Pair annihilation in laser pulses: Optical versus x-ray free-electron laser regimes

We discuss the theory and phenomenology of pair annihilation, within an ultrashort laser pulse, to a single photon. The signature of this process is the unidirectional emission of single photons with a fixed energy. We show that the cross section is significantly larger than for two-photon pair annihilation in vacuum, with x-ray free-electron laser parameters admitting a much clearer signal than optical beams.