# Laser pulse-length effects in trident pair production

## TL;DR

This paper investigates how the length and shape of laser pulses influence the trident pair production process, highlighting the role of pulse envelopes and bandwidth effects within a quantum electrodynamics framework.

## Contribution

It isolates the impact of laser pulse envelopes on trident pair production using a Furry picture approach, providing a clear analysis of pulse length effects and bandwidth phenomena.

## Key findings

- Pulse envelope Fourier transform encodes pulse length information.
- Monochromatic limit can be derived transparently.
- Bandwidth effects for short pulses can be separated and studied.

## Abstract

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.