# Measuring Bilbo

How do you measure the properties of something that’s really hard to detect? It turns out that because of the wonderful usefulness of conservation laws, you can infer what you can’t easily see by finding as much as you can from what you can detect, and then figuring out what’s left over. Somewhat like detecting the invisible Bilbo Baggins by spotting his shadow. The original discovery of the neutrino, in fact, was due to the beta energy spectrum being continuous, which only makes sense if there is a third particle being emitted, and conservation of charge dictated that the neutrino be neutral.

Ultra-Cold Atoms and Neutrino Masses

The proposed experiment is to trap a large amount of tritium at very low temperatures (meaning that the atoms are very nearly stationary), and look at the recoil of the helium that’s produced. When the tritium decays into helium, one of two things happens: either the helium captures the electron on the way out, becoming neutral helium, in which case the atom recoils in a direction opposite the direction of the neutrino; or the electron and neutrino both escape, in which case the helium ion recoils in a direction that depends on the exit direction of both the electron and the neutrino. In either case, the helium is moving, and if everything is done right, it’s moving considerably faster than the trapped tritium atoms.

To measure the neutrino mass, then, all you need to do is detect the helium and measure both the magnitude and direction of its velocity. If the electron was captured, that alone is enough to let you find the momentum (and thus mass) of the neutrino; if the electron escaped, you need to determine its velocity as well, but again, you can calculate the momentum of the neutrino.

Unfortunately the link to the Physics World article doesn’t work work for me, since it’s subscription-only. Fortunately Chad also provides a link to the ArXiv proposal

This sounds very familiar to me, since measuring the recoil from beta decay is the experiment I worked on as postdoc at TRIUMF. The idea in that experiment (for a metastable K-38 atom decaying to Ar-38, both with zero-spin nuclei) is that the parent decays and the daughter is no longer held in the trap, so the escaping beta and daughter can be detected. If the beta and Ar have traveled in opposite directions, it means the neutrino must be either counter-propagating or co-propagating with the beta, since there has been no change in the spin of the nucleus; this has implications for the type of weak interaction that has taken place (scalar or vector, i.e. does the W-boson have any spin) but each case has a different implication for the amount of recoil the Ar atom will have, and this shows up in the time-of-flight. The standard model predicts that, in this case, the beta and the neutrino will be emitted in the same direction. Here’s a PRL and ArXiv for that experiment.

In one approach of the Tritium experiment they’re banking on the electron being captured, so you remove the three-body complication, and having a metastable helium recoil to detect (rather than neutral Helium, which is a lot harder), but adding the complication of photons to detect as the He decays into that metastable state. The other approach involves the three-body momentum, in which the emitted beta is not captured. This allows them to detect a Helium ion, which is much easier to do.