For a long time, Protons were thought to be stable - that the laws of physics would not allow for a proton (which is baryonic matter) to spontaneously decay into positron and photon (non-baryonic matter) because of conservation of the baryon number. However, it has been recently worked out that the predominance of matter over antimatter in the universe is the result of a very slight imbalance in the ratio that occurred very early in its formation. This imbalance was exceptionally small; something like 1 in every 10,000 particles, but after most of the matter and antimatter annihilated, there what was left over was all the baryonic matter in our current universe. This means that in essence, rather than breaking the law of conservation of the baryon number, proton decay is actually the inevitable mechanism for bringing the baryon number back to equilibrium - correcting, if you will, the original imbalance that made all current matter in our universe possible.
Given a vast period of time (protons are theorized to have a half-life of 1031 years), a proton will decay into a positron and a pion that itself immediately decays to photon in the range of gamma radiation
This process has yet to be proven experimentally, but is predicted by many Grand Unification Theories (see theory of everything)
- Adams, Fred and Laughlin, Greg The Five Ages of the Universe : Inside the Physics of Eternity ISBN 0684865769