Why did everyone think the neutrino was massless? It was clear from the fact that neutrinos seemed to go very fast when given a relatively small amount of energy that they have a very small mass, but why did many physicists think it must be exactly zero? Sure, we think the photon has exactly zero mass too, but there's a good reason. If the photon has mass then the theories of relativity and electromagnetism would have to be different as well. So, why should we think the neutrino is massless?
In a recent talk at the University of Maryland given by Hitoshi Murayama of UC Berkley I was offered a pretty good answer. In 1958, Goldhaber, Grodzins, and Sunyar did an experiment that determined experimentally that neutrinos are always left-handed (have negative helicity) and anti-neutrinos are always right-handed (have positive helicity). Other experiments confirmed this result. This was remarkable, because other particles, like electrons, can have either helicity.
The reason this has to do with the mass of the neutrino is the following: Helicity is the property of how much the spin of the particle is aligned with the momentum. Suppose an electron traveling in the x-direction has a positive helicity as measured in one frame of reference. If we look in another frame of reference that's traveling faster than the electron in the x-direction, then in that frame of reference the electron will appear to be moving in the negative x-direction; its momentum will be reversed. The spin is the intrinsic angular momentum, though. If you imagine the electron as a ball spinning around the x-axis in the right-handed sense, in the other reference frame it will still be spinning around the x-axis in the right handed sense. The direction of the spin remains the same while the direction of the momentum switches, which means that the helicity has switched. To put it another way, if we look along the new direction of momentum, the rotation is now left-handed. The component of spin along the momentum has switched signs because the momentum switched directions.
Once we know that helicity is a frame dependent property, then the experimental results of Goldhaber look pretty fishy. How can all neutrinos be left handed if a left-handed particle looks right-handed to a different observer. The principle of relativity tells us that physics is supposed to be the same in all inertial frames of reference, so if the laws of physics we observe say there can't be right-handed neutrinos, that should be true in all frames of reference. This appears to be a contradiction.
There is a way out of the contradiction. One finds a frame of reference in which the helicity is reversed by going faster than the particle. If neutrinos are massless, then they move at the speed of light and we can't go faster than the particle to switch the helicity. If neutrinos are massless then it makes sense that they can all be left-handed, and anitneutrinos can be right-handed.
Of course, more recent experiments have detected neutrino oscillation, which tells us that neutrinos don't move at the speed of light and do have masses. So, it seems that we're back to the same contradiction we started with. How do we get out of it? It seems we are not entirely sure yet. Murayama discussed two basic paths one can follow. One can consider that maybe those things we thought were antineutrinos are actually just right handed neutrinos, meaning that a neutrino and an antineutrino are the same particle. The other path is the idea that right handed neutrinos do exist, but for some reason we don't see them. One can then come up with different reasons why we don't see these right-handed neutrinos. This is exciting, at least, because it requires us to consider physics beyond the standard model in order to reconcile these facts.
Sources:
- Big World of Small Neutrinos, Hitoshi Murayama physics colloquium at the University of Maryland
- http://www.pnl.gov/fermi/citations/goldhaber-cit.htm
- Classes, etc. etc.