# Nobelity: Neutrino Oscillations

This week (October 6, 2015), the Nobel Committee announced that Takaaki Kajita and Arthur B. McDonald were awarded this years Nobel Prize in Physics for

"the discovery of neutrino oscillations, which shows that neutrinos have mass"

So what are neutrinos, and why is their oscillation so interesting and Nobel-worthy?

The neutrinos (often written as the Greek character nu: $\nu$) are a fundamental particle. Like the electrons, quarks, muons, and taus, they are fermions, that is, spin-1/2 particles. This makes them matter particles, unlike the bosonic force carriers like the photon, $W$ and $Z$ bosons, the gluons, or the Higgs boson. Like the other matter particles, we can find that neutrinos come in three types that are almost identical (except, as it turns out, in mass). We call these types generations or flavors, and there is a natural way to pair them with the electron and its heavier generations (the muon and the tau), so we call the three flavors of neutrinos the electron-type, mu-type, and tau-type ($\nu_e$, $\nu_\mu$, and $\nu_\tau$). Collectively, we refer to the electrons and its partners as the charged leptons and the neutrinos and the charged leptons are all called leptons.

But they are very unusual matter particles. As I will explain, they are so light that they tend to travel near lightspeed, and are so weakly interacting they cannot be bound into nuclei. So you and I aren't made of neutrinos, in the same way that we are made of quarks and electrons. Still, after their discovery, neutrinos as particles are part of the Standard Model of particle physics, the list of particles and their interactions that allow us to predict with unparalleled accuracy, the behavior of things in the Universe on the smallest scales.

The Standard Model is complete, in that it can be used to calculate everything we see in particle physics across the energies we can directly test. That is, if you give me the list of particles which we know to exist, and the list of forces that we know to exist, I can tell you how those particles will behave with very high accuracy (I'm skating over some very important issues to do with the strong nuclear force, but the general idea is here). The Standard Model doesn't tell you "whys": why this number of particles, why these forces. It tells you "hows": how electrons respond to photons, how gluons interact, and so on. You can think of the Standard Model as the rulebook for a sport: it doesn't explain why the playing field is set up the way it is, but it tells you how the players move within the confines of the game.

But even within this The Standard Model it can calculate everything with six major exceptions:

1. It can't explain what dark matter is.
2. It can't explain what dark energy is.
3. It can't explain how the Universe generated more matter than antimatter.
4. It can't explain how the "Charge-Parity" symmetry is respected by the strong nuclear force.
5. It can't explain how the Higgs boson mass is stabilized to the value we measure it to be.
6. It can't explain how neutrinos have mass.

Each of these holes then is of massive interest to physicists. As physicists, as scientists, we want the gaps. We want to find the parts of our theory where everything falls apart, because patching those gaps is where we discover new things. It's also where we gain fame and glory and Nobel Prizes, and clearly we are in it for the money.

The Nobel Prize awarded was thus for the discovery of one of these holes in our understanding of particle physics. Not the solution to the problem, but for the discovery of the problem itself. Kajita and McDonald, as leads of the Kamiokande and SnoLab respectively, discovered that neutrinos change between flavors, $\nu_e$ can become $\nu_\mu$ or $\nu_\tau$, $\nu_\mu$ can become $\nu_e$ or $\nu_\tau$, and so on. That is, neutrinos oscillate. As I will explain, this discovery is equivalent to the discovery that neutrinos are massive, and that cannot be explained by the Standard Model alone.

Thus, the discovery of neutrino oscillation is the discovery of new physics. We don't understand what that new physics entails yet, but that's where the fun is.

OK, so now let me talk about what neutrino oscillation is, and why that means that neutrinos have mass. Then I'll explain why that can't be explained in the Standard Model, given that every other fermion in the Standard Model has mass, and that's not a problem.

First, let me explain how the discovery was made, as that's what the Nobel prizes were awarded for. Neutrinos interact only through the weak nuclear force. Whereas a charged particle can interact (or scatter) off of photons, and strong nuclear interactions can scatter off of gluons, the weak nuclear force proceeds through the $W$ and $Z$ interactions. Diagrams for this are shown here. One of the key points is that the interactions preserve flavor: an interaction via the charged $W^\pm$ boson turns a neutrino of one flavor into a charged lepton of the same flavor (or vice versa), and a neutrino scattering off the neutral $Z^0$ leaves with same flavor as it came in with.

