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The Flavor of Neutrinos

Pheno 2012, Part 2

Technicians in a boat examine the detectors at the Kamiokande neutrino observatory in Japan.

(Part 1 of my dispatches from the Phenomenology 2012 Symposium involved the theory of the Higgs boson, along with a summary of the latest experimental searches for it. Yesterday’s post was less about science than it was about communication, and why we physicists should work to improve our style of talking.)

Neutrinos have been in the news a lot over the last year, thanks to the OPERA experiment. I won’t rehash all of that today, since it isn’t particularly relevant for the Pheno 2012 conference. Instead, I want to cover a bit of the theory of neutrinos and the status of experiments involving them, much as I did with the Higgs boson on Tuesday. I have always been fond of neutrinos, and it was truly fun to realize how far neutrino physics has advanced since I first started paying attention in the mid-1990s. Ideas that were beyond conjectural in 1996 are completely accepted now, and experimental results have become really good.

(For some history and other aspects of neutrino physics I’m not covering here, see my earlier post.)

Neutrinos, in Theory

Neutrinos are neutral particles with very small masses.  They are also fundamental, meaning they are not built up of smaller constituent particles; this means they are akin to electrons, but unlike protons or neutrons, which are made of quarks. In fact, electrons and neutrinos are both examples of leptons, the class of low-mass particles that interact via the weak nuclear force (and the electromagnetic force if they are charged). According to the Standard Model (SM), there are three “generations” of leptons, each of which contains a negatively-charged lepton and a partner neutrino:

  • Electrons (e) and electron neutrinos (νe)
  • Muons or mu leptons (μ) and mu neutrinos (νμ)
  • Tauons or tau leptons (τ) and tau neutrinos (ντ)

Electrons are stable, but muons and tauons (which are both more massive) decay quickly into lighter particles. The generation of lepton is known as its flavor.

Each neutrino flavor is a different set of “coordinates”, combinations of the three mass states (labeled 1, 2, and 3). The specific position is determined by the “mixing angle”, which currently must be determined through experiment. (I made some up, so my picture should not be considered accurate.)

Neutrinos don’t decay, but they do change flavor. This is known as neutrino oscillation, and it’s due to an odd quantum property of the particles. Each of the three neutrino flavors is actually a mixture—a superposition—of three quantum states with different masses, which we label ν1, ν2, and ν3. Think of it as like the (x,y,z) coordinates on the surface of a sphere: the total “position” on the sphere’s surface is the neutrino flavor, but the “coordinates” are the hidden mass states. However, it doesn’t stick to one spot: the state of the neutrino travels across the sphere’s surface, eventually coming back to its starting point (hence the name “oscillation”). In less abstract terms, this means as a neutrino propagates, it changes from one flavor to another. I’ll discuss the implications of this change for experiments in the next section.

The sphere picture is pretty straightforward (though I admit my presentation of it may be less than clear!); the problem is that we don’t know all the details about the sphere. We know that the electron neutrino is a superposition of mass states, but we don’t know how much each mass state contributes to the whole—and we don’t know the exact mass of any of the states (whether it’s a mass state or a flavor state). The problem lies in the nature of the neutrinos themselves: they’re electrically neutral, so they don’t interact via the electromagnetic force. (Neutrons are also neutral, but because they are made of charged quarks, they have residual magnetic characteristics, so they can be manipulated using magnetic fields.)

The relative contributions of each mass state are known as the mixing angles, which we can represent by rotations by fixed amounts on the sphere shown above. We also can construct a way to describe the transitions between the different flavor states, and these rely on the distance the neutrinos travel and the differences in mass between the mass states. With the current state of our theoretical knowledge, we have to determine the mixing angles experimentally: no model predicts what values they should take. Additionally, the mixing angles don’t tell us which state or flavor is more massive than the others. While tauons are more massive than muons are more massive than electrons, the electron neutrino may not be the least massive of the group, and the ν1, ν2, and ν3 states may be ranked in any order: we have no way to know right now.

Neutrinos, in Experiments

Because neutrinos interact via the weak force, detecting them basically requires a direct hit between a neutrino and another particle, generally a nucleus. Electron neutrinos interact more readily than the other two flavors, but depending on the design of your experiment, you may be able to detect at least the electron neutrinos or all three. It’s generally hard to separate out the individual contribution from mu and tau neutrinos, unfortunately, so your best bet is to have a way to measure the number of electron neutrinosand the total number of neutrinos together.

The reason for this is that all neutrinos can bounce off particles (e.g., electrons), a process known as elastic scattering, similar to pool balls colliding. Additionally, electron neutrinos can change neutrons into protons, liberating a new electron. On the level of the fundamental forces, these different interactions can be seen as the exchange of W or Z bosons, as shown in the Feynman diagrams below:

Neutrino scattering Feynman diagrams. In the first case, any neutrino will do: it simply “bounces off” another particle. It exchanges a neutral Z boson in the process, so this is known as a “neutral current” interaction. Electron neutrinos can also interact via the W bosons, either by swapping themselves with an electron, or by changing a neutron into a proton. These are the charged current interactions. (Ref.: Physics Today 54 (8), 13.)

