The Weirdness of Neutrinos: beyond the 2015 Nobel Prize

As most of you are probably aware, the Nobel Prize in Physics was awarded this week to Takaaki Kajita and Arthur B. McDonald “for the discovery of neutrino oscillations, which shows that neutrinos have mass”. This is truly a fantastic discovery and one that is long overdue for recognition. To be clear, what Kajita and McDonald won the award for was the experimental verification of neutrino oscillations. The theoretical prediction of such oscillations was made as early as 1957 by Bruno Pontecorvo. The Standard Model long predicted three types of neutrinos, but it also predicted that they should be massless (this is one of the glaring holes in the Standard Model that people too often ignore). In 1968 Pontecorvo figured out that if neutrinos actually had mass then they could change into one another. This was suggested as a solution to the so-called solar neutrino problem. The masses of the individual neutrinos were subsequently experimentally verified (and have led to a previous Nobel Prize in physics). What hadn’t been observed until Kajita and McDonald came along was the oscillation between the different types (masses), even though it was widely accepted that such oscillations existed.

The thing is, neutrinos are puzzling for another reason. Neutrinos are neutral particles and so don’t have an electric charge. Unlike neutrons, however, they are fundamental which means, as far as we know, they can’t be broken down into constituent particles. This fact is important for what I am about to say. All particles that possess angular momentum, also possess a magnetic dipole moment. So, for example, a dipole moment can arise from an electron’s orbit about a nucleus as well as its intrinsic spin. This is well-known, standard physics. Another piece of well-known, standard physics (Maxwell’s equations) tells us that magnetic fields are nothing more than electric fields viewed from a reference frame that is moving relative to the source of the electric field. This is why we typically refer to the singular field as “electromagnetic.” It’s just one field but it has two different (or seemingly different) behaviors depending on how it is viewed. The sources of such fields are electric charges. This actually helps explain the concept of magnetic moment. The presence of angular momentum in a system indicates the presence of relative motion between the portion of the system with the angular momentum and some observer. If the system possesses electric charge, then it makes sense that a magnetic field would be present as well due to the relative motion.

So now consider a neutron (not a neutrino just yet). It is a fermion and thus has a spin of 1/2 which suggests that it has a magnetic moment. In fact it does. But how does a neutral particle develop a magnetic moment if the source of magnetism ultimately has to be charge? Well, the standard way to answer this is to simply say that the neutron is a composite particle that is actually composed of quarks which are not neutral. So we could easily dismiss the magnetic moment of the neutron as being some kind of relic of the relative motion between an observer and the constituent quarks which do possess charge. But what about the neutrino?

This model would suggest that neutrinos shouldn’t have any magnetic moment at all because they are fundamental (i.e. they do not have any constituents). And yet, they do. But why? And how?

As it turns out, there is a connection between mass and magnetic moment according to ideas dating back to Dirac! Semi-classically, one can also show that any particle that possesses spin also possesses a magnetic dipole moment. Either way, however, since the Standard Model predicts a zero mass for the neutrino, any magnetic moment would suggest physics beyond the Standard Model. There are plenty of suggested minimal extensions of the Standard Model that produce a solution to this conundrum (e.g. you can use Feynman diagrams to show that there is a one-loop approximation of the neutrino as a “mixture” of a W+ and an e-). But none of these is universally accepted. And so we are left with another bizarre property of the neutrino: it is a neutral, fundamental particle that has electromagnetic characteristics! In short, it is the ultimate Standard Model contrarian.


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