Logically speaking, this seems like an impossible concept to grasp. We see and expect things all things to eventually come to an end, from the mightiest stars to the smallest living things.
How is it possible that certain particles will never, ever lose pieces of their mass or become smaller over time? How can they last forever?
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What we call **_decay_ is always a particle, or several of them, finding a more _stable_ or _more (energetically) favourable_ state**.
For example, a single lonely **neutron decays into a proton**, an electron and an _antineutrino_. This happens because the latter 3 particles altogether add to less energy than the neutron; and are ore stable. We call this betas (minus) decay. Meanwhile, a proton cannot simply decay into a neutron (and maybe some other stuff): that would mean that a neutron is favourable over a proton, but we have just seen that it is the other way around (so much that some extra stuff can be created with the left-over energy).
However, it all depends on situation. **Inside an atomic nucleus, a proton sometimes can decay into a neutron** (plus a _positron_ and a neutrino). This is possible because together with many more protons, it might now be energetically favourable to lose a positive charge for stability. This is beta plus decay.
In general, **decay is always into one or several other things that are more stable and/or favourable** in some way. This satisfies the sane rules seen above, in particular that given the same surroundings, X cannot decay into Y while Y also decays into Y. Ultimately that’s equivalent to there not existing a _perpetuum mobile_: something that moves on its own, forever.
Furthermore, **the speed of decay is faster the more favourable the new state is**. Neutrons decay with a half-life of ~14 minutes. Meanwhile a _muon_, a heavy big brother of the electron, decays into an electron (plus two (anti)neutrinos) very fast. And an atom of uranium-238 takes billions of years. **The general rule is that if it _could_, then it _will_**. This is why some atoms can decay in more than one way, often one being much rarer than the other. There are atoms we suspect to decay veeerrryyy slowly, such as all of tungsten; we never observed the decay for most of its variants
but we expect as there _are_ better states to go to.
So far, this only explains why certain things like proton to neutron don’t happen on their own. Why not… proton to electron? Or proton to positron? Because there are further rules: **all basic physical properties, in particular _charges_, have to be preserved**. With the neutron (0 electric charge) decay we see that the results are a proton (+0), an electron (-0) and an antineutrino (0); plus some energy (). Indeed this matches. Also we always preserve energy (and momentum, and so on), and energy corresponds to mass vie E=mc²; so something cannot get heavier.
A proton has an electric charge of +1, and hence can only decay into things that sum to +1 as well; so definitely no decay into a sole electron, but a positron is still on the table. There are also more charges than just the electric one (with sci-fi-ish names such as _hypercharge_ and _isospin_) and we suspected that there is one more law (“charge”) which would indeed forbid the decay into a positron: **conservation of lepton number**; _leptons_ are electrons, positrons, together with their heavier relatives muon and tauon. We count antiparticles as negative, and then the issue is that proton (0 leptons!) into positron (1 lepton) is impossible.
This all not only explain why proton to only a positron should not happen, it also is why we always had those neutrinos popping up with decay: they balance some further aspects.
Okay, finally we can get to your question. **An electron has effectively nothing to decay to**. Every other elementary particle that involves a negative charge is heavier, so it would take(!) energy to get there. Won’t happen!
**With a proton, it is more difficult**. That conservation of leptons would ultimately imply that protons are stable. But physicists have for some time now conjectured that this is actually no true law, only a guideline. If we involve exotic particles, then it might be possible to decay a proton!
The simplest option left is a **proton decaying into a positron plus a _neutral pion_**. The latter is a particle more typically encountered as part of the forces inside an atomic nucleus, and a particularly weird one: it effectively a pair of something and its antiparticle. Indeed, those two particles almost instantly annihilate each other into light. So we ultimately end up with a proton decaying into a little positron plus light to balance the mass/energy. Just as we suggested before…
Question thus is: does the former decay really happen, **are leptons really preserved?** **We don’t know!**… some deeper theories such as _supersymmetry_ suggest that this one law is indeed fake, and then proton decay _can_ and thus _will_ happen. In the end, we will have to see where the theories and observations lead us to.
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