As the name implies, weak forces are weak, so these scatterings are really rare. So if you want to look for neutrinos, you need to get a lot of target material, and be willing to sift through a lot of junk to get those rare events. Neutrinos were discovered in fact by Ray Davis and John Bahcall in the Homestake Mine using a tank of 100,000 gallons of cleaning fluid. Every week or so, 10 or so atoms of chlorine would absorbe a neutrino emitted by nuclear reactions in the Sun, and transmute into an atom of argon, which was collected and counted. So, very small rates. The process is shown here as well: a $W^-$ is exchanged, simulataneously turning a $\nu_e$ into a $e$, and a neutron inside the chlorine atom into a proton, which turns chlorine (element 17) into argon (element 18). Due to the energy available from solar neutrinos, only the electron-type neutrino can participate. So Davis and Bahcall could only measure the number of $\nu_e$ passing through their experiment. But that seemed ok: the Sun should only emit $\nu_e$, not $\nu_\mu$ or $\nu_\tau$ (as the Sun is made of matter which, like us, contains only electrons, not muons or taus).

The Homestake experiment, however, found that the flux of $\nu_e$ from the Sun was 1/3 the prediction from experiment. Eventually, this rate was confirmed, and Davis shared the 2002 Nobel Prize in Physics for this discovery. But this "Solar Neutrino Problem" remained. One possibility was that there were 1/3 the number of neutrinos emitted from the Sun as we thought, but that was difficult to explain, as that number of neutrinos was predicted by using the energy emitted by the Sun in visible light, and using the well-known physics of nuclear fusion.

As an aside, there was a bit of a fad among science-fiction authors at this time to use the Solar Neutrino Problem to postulate that the Sun was turning off: that nuclear fusion at the core (where the neutrinos come from) had massively decreased for Reasons, and eventually that shut-down would make its presence known at the surface (where the light is emitted) which would be Bad. The Arthur C. Clarke novel Songs of a Distant Earth is the best known one (to me) with this as a plot device.

The other alternative is that neutrinos have mass, and neutrinos emitted as electron-type turn into muon-type or tau-type by time they reach the Earth from their emission point in the Sun. Why would massive neutrinos do this?

The key point is that there are three types of neutrinos, and they are all identical up to this somewhat arbitrary label of flavor. Flavor matters for the weak interaction: as I said, weak interactions preserve flavor. However, there is no reason that the three particles we would identify as a neutrino with some mass would have to be identified with any one of the three flavors. That is, if you have a neutrino with a precise mass (what is called a mass eigenstate in the parlence of our times), it doesn't have to be 100% $\nu_e$, or 100% $\nu_\mu$, or 100% $\nu_\tau$. It could be, but there's no reason it has to be.

In fact, this mixing of neutrino-types is what we find in Nature. In the Sun, neutrinos are emitted through weak interactions, so they are emitted as 100% electron-type $\nu_e$. However, what we are calling an $\nu_e$ is really a combination of the three "mass eigenstate" neutrinos, $\nu_1$, $\nu_2$ and $\nu_3$, each with a slightly different mass. We can visualize this as a wave: the $\nu_e$ is build of waves of $\nu_1$, $\nu_2$ and $\nu_3$. Since these neutrinos have slightly different mass, each wave piece in the combination $\nu_e$ propagates at slightly different speeds (after all, having mass is just the statement that you aren't traveling at the speed of light). So, each part of the wave goes from peak, to trough, back to peak at a slightly different rate. So, by time the combination neutrino reaches the Earth, the neutrino that passes through your detector is not made up of the same combination of $\nu_1$, $\nu_2$, and $\nu_3$ that it started as, and that means that, at that particular moment when the neutrino could interact in your detector, it doesn't have to interact exactly as the $\nu_e$ it started life as: it's some combination of $\nu_e$ and $\nu_\mu$ and $\nu_\tau$.

Sketch of neutrino oscillation, from http://www-hep.physics.wm.edu/~vahle/homepage/nuosc.html

It turns out that the Sun is very far away compared to the distance over which $\nu_e$ oscillate into other types of neutrinos. So, on average, by time the Solar neutrinos reach us, they are on average an equal mix of each of the three flavors. So Davis and Bahcall measured 1/3 the rate they "should" have.

Similarly, neutrinos are produced in the atmosphere from the decay of charged muons (which are themselves produced by the collision of high energy cosmic rays and the atoms in our atmosphere). These neutrinos start life as $\nu_\mu$, but by time they reach our detectors, they've oscillated and contain other flavors. Here, the distances traveled can be close to the relevant oscillation lengths, so we can measure properties of the neutrino masses. Finally, we can produce beams of neutrinos (by producing muons and taus and waiting for them to decay in flight) and shoot them towards neutrino detectors and look at the oscillations.

It turns out the thing that matters in this oscillation is in fact the mass squared difference between the different mass states. So by measuring the oscillation of neutrinos into different flavors, you measure the quantity $\Delta m^2$ between mass states, not the masses themselves. So while we know there are three neutrinos, we don't know if the lightest one is massive or not, just that two of the three neutrinos are massive.

Cherenkov Light in water from the OSU research nuclear reactor.

