Why must an electron-positron collision produce gamma rays?

[animagaletix]

Or, more specifically, what determinates the frequency of the photons emitted by a such a collision. I know that the number of photons produced depends on the spin and energy states of the initial particles.

 

[mfb]

Energy and momentum conservation.

The collision does not have to produce gamma rays, other products are possible if the energy is sufficient, and elastic scattering is always possible.

 

[mathman]

If the particles are going at relatively low speeds, then the annihilation will result in a pair of photons at 511 kev.

 

[snorkack]

Energy and momentum conservation.

And spin and parity.
Which does not determine branching fractions between equally allowed processes.

The collision does not have to produce gamma rays, other products are possible if the energy is sufficient,

There is always enough energy to produce neutrino/antineutrino pairs, of three flavour options, or gravitons.

 

[mfb]

With tiny branching fractions, yes (especially for the gravitons).
Decays of Positronium - 10^-18 for electron neutrino + antineutrino, even lower for the other flavors.

 

[mathman]

http://en.wikipedia.org/wiki/Electron–positron_annihilation

Above is short answer.