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General formulation in the realm of strong-field quantum electrodynamics isprovided for a process that occurs in the presence of a train of laser pulsesand, in the tree level, is represented by a two-vertex Feynman diagram withexchange of a virtual photon. A scheme of retrieving resonances in thecorresponding probability distributions is also formulated in these generalsettings. While the presented formalism is applicable to a variety of processeslike electron-positron pair creation and annihilation, M\"oller scattering,Bhabha scattering, etc., we illustrate it for a trident process. Specifically,we consider electron-positron pair creation in the muon--laser-fieldcollisions. We demonstrate that the probability distributions exhibitintegrable singularities close to the threshold of pair creation. Also, avariety of resonances is observed that originate from the poles of the Feynmanphoton propagator. While those resonances are, in general, obscured by strongquantum interferences, we show that they can be isolated by changing thecarrier envelope phase of the driving laser pulses. In that case, whiletransformed into the Lorentz-Breit-Wigner shape profile, the resonance positionand width can be determined.

Trident pair creation by a train of laser pulses: Resonance, threshold, and carrier envelope phase effects