Of course, to measure the oscillation, we need to be able to see the other flavors of neutrinos, not just electron-type. This is what this week's Nobel is for. The experiments led by Kajita and McDonald: Kamiokande and SNO, both are Cherenkov detectors. Cherenkov light is the eerie blue glow that gives nuclear reactors some of their creepy reputation. It's the equivalent of a sonic boom: light travels slower in air or water (or glass, or any transparent medium) than it does in a vacuum. If you take a charged particle and push it faster than the local speed of light in that medium, it builds up a wavefront that we see as light, just as a supersonic airplane builds up a wave that we hear as a sonic boom.

Neutrinos are neutral, so no Cherenkov light comes from them passing through a transparent medium. However, if they scatter off matter and emit a charged lepton, that charged particle can pick up so much energy that it moves faster than the local speed of light, and that light can be seen. So Kamiokande and SNO have giant tanks of water, and giant arrays of phototubes around the edge, looking inward for the light indicative of a neutrino interaction.

Super-Kamiokande (the follow-up experiment to Kamiokande) being filled with water in 1996, with technicians cleaning the photomultiplier detectors

Kamiokande used regular water, and could see interactions of any flavor of neutrinos with electrons; however, the $\nu_\mu$ and $\nu_\tau$ could only interact via the $Z$, and the $\nu_e$ could interact via the $Z$ and the $W$. This made the interaction of the electron-type much more likely than others. Given the rate of events, it was not possible for Kamiokande to see the small rate of $\nu_\mu$ and $\nu_\tau$ over the large $\nu_e$.

However, SNO used heavy water as a target (borrowed from the Canadian strategic nuclear reserve, as the heavy water was just sitting there, and it might as well do something useful in the meantime). Heavy water has hydrogen atoms which are deuterium isotopes: containing both a proton and a neutron (rather than just a proton). When any type of neutrino comes through, it can dissociate the proton and neutron of deuterium, breaking the nucleus apart. This gives a direct measurement of the total number of $\nu_e +\nu_\mu+\nu_\tau$, while measurements of the electron recoil gives the rate of $\nu_e$. This measurement confirmed that the flux of neutrinos from the Sun was what we predicted, but that some of them had converted to $\nu_\mu$ and $\nu_\tau$ en route.

Finally, using the Super-Kamiokande upgrade of Kamiokande, we could confirm the direction of atmospheric neutrinos (coming from muon decays). These neutrinos are much higher energy than those coming from the Sun; high enough energy to produce muons in the detector when interacting via $W$'s (Solar neutrinos just give pre-existing electrons a high energy kick). Muons give a different pattern of Cherenkov light than electrons, so the flavor can be measured in Super-K. The direction of the light also gives a clue of the incoming neutrino direction. Super-K sees neutrinos from all directions: the atmospheric neutrinos pass straight through rock, so it sees those produced from all over the planet. However, those coming up from underground are coming from the far side of the world, while those from above are coming from only a few tens or hundred kilometers above. The upgoing flux of neutrinos compared to downgoing indicated neutrino oscillation of muon-type neutrinos.

So, that's the experimental evidence: neutrinos oscillate, and that means at least two of the three neutrinos have mass. What's the big deal?

Well, the problem is that neutrinos can't have mass in the Standard Model. As I talked about previously (here and here), for fermions to have mass, the Standard Model needs to tie two different particles together: one that is "left-spinning" and one that is "right-spinning." For some bizarre reason, the Universe decided to treat the fermions differently depending on how they spin. Most importantly, the weak nuclear force only interacts with the left-spinners. The job of the Higgs boson is to equilize the different quantum numbers of the left- and right-spinners, allowing the fermions to have mass.

So the neutrinos we detect are the ones interacting with the weak nuclear force. That means they are all left-handed, by definition. The problem is that the Standard Model doesn't contain the equivalent right-handed neutrinos. It has right-handed charged leptons, and right-handed quarks, but not right-handed neutrinos. Such particles could exist, but since they don't interact via any of the forces we can directly probe (electromagnetism, strong nuclear, or weak nuclear), we can't see them.

So, we could imagine extending the Standard Model to include right-handed neutrinos, which would give us neutrino masses. Sometimes this extension I've seen written as the $\nu$-Standard Model (the "nu"-Standard Model. Get it?). But it involves new particles.

The other issue is that neutrinos are neutral, unlike any other fermion we know about. This means that the neutrino could be its own antiparticle. Maybe the needed right-handed neutrinos are just the antiparticles of the left-handed ones, rather than adding new states. If this is true, that means that the Universe doesn't care to differentiate between neutrino and anti-neutrino. Since neutrinos can turn into charged leptons and neutrinos into charged anti-leptons, that means there's a way to violate the number of leptons in the Universe. So depending on how neutrinos gain mass, there could be important new interactions that are not present in the Standard Model. We don't know yet, but step 1 is always finding out that a problem exists. Then we worry about solving it.