Three days ago, the Quanta Magazine published a playful simple article on particle physics

Neutron Lifetime Puzzle Deepens, but No Dark Matter SeenThe neutron's lifetime is some 15 minutes but there seems to be a cool, increasingly sharp discrepancy. If you measure how many neutrons are left in a "bottle" after time \(t\), it seems that there's one decay in 14:39 minutes. But if you measure a neutron "beam" and the protons that appear, it seems that they're being converted at the rate of one new proton per 14:48 minutes.

*This neutron's logo is actually from some cryptocurrency network.*

So the neutrons are apparently decaying about 1% faster than the protons are born. No other decays of neutrons are known. Relativistic effects for the beam are negligible.

If this discrepancy is real, there seems to be 1% of the neutron decays that go to something else. One month ago, a paper by Bartosz Fornal, Benjamin Grinstein promoted the idea that the neutron could very well decay to new, invisible particles.

The decay would be\[

n\to \chi\gamma

\] where \(\chi\) is a new, dark, spin-1/2 fermion, and \(\gamma\) is a photon. The mass of \(\chi\) has to be just a slightly smaller than the neutron mass – a coincidance ;-) needed to avoid some sick decays in nuclear physics – and the photons \(\gamma\) from such decays must have a completely universal, fixed energy (calculable from the \(\chi\) mass) which is a universal constant that may a priori belong to an interval and is of order \(1\MeV\).

In the effective Lagrangian, the decays are enabled by the quadratic and cubic terms \(\bar n \chi\) and \(\bar n \chi \gamma\), i.e. by a neutron-newfermion mixing; and by a cubic interaction that looks like the mixing with the extra photon (you need the photon to be represented by the whole \(F_{\mu\nu}\) in this cubic term, not just \(A_\mu\), by gauge invariance). So for a while, by the mixing interaction, the neutron changes to a virtual \(\chi\), and the \(\chi\) decays to a real neutron \(n\) and a real photon \(\gamma\).

The authors claim that such a model is consistent with everything we know.

One week ago, an experimental preprint claimed that they're sure that these photons of energy comparable to \(1\MeV\) don't exist so the theory is ruled out.

Well, maybe the visible photon among the decay products should be replaced with some dark boson as well? ;-) At any rate, it's an intriguing anomaly and an equally attractive (albeit obvious) strategy to explain it.

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