[ISL]

The most-likely explanation for the discrepancy between the methods is systematic uncertainty. I think it will be a rather spectacular surprise if the refined beam measurements continue to disagree with the bottle measurements a decade from now.

If the discrepancy persists, then there really will be a problem.

There is plenty of theoretical speculation, especially in the last couple of years, about what such a discrepancy, if true, might mean. Again, it would be a real surprise, but if neutrons have another decay pathway other than the known one, then the bottle method measures the total decay rate, while the beam method measures the electron/beta-decay rate only.

The emerging state of the art, should this discrepancy persist, will become experiments that measure both channels simultaneously.

[ncmncm]

Discovering a new decay pathway would be quite something. Then you would need to figure out why the beta pathway does not match what the Standard Model wants, and also why it does appear now to match what the Standard Model wants.

Nature seems to love tricks like this: Ha, you thought you understood how something is? Wrong, it just pretends to be like that! It is really much more eldritch, and you are damned. (I.e., the maths are too hard for actual people to work.) Good luck figuring out how it is only pretending to be that, too.