One particularly successful detector was the Sudbury Neutrino Observatory (SNO) in Ontario, which was a huge tank filled with heavy water (D2O). Heavy water replaces ordinary hydrogen with deuterium, which has a neutron attached to each nucleus (while ordinary hydrogen has no neutrons). A neutrino of any flavor scoring a direct hit on a deuterium nucleus kicked the neutron out, and detectors lining the outside of the SNO tank could pick up the telltale signature. On the other hand, when an electron neutrino scored a direct hit on a deuterium nucleus, it changed the neutron into a proton, which also could be registered by the detectors in a different way. (Therein lies a tale for another day!)

While the first breakthroughs in neutrino oscillation detection were found by observing neutrinos from the Sun (where they are produced in great quantity as a product of nuclear fusion), today many experiments catalog them when they are made in high-energy collisions. For example, the OPERA (Oscillation Project with Emulsion-tRacking Apparatus) collaboration in Italy detects neutrinos produced at the Large Hadron Collider (LHC). Similarly, MINOS (Main Injector Neutrino Oscillation Search) consists of two detectors, one at Fermilab in Illinois and one in northern Minnesota; comparison of the event rates between the detectors reveals information about how the flavors change as they travel the 450 miles (724 kilometers) through Earth’s crust.

Modern experiments have begun measuring the mixing angles and the mass differences between the states. Thanks to experiments including the Daya Bay experiment in China (as Wei Wang described at the conference), we know that all the mixing angles are nonzero, which means all three mass states of neutrinos are mixed together to create the flavors. Combined with cosmological measurements, we have an upper bound on the total mass of all three flavors added together—and the number is very small, much smaller than the electron mass, which is the smallest measured mass we know.

One interesting possibility was raised at a conference I attended in 1999, and came up again at Pheno 2012: perhaps another species of neutrino is hiding in the data. This additional flavor could belong to a fourth generation of particles, which implies two more quarks and an additional lepton added to the current Standard Model; the new neutrino (newtrino?) could also besterile, meaning that it doesn’t couple with a lepton—or interact via the weak force. (It still experiences gravitation, since everything does.) Cosmological data, as reported by Suzanne Staggs of Princeton, is consistent with four flavors of neutrino, though three flavors are still preferred for a number of reasons. LHC data puts strong constraints on a fourth generation of quarks and leptons as well, though sterile neutrinos are not ruled out strongly in any regime yet.

Another potentially interesting aspect of neutrinos that came up in a few talks is the possibility that neutrinos and antineutrinos are actually the same particle: if an electron neutrino meets another one, they annihilate. (Particles of this type are known as Majorana fermions.) Neutrino-neutrino scattering is not something that can be done easily: the main process by which it can occur is something known as double-beta decay. Beta decay occurs when a neutron within a nucleus changes into a proton, emitting an electron and an electron antineutrino (a similar process to the third Feynman diagram above); in double beta decay, two neutrons undergo disintegration simultaneously, producing two antineutrinos. If these two antineutrinos meet, and if an antineutrino is the same as a neutrino, then they annihilate, leaving no neutrinos at all. Of course, if looking for neutrinos that are actually present is hard, confirming their absence is even more challenging! However, it can be done, and some experiments are specifically looking for the effect.

As I mentioned before, in the ’90s when I first began keeping track of neutrino physics, things were very different. Many researchers still held on to the idea that neutrinos were massless (which means no oscillation), and only electron neutrinos had been detected experimentally. In the years that followed, neutrino oscillation was shown clearly in several experiments, showing a non-zero neutrino mass, and detecting mu and tau neutrinos (while still hard) is doable. The focus now is on mixing angles, mass differences—and ultimately finding the actual mass of each flavor. It’s a good time to study neutrinos, I think.

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15 Responses to “The Flavor of Neutrinos”


  1. 1 bryansanctuary May 18, 2012 at 12:46

    When you talk about mixing angles, it makes me think that neutrions have structure and are not point particles. What is the current consensus and evidence it is a point particle?

    • 2 Matthew R. Francis May 18, 2012 at 18:24

      I think it’s more that there’s no evidence neutrinos are anything but point particles. The way to determine substructure is through scattering—running them into other particles—and there’s no sign they are made up of more fundamental particles.

      The mixing angle is between different neutrino types, and there’s an analogous property for quarks. While a proton is comprised of two up quarks and a down quark, it’s more accurate to say the individual quarks are superpositions of up and down, but each quark type is (to the best of our current knowledge) fundamental. Does this make sense?

      • 3 bryansanctuary May 18, 2012 at 19:46

        Are you saying that these particles are, as superpositions of up and down, simply entangled states? That makes sense. The word “angle” makes me think of structure.

        Can you please define exactly what you mean by “fundamental”?

        Thanks

  2. 4 Pete January 9, 2013 at 11:43

    Hi. I think the Feynman diagram on the far right should have a W+ exchange boson. If I’m mistaken please can you explain why.


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