Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field and resummations

TL;DR

This paper investigates the nonlinear trident process in high-energy laser fields, revealing the dominance of one-step contributions at high energies, exploring nonlocal effects, and applying advanced resummation techniques for accurate predictions.

Contribution

It introduces new approximations linking high-energy trident to Coulomb pair production, analyzes nonlocality in next-to-leading order, and develops resummation methods for better convergence.

Findings

One-step process dominates at high energies.

Resummation methods improve convergence beyond perturbative series.

Nonlocal effects are significant in high-energy limit.

Abstract

We study nonlinear trident in laser pulses in the high-energy limit, where the initial electron experiences, in its rest frame, an electromagnetic field strength above Schwinger's critical field. At lower energies the dominant contribution comes from the "two-step" part, but in the high-energy limit the dominant contribution comes instead from the one-step term. We obtain new approximations that explain the relation between the high-energy limit of trident and pair production by a Coulomb field, as well as the role of the Weizs\"acker-Williams approximation and why it does not agree with the high-$\chi$ limit of the locally-constant-field approximation. We also show that the next-to-leading order in the large-$a_0$ expansion is, in the high-energy limit, nonlocal and is numerically very important even for quite large $a_0$. We show that the small-$a_0$ perturbation series has a finite radius of convergence, but using Pad\'e-conformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the large-$a_0$ approximation. We use Borel-Pad\'e-conformal methods to resum the small-$\chi$ expansion and obtain a high precision up to very large $\chi$. We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions.