Neutrinos are very mysterious particles. They do not carry electric or magnetic charge, and so they do not interact very much with anything else. In fact we are constantly being showered with neutrinos from space that fly straight through us without interaction, and in fact straight through the entire Earth without even being slowed down. They are so difficult to detect that the weak nuclear decays that generate them were at first thought to be violating energy and momentum conservation since the scientists did not know they were producing neutrinos. And even when their existence was later predicted and proven, they continue to baffle physicists.

One of the main reasons is their mass. For decades they were thought to be massless, just like the photon is. However in the 1990s it was discovered that neutrinos produced in our Sun were oscillating between the three different neutrino species - and such time dependent oscillations are forbidden for a massless particle due to the effects of time dilation in the theory of relativity. So we knew then that neutrinos carried a mass, and yet countless other experiments had provided an upper limit on the mass that was several orders of magnitude smaller than the next lightest particles in the Standard Model. Twenty years later we still cannot explain why the neutrino should have a mass, and yet be so much lighter than everything else.

One option is a type of theory called a seesaw model. 

In the simplest of the seesaw models, there are three neutrinos that have similar properties to the Standard Model neutrinos, but are not exactly the same. Each of the three neutrinos is paired with a much heavier neutrino that has not yet been detected in experiments. Not only is this second neutrino heavier than anything we have yet detected, but in most of these models it is also assumed to not interact with anything else in the Universe. It is not affected by any of the three forces in the Standard Model (although it does still feel the effects of gravity). 

In this model, the light neutrino is massless and its partner can be as heavy as we need it to be. (The reason why the lighter one is massless instead of just very light is a technical issue of gauge symmetry, and is beyond the scope of this article).

The key aspect of the seesaw model is an interaction between these two neutrinos. We assume that there is some probability that a light neutrino can suddenly change into a heavy neutrino, and that similarly the heavy neutrino can change into a light neutrino. It is important to stress that this is not a decay of the heavy neutrino, and also that this is not the same type of oscillation that is observed in physical neutrinos, but rather an effect of quantum mechanics which a physical neutrino can be alternate between these two states.

In essence the physical neutrinos in the Standard Model are a combination of both the light and heavy neutrino states. We cannot observe either directly, but only their combination. It is then easy to calculate the masses of the two physically observable neutrino states, and we find that if the heavier state has mass M, then the lighter state will have a mass proportional to 1/M. This is where the models get their name from, as the two types of neutrino seesaw between themselves, and as an increase in the mass of one will decrease the mass of the other.

So the question then is what is intuitively happening here to provide the lighter neutrino with a mass? Essentially the physical neutrino behaves as a massless particle, with the same interactions and properties of the lighter neutrino state. Sometimes it will suddenly convert to a very heavy neutrino state and behave as a sterile, heavy neutrino. What we observe and measure in nature is an average of the two states' masses.

The heavier this heavy state is though, the less time the neutrino can spend in it. And so increasing its mass makes the physical neutrino heavier, but because it cannot stay in that state as long the overall effect is the lessen the apparent mass of the physical neutrino.

And so the final result is that the neutrino is a massless particle that sometimes will become very heavy, but only for a very brief moment. Then the physically observed neutrino is an average of the two, and appears to observers to be a very light, but not quite massless particle.

That is the Seesaw Model in a nutshell.

NB: In keeping with the theme of this blog, I have avoided giving the mathematical formulae for the seesaw models. However they are also quite interesting, and anyone who wishes to discuss them further is welcome to find me in the forums or e-mail me for more details.