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### Neutrinos

Time for another dose of particles for the people (eh, working title). In previous installments (Part 1, Part 2, Part 3, Part 4) we started a basic theory (QED; electrons and photons) and added on muons, taus, and the Z boson. Now we’re going to add on a set of particles that have recently made some news, the neutrino.

Here’s the Particle Zoo‘s depiction of an electron-neutrino:

There are, in fact, three types of neutrino: one to pair with each of our electron-like particles. Thus in addition to the electron-neutrino, we also have the muon-neutrino and the tau-neutrino. As their name suggests, neutrinos are neutral and have no electric charge. Further, they’re extremely light.

The fact that neutrinos don’t have any charge means that they don’t couple to photons, i.e. there are no Feynman rules for neutrinos to interact with photons. In fact, the only particle we’ve met so far that does interact with the neutrino is the Z boson, with the following Feynman rules:

Exercise: Consider a theory with only neutrinos and Z bosons so that we only have the Feynman rules above. Check that this looks just like three copies of QED (a theory of electrons and photons).

Question: How is the theory of only neutrinos and Z bosons different from “three copies of QED?”
Answer: Unlike the photon, the Z boson has mass! This means that the Z boson doesn’t produce a long-range force like electromagnetism. We’ll discuss this soon when we introduce the W boson and explain that the W and Z together mediate the so-called “weak nuclear force.”

Exercise: Draw the Feynman diagrams for an electron and positron annihilating into a neutrino and anti-neutrino. What are the possible final states? (e.g. can you have a muon-neutrino and anti-muon neutrino? Can you have an electron neutrino and an anti-tau neutrino?) Given that neutrinos don’t interact electrically and that the Z boson interacts very weakly, what do you think this would look like in a particle detector? (Consider the significance of the phrase “missing energy.”)

This should start to sound very boring!

If you’re starting to get bored because we keep writing down the same QED-like theory, then you’re keeping up. So far we’ve introduced all of the basic players in the game, but we haven’t told them how to interact with each other in exciting ways: don’t worry! We’ll get to this in the next post on the W boson.

Let’s recap how boring we have been:

• We started with a theory of electrons and photons called QED.
• We then “doubled” the theory by adding muons which were heavier electrons that coupled in the same way to photons. Then we “tripled” the theory by adding taus, which are yet another heavy copy of electrons.
• Next we added a new force particle, the Z. This is a heavy version of the photon (with a weaker interaction strength), but otherwise our Feynman rules again seemed like a doubling of the rules in the previous step. (We now have 6 “copies” of QED.)
• Now we’ve added three neutrinos, which only interact with the Z in a way that looks just like QED. We now have 9 “copies” of QED.

I promise things will get a lot more exciting very soon. First, here’s a pop quiz to make sure you’ve been paying attention:

Question: Can you draw a diagram where an electron decays into any number of neutrinos? Why not?

Some properties of neutrinos

We don’t quite have the full story of neutrinos yet, but here’s a glimpse of what’s to come:

• Those familiar with chemistry will know that neutrinos are produced in beta-decay processes.
• There is a neutrino for each electron-like particle. This is not a coincidence.
• One of the great experimental discoveries in the past 15 years was that neutrinos have [a very tiny] mass. It turns out that this is related to another remarkable property: neutrinos change identity! An electron neutrino can spontaneously turn into a muon or a tau neutrino. What’s even more remarkable is that this turns out to have a very deep connection to the difference between matter and antimatter. This is something we’ll have a lot to say about very soon.
• Because neutrinos are so light they played a key role in the early universe. As the universe cooled down from the big bang, heavy particles could no longer be produced by the ambient thermal energy. This left only neutrinos and photons buzzing around to redistribute energy. This turned out to play an important role in the formation of galaxies from quantum fluctuations.

In the interests of getting to the electroweak model of leptons, I will not do justice to the rich and fascinating history of neutrino physics. Here are a few highlights that I’ve found interesting.

• The Super Kamiokande detector in Japan was originally built to look for signals of proton decay that is predicted by many models of grand unification. These proton decay signals were never found (and are still being searched for), but in 1998 Super-K made a breakthrough observation of neutrino oscillation.
• Neutrino oscillation solved the solar neutrino problem.
• More recently, last month the OPERA experiment at the Gran Sasso Laboratory in Italy found further evidence for neutrino oscillation by directly observing a tau-neutrino coming from a beam of muon neutrinos which had traveled 730 km from CERN.
• One of the great theorists of the 1900s, Wolfgang Pauli, postulated the existence of a neutral, light particle to explain apparent violations to energy conservation coming from nuclear decays. He called the proposed particle a “neutron,” but also noted that it would be extremely difficult to detect directly. Later Chadwick discovered the neutron (what we call the neutron) but it was clearly too heavy to be Pauli’s “neutron,” so Fermi renamed the latter to be the neutrino (“little neutral one”). Here’s a nice Logbook article in Symmetry Magazine about Pauli’s original postulate that such a particle should exist.
• Neutrino physics has become one of the focus points of Fermilab’s research program into the ‘intensity frontier.’ The general idea is to generate a beam of high-energy neutrinos (using the Tevatron’s proton beam) and shoot it towards targets at different distances (up to 450 miles away in Minnesota!). Because neutrinos are so weakly interacting, they pass harmlessly through the earth at a slight downward angle until a small number of them interact with large underground detectors at the target site.
• There are lots of neat proposals about interesting things one can do with neutrinos. To the best of my knowledge, most of these are still in the “interesting idea” phase, but it’s a nice example of potential spin-off technologies from fundamental research. Some examples include
1. Probing geological activity deep underground, or even forecasting earthquakes.
2. One-way communication with deep ocean submarines.
3. Non-intrusive nuclear reactor inspection to check if nuclear reactors were being used to produce weapons-grade plutonium.
4. Even more dramatically, neutralization of nuclear weapons.

Coming soon

Make sure you’re thoroughly familiar with the different particles we’ve introduced so far and how we’ve allowed them to interact. Next time we’re going to spice things up a lot by introducing the W boson and some of the remarkable things it does for us. By then we’ll have nearly all of the pieces necessary to describe the electroweak theory of leptons and we can discuss neutrino oscillations, CP violation, and the Higgs boson. After this we’ll move on to the quark sector, which we’ll see is partly a “copy” of everything we’ll have done with the leptons.