PORT ELECTRON, ON the Isle of Leptons, was our very first stop, and subsequently we discovered and visited the Muon and the Tau lepton, important features on the same island. These places are easy to get to by sea and road – they are electrically charged, so electromagnetism gives us easy access. But studying their airports, learning about the weak force, we have several times come across rumours of neutrinos. We have seen departure boards listing flights to Electron Neutrino, Muon Neutrino and Tau Neutrino, and we have seen people getting on and off these flights, so presumably the destinations exist. But so far we know next to nothing about these mysterious settlements. They are inaccessible by road or rail – the electromagnetic and strong forces just don’t go there – and while the weak force can get us there by air, so far we have had little more than a high-altitude fly-by. Enough to see that they are a crucial part of our landscape, and we have seen that they are important players in beta decay and the reactions that keep the Sun burning, but little else. The difficulty of the terrain notwithstanding, it is time to rectify that.
Neutrinos were first postulated in 1930, by Austrianfn1 theoretical physicist Wolfgang Pauli.fn2 Famously and rather shamefacedly, he said, ‘I have done a terrible thing, I have postulated a particle that cannot be detected.’
The reason he did this was to do with beta decay. As we have seen, in beta decay, a decaying nucleus emits an electron. These electrons can be detected and their energy can be measured. One of the basic laws of physics is that energy and momentum are both conserved. The totals before the decay will be the same as the totals afterwards. We can use that to make some predictions.
Imagine the nucleus is stationary before it decays. The total momentum is zero. So after the decay, the total momentum must also be zero, since total momentum is conserved. This means that if the electron moves off in one direction, the nucleus must recoil in the opposite direction, to cancel out the electron’s momentum, and leaving the total as zero.
Likewise, energy is conserved. The electron and the recoiling nucleus have some kinetic energy, and the final mass of the nucleus will have reduced slightly during the decay, by an amount exactly sufficient to provide the mass of the produced electron and that kinetic energy.
If you put all that together, it is possible to solve the conservation equations and predict exactly the unique momentum the electrons must all have. Other types of radiation (alpha and gamma) bear this out. Alpha particles and gamma rays have a fixed energy for a given nuclear decay. But for beta radiation, the answer is … wrong. The electrons have a spread of momenta and energies, always less than the prediction. This is a problem.
There are only two options. Either energy and momentum conservation don’t work in beta decays (which was proposed as a solution by Danish physicist Niels Bohr), or we are missing something in the decay. Pauli went for the latter, inventing the neutrino, which could carry off variable amounts of energy and momentum and thus balance the nucleus and the electron. Energy and momentum would still be conserved, but the electron could now have a range of energies, as observed, with the maximum occurring when the neutrino had almost zero energy, and the minimum occurring when the neutrino carried away the maximum it possibly could. All the energies in the range would be consistent with conservation of momentum, and they would be distributed randomly according to the probabilistic nature of quantum mechanics.
From our point of view as explorers, we are sitting in the arrivals hall of the airport near the up quark. We see more passengers landing that are emerging in the arrivals hall. Either some passengers are vanishing (which would be very disturbing), or they are transferring to connecting flights onwards to the neutrino.
Thankfully, the latter is the case. Pauli was right about the existence of the neutrino. But he was wrong about the impossibility of detection. Getting to the Neutrino Sector of the Isle of Leptons is very difficult, but it can be done.
In the original conception of the Standard Model, neutrinos were in a unique position – the only massless matter particle. The reason for this was to do with the weak force, the only force they experience.
As we saw studying the airlines on our map, the weak force interacts with only one chirality: left-handed particles and right-handed antiparticles. Since the only force the neutrinos experience is the weak force, this means that the right-handed neutrino and the left-handed antineutrino are totally inaccessible in the Standard Model. There is no access by road, rail or air. Electromagnetism, the strong force and the weak force do not connect to them! It would be less disturbing if such particles didn’t even exist – after all, how could we even tell if they did?
How does this relate to the masslessness of neutrinos in the original Standard Model? There is a fascinating connection involving both relativity and quantum field theory that we will have to negotiate in order to access and understand the Neutrino Sector properly.
When looking at the strange asymmetric behaviour of the weak force, and the way it affects only left-handed particles and right-handed antiparticles, we only discussed massless particles, for good reason. Because once a particle has mass, the definition of left- and right-handed particles gets a little more complicated. The helicity – the direction of spin relative to the direction of motion – no longer defines the chirality. It is still possible to define chirality as the feature that the weak force cares about, but for a massive particle, chirality is no longer exactly the same thing as helicity.
If you think about it, this has to be true, because the helicity of a particle depends upon the relative speed of the observer and the particle. If we chase a positive-helicity particle and overtake it, the spin does not change direction, but the relative motion does, so the helicity would flip over. This is the same effect as if we look at the hands of a clock from behind its face – they go anticlockwise.
So by overtaking a particle, we alter the helicity. If this changed the weak force, that would be unambiguously observable, and it would give us a way of measuring absolute speed, in violation of relativity. We could use the strength of the weak force to define the absolute direction of travel of particles, without reference to anything else. Just as bad, say we catch the particle up but don’t overtake it, so that relative to us it is stationary. For a stationary particle, there is no direction of motion, so no defined helicity. So what does the weak force do?
What does happen is that when I catch up with and overtake a particle, the helicity changes, but the chirality does not change, and the weak force does not change.
Massless particles all travel at the speed of light, and it is not possible to bring them to rest or overtake them. In this case, helicity and chirality are identical. For massive particles, the helicity is still correlated to the chirality, but is not identical to it.
The upshot of this is that for massive particles, a particle with a definite helicity does not have a definite chirality, and conversely a particle with a definite chirality does not have a definite helicity. So if we create a pure beam of particles with a definite helicity, it must contain both chiralities. For a massive particle, both chiralities must exist in nature; but for a massless particle, we can get away with having only one chirality.
Going back to the idea of a massless neutrino then, if the neutrino is massless we can build a theory containing only the left-handed neutrinos and right-handed antineutrinos. Only the particles that actually interact with the Standard Model forces need to exist. The right-handed neutrinos and left-handed antineutrinos need never even exist.
Appealing to Occam’s razor, non sunt multiplicanda entia sine necessitate,fn3 or the simplest answer is usually the correct one. The Standard Model was originally constructed so that it did not contain right-handed neutrinos, nor left-handed antineutrinos. They were a blank space on the map. And this meant that the neutrino had to be massless. What we are saying is that in the so-far-uncharted neutrino badlands, which can only be reached by air, only the airports exist.
But is this really true?