Pair annihilation in laser pulses: optical vs. XFEL regimes

We discuss the theory and phenomenology of pair annihilation, within an ultra-short laser pulse, to a single photon. The signature of this process is the uni-directional 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 XFEL parameters admitting a much clearer signal than optical beams.