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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.

• Lu

• nice post! can I ask what program you use to draw feynman diagrams?

• Dear

I would like to translate these articles into Japanese and post to my BLOG. Because I will explain this exciting facts to the young persons in Japan.

regards.

• Thanks Lu! I’ll get to the Higgs boson soon. First the W boson and flavor physics. Then the Higgs boson, QCD, and theories of new physics.

Mike — I use the TikZ/PGF package LaTeX.

Cheers,
Flip

• Thanks Flip.

Wow, you are the ‘shiz nit’!
I always look forward to your awsome posts. Thanks for taking te time (you must be ‘wide open’ busy) to make me smarter.

Big Mike

• Ted

Great post, as usual. I always feel like I am learning something even if most of it is way over my head.

A few questions you might indulge: The electron-neutrino blurb that accompanies the Particle Zoo pillow ad indicates that the neutrino travels “close to the speed of light.” How slow can an electron-neutrino travel? That may be an odd way of asking whether an e-n must travel at a single speed. What determines that speed? (No equivalent index of refraction, right?)

Also, we know that the speed of light slows as it travels through a medium (less than speed of c in a vacuum). Is that true for an electron-neutrino, too? Seems like the e-n would not slow because little or no interactions with the medium.

Last, photons (although no rest mass) have momentum, right? Do electron-neutrinos have momentum? Seems odd to have mass and velocity but limited interation with matter. (“if a tree falls in the forest . . . .”)

This may be your work but it is a wonderful distraction to my day. Thanks again for the great posts.

Ted

• Hi Ted!

Regarding the speed of light and the speed of massive stuff:

It’s somewhat counter-intuitive, but there is a big difference between truly massless particles (like the photon) and particles that have any mass—no matter how small. The difference is this: I can always *in principle* catch up to a particle with mass. A fancy way of saying this is that one can “boost into the particle’s rest frame.”

Imagine driving on the freeway. As you get onto the freeway, it seems like all the other cars are zooming past you. Once you speed up however, the relative velocity between the your car and the other cars gets smaller. If you exactly match the velocity of another car, then you are relatively at rest with that car. I.e. measurements of that car’s speed (e.g. with a radar gun) taken from your car will give zero. This is the same thing with neutrinos: if a neutrino is zooming past you, you can (in principle) rev up your engines and catch up to it.

Light behaves differently. No matter how fast you go, light always travels at the speed of light. You can never “catch up” to light. You can’t even gain any relative velocity on light. This is the basis for special relativity and all of its weird effects.

So, the lesson:
* Light: always travels at the speed of light.
* Neutrinos (or anything else massive): can travel at any speed below the speed of light depending on the motion of the observer.

Re: index of refraction

Now all of the above arguments hold in vacuum. As you mentioned different things happen in some medium, e.g., glass where you get an effective index of refraction. I haven’t really thought about the effect of a medium on neutrinos — though I know this is an important effect for neutrino oscillations (something I’ll get to soon).

I think the glib answer is, “yes, there is an analogous effect for neutrinos,” but since neutrinos *already* travel at a speed below the speed of light (and a speed that depends on the observer), this isn’t such a big deal. (It can be a big deal for other reasons, namely the oscillation of neutrions.)

Momentum

If something has energy then it has momentum. (I have an old post about E=mc^2 that might clarify some of these ideas… if you click on my bio there should be a list of my posts.) Neutrinos have energy, and so they also have momentum.

… but maybe I should clarify because I should be careful what I mean by “momentum.” In the previous paragraph I meant “4-momentum.” Here’s a handy explanation:

Let us define momentum to be “energy traveling in some direction.” (Don’t take this as a rigorous definition! It does, however, capture the essence of the idea.) Momentum in the x direction is “energy traveling in the x direction.” There are three Euclidean directions, so there are three kinds of momentum. A fourth kind of momentum is “energy traveling in the time direction.” What could this possibly mean? This is mass. This is the energy something has when it’s not moving in any direction. This is precisely what mass is. For reasons that are not important at the moment, “energy in the time direction” also includes any energy moving in space.

Thus:
* Photons have momentum. They have 3-momentum (because they’re never at rest) and they also have “energy moving in the time direction” because anything with 3-momentum also has 4-momentum.

* A particle at rest has no 3-momentum but it still has “energy moving in the time direction” — this is just its mass.

* A particle in motion has 3-momentum associated with the direction of motion. It also has “energy moving in the time direction” associated with both its motion and its mass.

These statements come from self-consistency in relativity and do not have any ambiguity about observers (what you refer to with the “if a tree falls in the forest” statement). There are, however, all sorts of crazy “if a tree falls in the forest” paradoxes in quantum mechanics. (They’re not really paradoxes, but they’re very counter-intuitive.)

• John Wells

Dear Flip,

Thanks for the great physics articles. I do have a couple of questions.

Since neutrinos are nearly massless and have no charge, do they pass through black holes or are they trapped?

Since photons have no mass or charge, how does the gravity of the black hole capture them?

Thanks, JM Wells

• Hi John!

Neutrinos will indeed fall into a black hole if their trajectory brings them close enough. Recall that the reason why black holes are ‘black’ is that even light (which has no mass and no charge) gets trapped.

Black holes interact gravitationally. The “charge” for gravity is energy. (Recall: the “charge” for electromagnetism is electric charge, the “charge” for the Z-force is a different charge, etc.) Note that the gravitational charge is *not* mass — while mass is a kind of energy, you can also have energy without mass (like photons).

Hope that clears things up a bit — please feel free to ask follow up questions if it didn’t!

Actually, this question reminds me of a very cute exercise in quantum field theory: do two photons (which have no mass interact gravitationally? It turns out that the answer (after some involved calculation) is *yes*, which is a rather cute result. (It also turns out that they also interact very weakly though the electric force, but this is a very quantum effect… I challenge you to draw the Feynman diagram for this!)

• if this is reasonable and not too lowly a question, could you please explain or comment on the different approaches, that define the relationship of particle physics versus plasma physics and perhaps any “field theories” each leans toward.

• Hi Agnes — I don’t think I quite understand your question, partially because I know *very* little about plasma physics. 🙂

I do know, however, the formal tools used in high energy physics are very closely related to the tools used in condensed matter physics.

Cheers,
Flip

• xhesi

love your post, I’m 14 and i really enjoy quantum/particle physics and you’re really helping me understand it. Thanks!!!

• hosam otaibi

An electron neutrino can spontaneously turn into a muon or a tau neutrino.
how can we differenciate between these three tipes?