Niels Martens
Supervisor: Dr. J.G. Messchendorp
8 okt 2010
Introduction
Introduction
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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Introduction
Introduction
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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Introduction
Introduction
Parity violation in weak interactions
• Parity operation: x -x
• V -V
• AA
• Goldhaber experiment (1957): measuring neutrino
helicity
• Electron capture in 152Eu
e 152Eu152Sm e
• Two co-linear events of opposite parity expected:
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Introduction
Introduction
Parity violation in weak interactions
P
• Only lefthanded photons observed only lefthanded
neutrinos
• Later experiments: only righthanded anti-neutrinos
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Theory
Neutrinos in the Standard Model
• Fermion; spin-½
• Massless
• only lefthanded neutrinos, righthanded
anti-neutrinos
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Theory
Neutrinos in the standard model
• Massless spin-½ particles are described by the
Dirac eqation for massless particles:
i L 0
i 0
i R 0
p
p
R, L R, L
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Theory
Massive neutrinos – Dirac
neutrino
• Flavour oscillations (small) neutrino mass!!
• How to incorporate this in SM/ extend SM?
(1) Dirac mass
(i mD ) 0
i L m R
i R m L
Boost can change handedness
coupling between two helicity states
A single four-component spinor
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Theory
Massive neutrinos – Dirac
neutrino
• Dirac mass term in Lagrangian
LMass mD mD ( L R )( L R )
mD ( L R R L )
• What other mass terms are possible?
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Theory
Massive neutrinos – Majorana
neutrino
(2) Majorana mass
L
Mass
L
c
1
c
mL ( L R R L )
2
R
Mass
L
c
1
mR ( L R R Lc )
2
• Neutrino is chargeless, so it can be its own
antiparticle
mM couples particle and antiparticle
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Theory
General case: Dirac-Majorana-mass
(3) Dirac-Majorana mass term
c
c
2L mD ( L R L ) mL L mR L R h.c.
c
L, L
mL
mD
c
R
mD
mR
c
R
Rc
h.c.
R
• Diagonalizing M gives two mass eigenvalues:
m1, 2
1
(mL mR ) (mL mR ) 2 4mD2
2
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Theory
Different scenarios
m1, 2
1
(mL mR ) (mL mR ) 2 4mD2
2
(a) mL mR 0 m1,2 mD
: pure Dirac case
(Dirac field)
(b) mD 0 m1, 2 mL, R : pure Majorana case
c
c
,
1
L
R
2
R
L
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Theory
Different scenarios
(c) Seesaw model
mR mD ; mL 0
mD2
mD2
m1
; m2 mR 1 2 mR
mR
mR
• Explains:
1 L Rc , 2 Lc R
– light mass of neutrinos
– the experimental fact that only lefthanded neutrinos couple to
the weak interaction.
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Experiments
Related experiments
• Tritium β-decay
• Flavor oscillations
• Neutrinoless double β-decay
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Experiments
Neutrinoless double β-decay
• β—decay: n p e e
• Double β--decay:
( A, Z ) ( A, Z 2) 2e 2 e
• Could any nucleus be used?
No:
* M N ( A,Z ) M N ( A,Z 2) 2me 2m
e
* Single β-decay must be forbidden
M N ( A,Z ) M N ( A,Z 1) me
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Experiments
Neutrinoless double β-decay
• Semi-empirical mass/Weizsäcker formula:
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Experiments
Neutrinoless double β-decay
• 35 naturally occurring isotopes which decay via
2β , all even-even
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Experiments
Neutrinoless double β-decay
-
• So how can 2β show that the neutrino is a
majorana particle?
Neutrinoless double beta decay
( A, Z ) ( A, Z 2) 2e X
2 e
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Experiments
Neutrinoless double β-decay
• 2 necessary conditions:
– Particle-antiparticle matching
– Helicity matching
m 0
Virtual neutrino line
e
M
Mass
L
c
c
1
1
c
c
mL ( L R R L ) mR ( R L L R )
2
2
• If neutrinoless double β-decay occurs, the
neutrino is a massive majorana particle.
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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
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Experiments
Neutrinoless double β-decay
1
2
2
M m
T1/ 2
• 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
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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
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Experiments
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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Experiments
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 0νββ observations would prove that the
neutrino is a Majorana particle and give the
neutrino mass, but at the moment 0νββexperiments 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) 198–212
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