Laser pulse-length effects in trident pair production

Laser pulses facilitate multiphoton contributions to the trident pair production $e_L^{-}\to e_L^{-}+e_L^{-}+e_L^{+}$ , where the label $L$ indicates a laser field dressed electron ($e^{-}$) or positron ($e^{+}$). We isolate the impact of the pulse envelope in the trident S matrix element, formulated within the Furry picture, in leading order of a series expansion in the classical non-linearity parameter $a_0$. Generally, the Fourier transform of the envelope carries the information on the pulse length, which becomes an easily tractable function in the case of a ${\cos }^2$ pulse envelope. The transition to a monochromatic laser wave can be handled in a transparent manner, as also the onset of bandwidth effects for short pulses can be factorized out and studied separately.