Abstract
We study the photon trident process, where an initial photon turns into an electron-positron pair and a final photon under a nonlinear interaction with a strong plane-wave background field. We show that this process is very similar to double Compton scattering, where an electron interacts with the background field and emits two photons. We also show how the one-step terms can be obtained by resumming the small- and large-$\chi$ expansions. We consider a couple of different resummation methods, and also propose new resummations (involving Meijer-G functions) which have the correct type of expansions at both small and large $\chi$. These new resummations require relatively few terms to give good precision.
Highlights
The strength of a high-intensity laser is usually expressed in terms of a0 1⁄4 E=ω,1 where E is the field strength and ω a typical frequency scale
The OðαÞ processes nonlinear Compton scattering e− → e− þ γ followed by nonlinear Breit-Wheeler pair production γ → e− þ eþ were observed more than two decades ago at SLAC [1]
There the lasers had a0 < 1 and the observation could be explained in terms of perturbative physics
Summary
The strength of a high-intensity laser is usually expressed in terms of a0 1⁄4 E=ω,1 where E is the field strength and ω a typical frequency scale. We use the same methods as we previously used in [15,27] to study the trident and double Compton Those two processes had already been studied in a couple papers, we were able to show that certain terms that had been omitted in the previous literature on the locally constant-field (LCF) regime are crucial for point (2). Our results show that the most complicated terms in all these three second-order processes are closely related Since these replacements involve e.g., changing sign of some lightfront-longitudinal momenta (which are all positive for real particles), these relations cannot be used to directly translate numerical results of e.g., the spectrum in double Compton into results for photon trident.
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