Protons are the most stable composite particles in nature. Protons never decay. There are experiments designed to catch decaying protons but proton decay has never been observed.
Electrons are the most stable non-composite particles in nature. Electrons do not have any parts. They are truly elementary.
All composite particles in nature decay into proton, photon, electron, and electron type neutrino which are the stable particles of nature.
It seems that nature wants to return to a simpler state by freeing itself from the complications of compositeness.
The non-composite elementary particles other than the electron such as muons, and tau decay too. They eventually decay into electron or electron type neutrino after few transformations. There are rules for these transformations.
Elementary particles other than electron, photon, electron type neutrino decay too because nature wants to return to a simpler state by freeing itself from the complications of any kind.
Only the massive particles decay (except for electron and proton).
In physics “massive” refers to particle’s “rest mass” which is different from its effective mass. The “rest mass” is the mass of a particle while it is at rest but this is rather hypothetical because particles can never be at rest. They are always moving or wiggling. Even though the “rest mass” is rather hypothetical it can still be measured.
Some elementary particles have no rest mass. Their effective mass which is subject to the gravitational attraction comes from their energy. Gravitational force of very massive stars can bend the light (photons) coming from other stars. This is because the gravitational field acts on the effective mass of the photons.
Photons and gluons are massless particles. Massless means having zero rest mass. Photons and gluons are force carriers. Photons facilitate the electromagnetic force, and gluons facilitate the strong nuclear force. Most force carriers are massless but there are exceptions. The force carriers of the “weak nuclear force”, W and Z are massive.
Neutrinos are special (they do not decay but they oscillate into each other)
Electron type neutrino figures prominently in all discussions of elementary particles. There is a reason for that. Electron type neutrino is as fundamental as the electron.
Until few years ago neutrinos were taught to have zero rest mass. Later, because of the evidence for neutrino oscillations (electron type neutrino turning into muon and tau type neutrinos), the neutrinos are now known to have non-zero rest mass but we don’t know how much. We only have upper limits for the neutrino rest masses.
Neutrino oscillation is very mysterious. If massive particles decay in principle then we should expect the neutrinos to decay. They do but nature has a surprise for us there. The decay of neutrinos is more like a transformation. An electron type neutrino can be turned into an electron under the influence of the “weak nuclear force.” Similarly, the muon type neutrino can transform into a muon, and tau type neutrino can transform into a tau with the help of the “weak nuclear force.” Conceptually, this transformation is different from a decay where the massive particle splits into less massive particles. When an electron type neutrino transforms into an electron the new particle has a higher rest mass. Can the reverse happen? Can we transform an electron into a neutrino?
Neutron is the longest lasting unstable composite particle
Unstable particles (all massive particles other than proton and electron) decay but they have different lifetimes. Neutron is the longest lasting unstable composite particle.
In the nucleus of an atom neutron is as stable as a proton (except in the case of very heavy nucleus containing many protons and neutrons). Free from the nucleus the neutron decays into a proton an electron and electron type antineutrino in 886 seconds on average. The 15 minutes of fame, as it were, is relative eternity in the world of elementary particles with nonzero mass.
Protons do not decay but they can be broken
Protons do not decay naturally but they can be broken. We can split the protons by smashing them against each other with tremendous force. This is what they do in the Large Hadron Collider (LHC) at CERN. The objective is to create a very high energy density in a small volume. In the past century we learned that when we create a stir in the primordial fabric by creating an energy density in a small region of space new particles emerge from the center of that vortex. We also learned that particles can be transformed into each other. There are certain restrictions and rules, but in general, any particle can be turned into pure energy and then from pure energy into another type of particle. At this point in human history, we cannot control the conversion process precisely but we know how to do it in a dirty way.