- Discussion of free neutron lifetime, branched off from proton radius thread
The neutron lifetime? It's not settled even now ;-)). I think it's also in the above quoted history plots in the PDG Review of Particle Physics.
I'm splitting this off the proton radius thread.
The first measurements of the neutron lifetime worked as follows: you get a nuclear reactor as a neutron source and open a port in it to get a beam of neutrons. You count the number of neutrons in the beam and the number of protons (from neutron decay) in the beam and from that infer the neutron lifetime. Because you don't see every proton produced in neutron decays, the key to this measurement is understanding how many protons you saw vs. how many you missed. In 1951 the technique was refined by looking at proton-electron coincidences, and the first measurements came out around 1100 +/- 200 s.
The next major improvement was Christensen et al. in 1971, which used a clever geometry to reduce the acceptance systematic errors of the earlier generation. They got 918 +/- 14s. You can see the error bars (and central value) drop like a stone in 1971.
Since then, these experiments have gotten more and more sophisticated. To avoid gamma ray backgrounds, which are a problem in Christiansen-type measurements, protons are trapped and then counted. Lifetimes for the best of the measurements are around 888 +/- 2.something s. They are limited not so much by the counting of protons, but by the counting of neutrons in the beam.
That's the "beam" method.
The "bottle" method is conceptually simpler. You get some ultracold neutrons. You count them and put them in a container. You wait. You count them again. Now calculate the lifetime. Instead of a proton appearance experiment, you have a neutron disappearance experiment. Perhaps more importantly, you are fairly immune to miscounting, since the numbers cancel in the ratio. The world average for such measurements is about 880 +/- 1 second. However, later measurements are higher and have larger errors: this is really driven by the 2005 measurement at NIST.
The problem with this kind of experiment is neutrons "leaking" out of your bottle. They can interact with the bottle walls, or thermal motion can cause them to go out the top, and so on. Experiments work hard to minimize this, count what they can't minimize and adjust their geometries and extrapolate to a "perfect" one to make sure all these effects are accounted for.
From a theoretical point of view, Grinstein et al. made the observation that if a neutron had a decay channel that did not involve a proton, it would give you exactly the effect seen: proton appearance experiments would give a longer lifetime the neutron disappearance experiments. The 1% discrepancy we see could be accounted for by having 99% of the neutrons decaying normally and 1% decaying through a proton-free process. That number is small enough not to be excluded by other measurements.
From an experimental point of view, if there is some mistake, where is it likely to be? In the beam experiments, it's losing a proton with noticing, and it the bottle experiments its losing a neutron without noticing. Those would tend to bias the beam experiments high and the bottle experiments low. That's what we see.