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The process of electron-positron annihilation into two photons in thepresence of an intense classical plane wave of an arbitrary shape isinvestigated analytically by employing light-cone quantization and by takinginto account the effects of the plane wave exactly. We introduce a generaldescription of second-order 2-to-2 scattering processes in a plane-wavebackground field, indicating the necessity of considering the localization ofthe colliding particles and achieving that by means of wave packets. We definea local cross section in the background field, which generalizes the vacuumcross section and which, though not being directly an observable, allows for acomparison between the results in the plane wave and in vacuum without relyingon the shape of the incoming wave packets. Two possible cascade or two-stepchannels have been identified in the annihilation process and an alternativeway of representing the two-step and one-step contributions via a "virtuality"integral has been found. Finally, we compute the total local cross section toleading order in the coupling between the electron-positron field and thequantized photon field, excluding the interference between the twoleading-order diagrams arising from the exchange of the two final photons, andexpress it in a relatively compact form. In contrast to processes in abackground field initiated by a single particle, the pair annihilation into twophotons, in fact, also occurs in vacuum. Our result naturally embeds the vacuumpart and reduces to the vacuum expression, known in the literature, in the caseof a vanishing laser field.

Electron-positron annihilation into two photons in an intense plane-wave field