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

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

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.

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

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

Neutrinos in the Standard Model Fermion; spin-½ Massless only lefthanded neutrinos, righthanded anti-neutrinos

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.

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.

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.

Massive neutrinos – Majorana neutrino (2) Majorana mass Neutrino is chargeless, so it can be its own antiparticle  mM couples particle and antiparticle

General case: Dirac-Majorana-mass (3) Dirac-Majorana mass term Diagonalizing M gives two mass eigenvalues:

Different scenarios (a) : pure Dirac case  (Dirac field) : pure Majorana case 

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

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.

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).

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

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?

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!

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.

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

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.

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

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)

Heidelberg-Moscow experiment

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.

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