26
8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Embed Size (px)

Citation preview

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

8 okt 2010

Massive neutrinosDirac vs. Majorana

Niels MartensSupervisor: Dr. J.G. Messchendorp

Page 2: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: 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

Page 3: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 4: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 5: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

5

IntroductionIntroduction

Parity violation in weak interactions

• Only lefthanded photons observed only lefthanded neutrinos

• Later experiments: only righthanded anti-neutrinos

P

Page 6: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

6

Theory

Neutrinos in the Standard Model

• Fermion; spin-½

• Massless

• only lefthanded neutrinos, righthanded anti-neutrinos

Page 7: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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,,

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

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

Page 9: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

9

Theory

Massive neutrinos – Dirac neutrino

• Dirac mass term in Lagrangian

• What other mass terms are possible?

))(( RLRLDDMass mmL

)( LRRLDm

Page 10: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 11: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 12: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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 ,

Page 13: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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 ,

Page 14: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

14

Experiments

Related experiments

• Tritium β-decay

• Flavor oscillations

• Neutrinoless double β-decay

Page 15: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 16: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

16

Experiments

Neutrinoless double β-decay

• Semi-empirical mass/Weizsäcker formula:

Page 17: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

17

Experiments

Neutrinoless double β-decay

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

Page 18: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 19: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 20: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 21: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 22: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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

Page 23: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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)

Page 24: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

24

Experiments

Heidelberg-Moscow experiment

Page 25: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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.

Page 26: 8 okt 2010 Massive neutrinos Dirac vs. Majorana Niels Martens Supervisor: Dr. J.G. Messchendorp

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