This may just be beyond the grasp of the everyman, but I'm trying, and failing, to grasp how conservation of mass-energy works in cases of beta decay and electron capture.
A neutron has a mass of one dalton. The combination of a proton and an electron also has a mass of one dalton. This allows us to assign an overall "mass number" to elements and their specific isotopes. We can say, for instance, that because Carbon-14 and Nitrogen-14 have the same mass number, they have equivalent masses, even though nitrogen has one more proton; it also, in its charge-balanced state, has one more electron than the carbon, and so is equivalent in mass to the carbon atom, just distributed differently.
However, Carbon-14 directly decays into Nitrogen-14 by $\beta^-$ decay of one of its neutrons. The "reactant" is one neutron from the carbon nucleus, and the products are one proton, one electron, and one electron antineutrino. This extra particle, a lepton similar to the electron, is not massless (and mass is an absolute quantity so you can't have "negative mass"), and therefore it would seem that the combined mass of a proton and electron are not in fact equal to that of a neutron.
It gets even weirder when you see it work in reverse. Atoms that have too few neutrons can lower their atomic number by electron capture; the electron is "absorbed" by a proton in the nucleus, forming a neutron, and this interaction results in the emission of an electron neutrino (also not massless).
So, if you were to see a neutron decay to a proton, then capture an electron to become a neutron again, you would have seen it emit a lepton and anti-lepton, both of them having a small but nonzero mass, and yet because a neutron is a neutron, the mass of the particle before these two transformations should be equivalent to the one after.
Obviously I'm missing something. Is there an energy input required (possibly from the neutrino-antineutrino annihilation but it could come from anywhere) that is omitted from the basic nuclear chemistry equations, that because of mass-energy equivalence is re-adding the mass lost as leptons? Is there indeed such a thing as "negative mass", and the mass of the anti-lepton is somehow modified by its spin sign? Or is this a subatomic case of the Second Law of Thermodynamics, and in fact not all neutrons are created equal?