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

Greger Torgrimsson

doi:10.1103/PhysRevD.102.096008

paper

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

arXiv:2007.08492 · doi:10.1103/PhysRevD.102.096008

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 Weizsäcker-Williams approximation and why it does not agree with the high- $χ$ 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 Padé-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-Padé-conformal methods to resum the small- $χ$ expansion and obtain a high precision up to very large $χ$ . We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions.

arXiv comment22 pages, 10 figures

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

Abstract

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