Can an electron "annihilate" with something other than a positron? Processes like the electron-positron annihilation are widely known and they give us the impression that "matter annihilates with antimatter." However, I am wondering if this repeated phrase holds for other kinds of reactions.
Can an electron and an antimuon annihilate each other into photons? If not photons, can they annihilate into other particle species? If yes, how is the process different from the electron-positron annihilation? How is it similar?
Clearly the lepton flavor number wouldn't be conserved if they annihilate into photons, so the weak interaction would have to be involved, but what exactly are the processes?
 A: Yes, although this is fairly complicated. Lepton number symmetry is an anomalous symmetry of the Standard Model, which means that while it holds in the classical theory, it does not hold at the quantum level (Wikipedia mentions this). Hence, there are quantum processes that violate lepton number conservation, but I only know of this happening non-perturbatively in processes involving instantons and sphalerons. At ridiculously high energies (read: beyond the LHC) it is theorized within the Standard Model that you might get, for example, a proton and an electron annihilating into $W$ bosons through a non-perturbative process. Shifman's Advanced Topics in Quantum Field Theory has a discussion about this in Chap. 5.
This is fairly different than electron-positron annihilation. Electron-positron annihilation is something that happens at tree level, which means it is relatively common. This electron-proton annihilation, on the other hand, is an extremely suppressed effect that is expected to happen in the conditions of the primordial universe.
As for electrons and antimuons annihilating into bosons, I don't recall hearing anything about this. Since flavor symmetry is only an approximate symmetry (as noted by Wikipedia), I wouldn't be surprised if something like that exists—in QM, anything that isn't forbidden is mandatory. However, I can't think of an exact process.
A: No. Particle annihilation is usually understood as a reaction of particle and anti-particle to leave only photons (possibly virtual) bosons, most probably photons. https://en.wikipedia.org/wiki/Annihilation
