As you may already know, nucleons are made of quarks; protons (uud) and neutrons (udd) were the masses are 938.3 MeV and 939.6 MeV, respectively. The key point is that the majority of the nucleon mass comes from quark interactions.
To see this, consider the following points:
if you were to mass a “free” up or down quark, they would have a mass of only a few MeV.
if you restricted these quarks to within the nucleus (about 10^(-15) m), they would have masses on the order of several hundred MeV. Memory tells me somewhere on the order of a few hundred MeV (300-400 MeV). This is derived from the zero point energy for 10^(-15) m well.
So to account for the missing 600-700 MeV, one has to look at the quark interactions within the nucleons. And the current ability to calculate this (via QCD) is currently beyond our theoretical abilities.
So to say that the nucleons have different masses because of the differences in the masses of the neutrinos, is not correct. The majority of the nucleon masses comes from quark interactions!
If we take a native model to try to explain the differences in mass, the down quark is a few MeV more massive than the up quark (no one knows why). Because of the zero point energy of being trapped within a distance of 10^(-15) m, each nucleon should each have a mass of around 1 GeV. So the only difference between the proton and neutron will be on the order of MeV, and this difference can be thought of as a result of
• the differences between the proton (udu) and neutron (udd) is that the has neutron’s second down quark is heavier than the proton’s second up quark. So the greater mass of this down quark gives the neutron a greater mass than the proton.
• the electrostatic forces among two ups and a down (proton) will differ from those between those two downs and an up (neutron).
So the instability of the neutron (beta decay) is due to it having a slightly greater mass than the proton. And as the saying goes, nature always seeks the lowest state of energy (mass).