Merry Xmas, Ymas, and Zmas—and a variable New Year!
For a long time I’ve been meaning to update this list of open questions on the Physics FAQ:
• Open questions in physics, Physics FAQ.
Here’s what it said about neutrinos as of 2012:
• What is the correct theory of neutrinos? Why are they almost but not quite massless? Do all three known neutrinos—electron, muon, and tau—all have a mass? Could any neutrinos be Majorana spinors? Is there a fourth kind of neutrino, such as a “sterile” neutrino?
Starting in the 1990s, our understanding of neutrinos has dramatically improved, and the puzzle of why we see about 1/3 as many electron neutrinos coming from the sun as naively expected has pretty much been answered: the different neutrinos can turn into each other via a process called “oscillation”. But, there are still lots of loose ends.
It’s held up fairly well: all of those questions are still things people wonder about. But I should add a question like this, because it’s nice and concrete, and physicists are fascinated by it:
• Is the tau neutrino heavier than the mu and electron neutrinos, or lighter?
This is a bit sloppy because the neutrinos of definite mass are linear combinations of the neutrinos of definite flavor (the electron, mu and tau neutrinos). The neutrinos of definite mass are called mass eigenstates and the neutrinos of definite flavor are called flavor eigenstates. This picture by Xavier Sarazin makes the two competing scenarios clearer:
In the normal hierarchy the mass eigenstate that’s mainly made of tau neutrino is the heaviest. In the inverted hierarchy it’s the lightest.
We don’t know which of these scenarios is correct. The problem is that we can’t easily measure neutrino masses! The rate at which neutrinos oscillate from flavor to flavor gives us information about absolute values of differences of squared masses! Currently we’re pretty sure the three masses obey
So, and are close and is farther, but we don’t know if is bigger than the other two (normal hierarchy) or smaller (inverted hierarchy).
We also don’t know which is bigger, or And as the FAQ points out, we’re not even sure all three masses are nonzero!
By the way, I will bet that we’ve got the normal hierarchy, with My reason is just that this seems to match the behavior of the other leptons. The electron is lighter than the muon which is lighter than the tau. So it seems to vaguely make sense that the electron neutrino should be lighter than the mu neutrino which in turn is lighter than the tau neutrino. But this ‘seems to vaguely make sense’ is not based on any theoretical reason! We haven’t the foggiest clue why any of these masses are what they are—and that’s another question on the list.
I also want to change this question to something less technical, so people realize what a big deal it is:
Could any neutrinos be Majorana spinors?
A less technical formulation would be:
• Is any kind of neutrino its own antiparticle?
On the one hand it’s amazing that we don’t know if neutrinos are their own antiparticles! But on the other hand, it’s really hard to tell if a particle is its own antiparticle if its very hard to detect and when you make them they’re almost always whizzing along near the speed of light.
We’d know at least some neutrinos are their own antiparticles if we saw neutrinoless double beta decay. That’s a not-yet-seen form of radioactive decay where two neutrons turn into two protons and two electrons without emitting two antineutrinos, basically because the antineutrinos annihilate each other:
Physicists have looked for neutrinoless double beta decay. If it happens, it’s quite rare.
Why in the world should we suspect that neutrinos are their own antiparticles? The main reason is that this would provide another mechanism for them to have a mass—a so-called ‘Majorana mass’, as opposed to the more conventional ‘Dirac mass’ that explains the mass of the electron (for example) in the Standard Model.
I will bet against the observed neutrinos being their own antiparticles, because this would violate conservation of lepton number and an even more sacred conservation law: conservation of baryon number minus lepton number. On the other hand, if some so-far-unobserved right-handed neutrinos are very heavy and have a Majorana mass, we could explain the very light masses of the observed neutrinos using a trick called the seesaw mechanism. And by the way: even the more conventional ‘Dirac mass’ requires that the observed left-handed neutrinos have right-handed partners, which have so far not been seen! So here’s another interesting open question:
• Are there right-handed neutrinos: that is, neutrinos that spin counterclockwise along their direction of motion when moving at high speeds?
So many unanswered questions about neutrinos!
My list of references hasn’t held up as well:
For details, try:
• John Baez, Neutrinos and the nysterious Maki-Nakagawa-Sakata Matrix.
• Paul Langacker, Implications of neutrino mass.
• Boris Kayser, Neutrino mass: where do we stand, and where are we going?.
The first of these has lots of links to the web pages of research groups doing experiments on neutrinos. It’s indeed a big industry!
In fact the first page is now full of silly random posts, but oddly still titled NeutrinoOscillation.org. Paul Langacker’s page is missing. Boris Kayser’s review uses an old link to the arXiv, back when it was at xxx.lanl.gov. His review is still on the arXiv, and it’s nice—but it dates to 1998, so I should find something newer!
What are the best places to read a lot of clearly explained information about neutrino puzzles? Are there other big neutrino puzzles I should include?