The neutron is a bit of a headache for physics. A neutron is an electrically neutral particle that helps glue protons together in the nucleus of atoms. Inside the atom, it is happily stable.

But a neutron alone is an unhappy beast. After about 10 minutes, it will emit an electron and an antineutrino and turn into a proton. The decay is all good, but there's a problem with the "about 10 minutes" part of things. In one set of experiments, we have determined that the half-life of a lonely neutron is 879.6s. But, in another set of experiments, we’ve found that the neutron has a half-life of 888s (these numbers might be slightly out of date now). The chance of these two being different by accident is now about one in 100,000.

One possible explanation for the difference is that a subset of neutrons decays to a relatively light particle of dark matter. Now, a pair of papers has punctured that proposal.

Maybe it’s physics, not the experiment?

What is the difference between the two experiments? The method that finds the shorter half-life counts the number of neutrons in a bottle after an elapsed time. The second experiment counts the number of protons emitted by a beam of neutrons. The beam method would not count neutrons that did not decay to a proton.

As the certainty in the difference grows, so does pressure to find an explanation. One possibility is that sometimes neutrons decay into a baryonic dark matter particle. Baryonic just means that the dark matter particle belongs in the same class of particles as protons and neutrons, rather than the groups that contain electrons and neutrinos or light. If the particle was electrically neutral and weakly interacting, we wouldn’t detect it by accident in either experiment. The proton-emission-counting technique would miss this decay channel entirely, since it doesn't make a proton. Hence we would expect a difference in measured half-life.

To fit this idea into the world around us, we know that the new dark matter particle has to be heavy enough to cope with the observed stability of isotopes (an element has a fixed number of protons but can differ in the number of neutrons—these are called isotopes) and the stability of the proton. Apart from the mass of the dark matter particle, the process that creates it has to be quite rare, or we would observe a completely different half-life for the neutron.

Therein lies the problem. The decay from neutron to a dark matter particle must be rare and the dark matter particle so difficult to detect that we wouldn't expect to see it by accident in any of our experiments. Which also means we would have a hard time seeing it if we tried to find it.

Conveniently, there is a place where there are enough neutrons around that any particles they produce should be obvious. Neutron stars are filled with neutrons that are banging on each other a lot. Under reasonable circumstances, we might expect neutrons decaying to dark matter to affect the properties of neutron stars.

The Universe is our laboratory

This is exactly what two groups of researchers have investigated. Using neutron star models, they've calculated the mass range of neutron stars, taking into account the possibility of neutrons decaying to dark matter.

Stars, it probably doesn’t need to be said, are pretty complicated objects. But neutron stars are the least complicated of all stars. Neutron stars are very dense, having about a solar mass in a sphere just a few kilometers across. If a star remnant is too light, then it cannot form a neutron star and instead ends its life as a white dwarf. At about three solar masses, no one is really sure what happens. Above ten solar masses, the remnant clearly collapses to a black hole. Observationally, we don’t observe neutron stars with less than one solar mass, and we’ve not found any neutron stars much heavier than two solar masses.

This nice, tight mass range—combined with the comparative simplicity of neutron stars—means that adding a neutron decay path into a neutron star doesn’t require too many assumptions. The resulting calculation allows for pretty good predictions for how this will change the mass range for which neutron stars will form.

It turns out that dark matter causes more problems than it fixes—at least for low-mass dark matter. Adding dark matter with mass up to 1.2GeV renders neutron star models incompatible with observations, effectively eliminating that possibility.

To make dark matter, the solution requires the Universe to perform some gymnastics. First, any single dark matter particle has to have just the right self-repulsion to generate neutron stars with the right mass range. Another option is that dark matter has some form of charge (a “dark” equivalent of electrical charge), but a property like that would imply that there is a whole zoo of dark matter particles out there that play with each other but not with us. The idea of multiple dark particles has been considered—it's often called "the dark sector"—but there's no experimental evidence for it at the moment.

When all is said and done, it seems to me that decay to dark matter is less likely than a systematic difference between the two experimental techniques. I suspect that something like adding a proton counter to the bottle experiment, for instance, will show that the systematic difference between the two experiments is real. I also suspect that the systematic difference will be instrumental and not due to neutrons behaving in an unexpected way.

Physical Review Letters, 2018, DOI: 10.1103/PhysRevLett.121.061801, 10.1103/PhysRevLett.121.061802, (About DOIs).