The Neutrino as a Majorana Particle and Ray Davis's null first experiments

[zhermes]

My interests are in astrophysics, so please forgive my ignorance of particle physics.

I've just read Frank Close's book, "Neutrino"---excellent read, I'd recommend it---in which he points out that Ray Davis' first experiments to detect neutrinos from nuclear reactors (with no detections) demonstrated that neutrinos and antineutrinos were different. This is because the detector was only sensitive to neutrinos, and the nuclear processes taking place in the reactor were actually producing antineutrinos.

Anyway, I've been hearing a lot about people exploring whether or not neutrinos are Majorana particles (I think that involves looking at "double beta-decay", for some reason...). So what's the loop-hole that allows neutrinos to be their own anti-particles while still not interacting symmetrically?

Thanks!
z

 

[The_Duck]

I am not too familiar with this and so may be completely incorrect, but I think it has to do with handedness. The weak interaction cares about the helicity of the neutrinos, so for example the antineutrinos emitted in beta-decay in conjuction with an electron are always right-handed. On the other hand [get it?] if you have beta decay with emission of a positron and a neutrino, the neutrino is always left-handed. But if the neutrino is a Majorana particle we should just look at these as two different helicity states of the same particle.

 

[zhermes]

If it had a different spin, wouldn't that still be a different particle then?

 

[Parlyne]

Let me try to clear this up a little. When we think of a massless fermion, we can think of four states that should be distinct - the left-handed particle, the right-handed particle, the left-handed antiparticle and the right-handed antiparticle (for simplicity, $$\psi_L, \psi_R, \overline{\psi}_L, \mathrm{and}\ \overline{\psi}_R$$). This is really just the statement that we have a particle and its antiparticle, each of which can be either spin-up or spin-down, expressed in the helicity basis - that is, where the spin is measured along the direction of motion.

Once we're talking about massive particles, we can still make the decomposition in this manner; however, the definitions of the helicity states become frame-dependent. In particular, a boost will mix $\psi_L$ with $\psi_R$ and it will also mix $$\overline{\psi}_L$$ with $$\overline{\psi}_R$$. This is why a massive particle must have all four states represented in some way.

The idea with a Majorana particle is that the $\psi_R$ and $$\overline{\psi}_R$$ states are identified as being the same (up to a phase factor) and similarly for the left-handed states. Since the $$\overline{\psi}$$ states were initially defined as antiparticle states, it should be clear that this can only possibly work for particles that have no conserved charges.

To understand why this doesn't pose a problem for neutrino detection experiments that detect neutrinos and antineutrinos differently, we need to consider the way neutrinos interact under the weak force. This requires the discussion of a different basis for the spin states, the chiral basis.

It is, unfortunately, a little difficult to give an informal definition of the chiral states. The basic idea is that there are two irreducible spinor representations of the Lorentz group in 3+1 spacetime dimensions and that a generic particle (or antiparticle) spin state is a combination of these. And, it just so happens that the helical states are the chiral states for a particle traveling at the speed of light.

This discussion is necessary because (charged-current) weak interactions can only involve left-chiral particles and right-chiral antiparticles. Neutrinos can only interact with a detector by changing into or annihilating with a charged lepton through a charged-current process or by scattering off a detector particle through a neutral-current process. The former are much easier to detect and are exactly the kinds of processes that were looked for in the initial neutrino-detection experiments.

If neutrinos are, in fact, Majorana particles, the particle/antiparticle distinction made in such detection experiments is, effectively, a distinction between the left-handed and right-handed states. Since neutrinos are very light, when they have any noticeable amount of energy, their speeds will be very close to c, meaning that their helical states and chiral states are almost identical. Therefore, given interactions sensitive to chirality, left-handed particles will look like particle states and right-handed particles will look like anti-particle states, even though the particle/antiparticle distinction isn't actually valid.

 

[zhermes]

@Parlyne : I definitely didn't get the majority of what you posted. None-the-less, the parts I did (kind of) get were actually quite helpful.

Thanks!