# Atmospheric Neutrinos, Redux

To go into a bit more detail about atmospheric neutrinos than in my previous post, let’s start with a detector at Earth’s surface:

Now consider a downward neutrino of energy E at a zenith angle θ. We’re considering long (on geological scales) baseline oscillations, so this neutrino has an oscillation baseline that is effectively 0. If we consider an upward neutrino at the equivalent zenith angle, the neutrino now has to go through a significant chunk of the planet. It’s baseline is basically 2Rcosθ, where R is the radius of Earth. We can also see that the upward going neutrino still has the same zenith angle with respect to the surface when it first leaves the atmosphere and enters the planet.

If we assume a perfectly spherical Earth and an isotropic cosmic ray flux, the fact that both neutrinos hit the surface at the same angle is very important. It means that the two sources of neutrinos have the same flux as seen by our detector. So, if no oscillations happen, the ratio of upward to downward neutrinos is unity, even if we look at them as functions of energy and direction.

If there are neutrino oscillations, we will instead see the ratio evolve as a sinusoid in (cosθ/E):

$\frac{R_{\rm up}(E,\theta)}{R_{\rm dn}(E,\theta)} = \sin^2(2\Theta)\sin^2\left(\frac{R\Delta m^2 \cos\theta}{2E}\right)$

If we add in units, this becomes

$\frac{R_{\rm up}(E,\theta)}{R_{\rm dn}(E,\theta)} = \sin^2(2\Theta)\sin^2\left(1.62\times10^4\frac{\Delta m^2 \cos\theta}{E}\right)$

where E is in GeV and Δm2 is in eV2. We can then readily see that, for example, for a pretty typical angle of cosθ=0.5 and E=10 GeV, we should be sensitive to a mass splitting of order 10-3 eV2 or so with a pretty modest dataset. The actual splittings are all reasonably close to this, so atmospheric neutrinos are useful in studying some types of oscillations.

In reality, things are a bit more complicated than this. There are in fact three types of neutrinos that we know about, so we have to consider that there are multiple neutrino mixing angles and neutrino mass splittings if we want to be more rigorous.

The initial neutrino flux also isn’t just a single type of neutrino. Muon neutrinos as well as muon antineutrinos will be the predominant types of neutrino created in cosmic ray showers, but there will still be electron neutrinos generated by muon decays in flight, decays of heavier mesons and hadrons (you can also get tau neutrinos from some of these), and even from a small fraction (about 0.01%) of pion decays.

Furthermore, Earth isn’t completely spherical and the cosmic ray flux is probably not completely isotropic, so there will be slight differences due to that. The effect of oscillations is pretty large, so probably these would only affect precision measurements but would have basically no bearing on an attempt just to see if there are oscillations. (Actually, I don’t know if these things even have any real effect on current experiments).

Finally, matter does affect how neutrinos oscillate. In particular, electron neutrinos have an effective mass change due to their extra interactions with electrons (readily found in matter) that other neutrinos don’t have. This means that the mixing parameters are all somewhat different depending on the density of the matter.

In the end, if you really want to make a precise measurement with atmospheric neutrinos, it’s probably best to come up with some simulation to account for any effects that might be large enough to be seen in your experiment.

# What Are Atmospheric Neutrinos?

Returning to the subject of the Nobel Prize, you might be wondering what the physics prize this year was actually about.

What matters for these experiments is (1) neutrino flavor, (2) neutrino baseline (distance traveled from being in a more or less known flavor configuration) and (3) neutrino energy. Atmospheric neutrinos are one of the several different ways that we can study oscillations.

High energy particles coming in from space (i.e. cosmic rays) are generally nuclei (most often just protons). Upon reaching the atmosphere, these particles often have enough energy to undergo inelastic collisions with the particles in the atmosphere. The most common types of events would be hadronic showers, where the strong force allows for more hadrons to be created. The most common hadrons created in showers are pions, which are the lightest mesons (bound quark-antiquark states). Charged pions decay through the weak force into neutrinos and charged leptons. It turns out that pions decay to muons and muon neutrinos well over 99% of the time. Thus, cosmic rays create muon neutrinos (and antineutrinos) within the atmosphere. Typical energies are also much higher than is found in nuclear processes, so atmospheric neutrinos can be distinguished from solar and beta decay neutrinos.

