PINGU - which neutrino is heaviest?

To continue with a theme from an earlier post - neutrino oscillations, we have learned much about neutrino physics over the past decade.  They have mass, and can oscillate from one into another.  We know the mass differences, and we know the relative oscillation probabilities (mixing angles).  But, there are still a couple of very important open questions:

1) Are neutrinos their own antiparticles?  This would mean that they are a type of particle known as "Majorana particles."

2) Do neutrinos violate CP (charge-parity) conservation?

3) What is the mass of the lightest neutrino?  We know the mass differences, but less about the absolute scale - it is less than of order 1 electron volt, but it could be 0.1 electron Volt or 1 nanoelectron volt.

Experiments to answer these questions are large and difficult, with some proposed efforts costing more than a billion dollars and taking more than a decade to build,. and another decade to collect data 

However, IceCube has pointed the way to relatively cheaply answer the third question.    We can do this by building an infill arrray, called PINGU (Precision IceCube Next Generation Upgrade), which will include a much denser array of photo sensors, and so be sensitive to neutrinos with energies of a few GeV - an order of magnitude lower than in IceCubes existing DeepCore infill array.

PINGU will precisely measure the oscillations of atmospheric neutrinos as they travel through the Earth.  Oscillations happen equally well in a vacuum,  as in dense material.  However, low-energy electron-flavored neutrinos (with energies of a few GeV) will also weakly and collectively scatter from the electrons in the Earth as they travel through it.  This will shift how they oscillate.  Importantly, the shift depends on whether the lightest neutrino is mostly the electron neutrino, or mostly other flavors.  I said 'mostly' here because, although neutrinos are produced as electron-, muon- or tau- neutrinos, because of oscillations, as they travel through they Earth, they travel as a mixture of these states.  But, one of the states is mostly electron neutrinos, and we'd like to know if it is the lightest state or not.  The graphic (top) shows the probability of oscillation vs. neutrino energy and zenith angle (angle that it emerges from the Earth) for the two possible hierarchies.  "Normal" means that the mostly-electron neutrino is the lightest, while "Inverted" means that its not.   The oscillogram is taken from the PINGU Letter of Intent; similar plots have been made by a number of people.

We think that we can make this measurement with another 40 strings of digital optical modules, spread over an area smaller than DeepCore.  Standalone, this will cost roughly $100M (less if it is built in tandem with a high-energy extension for IceCube), and take 3 years of installation.  Data taking will take another 3 years or so.

It is worth pointing out that this measurement will also boost efforts to study question 1 via neutrinoless double beta decay, a reaction in which an atomic nucleus decays by converting two protons into neutrons, while emitting two electrons, and no neutrinos.  The comparable process, two-neutrino double beta decay, involves the emission of two electrons and two neutrinos.  This has been observed, but the neutrinoless version has not. The lack of neutrino emission can be inferred by the absence of missing energy.   The expected rate of neutrinoless double beta decays depends on which neutrino is heaviest, among other things, so knowing the answer to question 3 will help provide a definitive answer to question 1.