The chances are you have heard quite a bit about the Higgs boson. The goody-two-shoes of particle physics, it may have been hard to find, but when it was discovered it was just as the theory – the Standard Model – said it should be. It has followed all the rules, so far. Neutrinos, on the other hand, are trouble.

Neutrinos are unique amongst the fundamental matter particles in that they carry no electromagnetic charge. In fact the only force of the Standard Model that neutrinos deign to notice is the weak nuclear force. This makes them very hard to detect, one reason they get away with so much.

Physicists go to enormous lengths to spot neutrinos. Cutting-edge neutrino detectors have included a giant bubble full of deuterium under Canada, an enormous underground lake surrounded by photomultipliers in Japan, tonnes of steel under the US, and the entire Antarctic ice-pack. A few weeks ago I stood in a huge golden box in CERN, which is now full of 725 tonnes of liquid Argon. This is protoDUNE, a one-twentieth-volume prototype of the neutrino-detector-which-is-to come, DUNE, to be sighted in the Sanford Underground Research Facility in South Dakota, USA. The DUNE detector will measure a beam of neutrinos produced at the Fermilab accelerator complex, hundreds of kilometres away near Chicago. ProtoDUNE recently saw its first particle tracks.

The main reason for all this effort is the fact that neutrinos are the only particle known to disobey the rules of the Standard Model.

In the Standard Model, as originally conceived, neutrinos were supposed to be massless. This was another way they had found to be “special”, since all the other fundamental particles have mass. This specialness, however, fitted quite well with the fact that the only Standard Model force they interact with is the weak force, as follows.

Matter particles carry angular momentum – spin. This means they have a “handedness”, like a corkscrew. As they travel, their spin can either be clockwise with the motion, like a right-handed screw, or anti-clockwise – left-handed.

For reasons we don’t understand, the weak force plays favourites with this handedness. It only affects left-handed particles (and only right-handed anti-particles). This means a right-handed neutrino would not be affected by any of the forces in the Standard Model. A rather useless particle. In fact, in the Standard Model, by application of Occam’s razor, there were no right-handed neutrinos, and no left-handed anti-neutrinos. Why postulate them if they don’t do anything?

Now for particles with mass, this doesn’t work. If a particle has mass, it must travel slower than the speed of light. So in principle at least, it is possible to overtake it, and that would flip the handedness, turning a right-handed particle into a left handed one. But it doesn’t make sense for the weak force to suddenly switch off or on depending how fast the observer is travelling. So we end up with one definition of handedness based on the spin (which can flip if you overtake it) and one based on the weak force (which can’t). We call these two types of handedness “helicity” and “chirality” respectively.

For a massless neutrino, these two things coincide. A massless particle travels at the speed of light, so can never be overtaken. So both the helicity and the chirality are fixed. A left-handed particle is always left-handed. This is why we could have a Standard Model with no right-handed neutrinos.

But neutrinos have mass.

It is very small, but it is there and it messes things up. I told you they were trouble.