What determines the outcome of matter-antimatter collisions?


When I picture a matter-antimatter particle pair interaction, I tend to picture two particles with equal mass but opposite momenta colliding, ‘annihilating’ one another and leaving photons or the energy to form other particles in their place. But if the particles’ energy is conserved and transformed into electromagnetic radiation, how is momentum conserved? Are there always an even number of photons generated and headed at energies and directions that perfectly counterbalance one another? What determines the photons’ frequency or the types of particles that emerge from the energy that remains after a matter-antimatter ‘annihilation’?

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Photons have momentum, and yes, they are generated in pairs with momentum’s that sum to the momentum of the two colliding particles if those are the only particles produced. All particle physics reactions ultimately conserve both energy and momentum. The exact energy of each produced particle may vary, but the sums are always conserved. The type of particles depend on the type of interaction involved, as well as the energy “budget” of the interaction, which is the sum of the particles’ energies. If the energy is enough to make a more massive particle that also participates in the electromagnetic force, it can. The probabilities of such cases are able to be calculated, though the math is not very trivial.