Because neutrinos don’t really interact much with anything else, cosmic ray neutrinos can also pass straight through Earth. If a neutrino detector can reconstruct the direction of the neutrino, it can then look for short baseline neutrinos (from above) and long baseline neutrinos (from below). A pretty broad energy spectrum is also found. It also happens that neutrino oscillations (in a simplified two-neutrino case) evolve like:

$P(\nu_\ell\rightarrow\nu_{\ell'})\propto \sin^2 \frac{\Delta m^2 L}{4E}$

Theshape of the oscillations depends on the mass splitting and on the ratio of baseline to neutrino energy. If the mass splitting is too small, then not enough oscillations will happen to measure them. If the mass splitting is too large, the oscillations will be happening so fast that any realistic detector will just measure the unoscillated spectrum with an extra scaling constant of 1/2.

Fortunately, it just so happens that one of the mass splittings relevant to a sample of nearly pure muon neutrinos leads to oscillations that are readily measurable to the GeV-scale atmospheric neutrinos. So, the oscillations should be apparent if one looks at the ratio of the upward-going (long baseline/oscillated) neutrinos to downward-going (short baseline/unoscillated) neutrinos. A characteristic sinusoidal shape should be seen if this ratio is plotted as a function of L/E. This allows for precision fits of oscillation parameters using atmospheric neutrino data.

# 2015 Nobel Prize Goes to Neutrinos

Earlier today, it was announced that the 2015 Nobel Prize in Physics has been awarded to Takaaki Kajita and Arthur McDonald for their work on neutrino oscillations. Kajita received the prize for work on Super-Kamiokande and McDonald for the Sudbury Neutrino Observatory (SNO). There have already been several neutrino-related Nobel Prizes, but this one honors the experiments that definitively showed that neutrino oscillations really do exist. Both experiments found evidence of neutrino oscillations in atmospheric neutrinos, created in showers caused by high energy particles interacting with air high in the atmosphere.

# Nobel Laureate Charles Townes Dies

In sad news, Charles Townes died on Tuesday. Townes is one of the people credited for helping invent the laser, without which many important pieces of technology could not exist. He helped build the first maser (the microwave equivalent of the laser) at Columbia in the 50s and was awarded the Nobel Prize along with two others in 1964. He also spent some time serving as provost of MIT.

# Physics Today on the Nobel Prize

Physics Today has a short article on the work that led to this year’s Nobel Prize. This isn’t something that I know very much about, so I’ll leave the explanation to them. A very short summary is that the development of blue LEDs took much longer than red and green and (not surprisingly) came down to finding the right materials and the right production techniques.

# Physics Nobel Prize

The winners of this year’s Nobel Prize in physics were announced a few hours ago. The prize went to three Japanese physicists for their work in developing blue LEDs, which apparently could have some nice properties in the future. I don’t think this was a very high profile topic that many people expected would win the prize. The committee mentions that this choice was motivated at least in part by the potential good LED technology could do in the future rather than basing the award on importance to physics research.

# Slate on Women Who Deserve a Physics Nobel

The announcements of this year’s Nobel Prizes have already begun. The physics prize is expected to be announced within the next day or so.

Slate has an article naming some women who they think would deserve a Nobel Prize in physics. The prize has only gone to men for the past 50 years. Among the people they mention are Vera Rubin, who pioneered the use of galaxy rotation curves to find one of the most  important pieces of evidence for dark matter, and MIT professor Millie Dresselhaus. Realistically, Rubin likely won’t have much of a chance of winning until someone makes a definitive discovery of dark matter and even then, there are many people who might have a shot at a piece of a dark matter prize.

There are probably a lot of reasons why the prize has only gone to men for the last 50 years, but I would guess that they largely stem from the large gender imbalance within the field, particularly at higher level positions and among older physicists who are most likely to win the prize. Prizes often go to lab heads and PIs, who aren’t necessarily (and probably usually aren’t) the ones who actually do the most important parts of the work. According to the article, the fraction of women who get PhDs in physics  in the US has increased about tenfold since the 60s (to 20%, which is still one of the lowest numbers in major academic fields). Similar increases have probably occurred in many other countries, so we may start seeing more women winning the prize as more women become PIs.