Abstract
The laser intensity dependence of nonlinear Compton scattering is discussed in some detail. For sufficiently hard photons with energy ω′, the spectrally resolved differential cross section dσ/dω′| ω′=const, rises from small toward larger laser intensity parameter ξ, reaches a maximum, and falls toward the asymptotic strong-field region. Such a rise and fall of a differential observable is to be contrasted with the monotonously increasing laser intensity dependence of the total probability, which is governed by the soft spectral part. We combine that hard-photon yield from Compton scattering with the seeded Breit–Wheeler pair production in a folding model and obtain a rapidly increasing e + e − pair number at ξ ≲ 4. Laser bandwidth effects are quantified in the weak-field limit of the related trident pair production.
Highlights
Quantum Electro-Dynamics (QED) as pillar of the standard model (SM) of particle physics possesses a positive β function [1] which makes the running coupling strength α(s) increasingly with increasing energy/momentum scale s [2]
In doing so we remind the reader of the subtle Ritus notation probability upon u-integration,4 i.e. the celebrated result P ∝ αχ2/3 in Ritus notation [58], while the hard u-part I> in Eq (13) is at the origin of Eq (6) when converting to cross section
We employ the formalism in [79] and its numerical im- ular, we focus on the ξ dependence
Summary
Quantum Electro-Dynamics (QED) as pillar of the standard model (SM) of particle physics possesses a positive β function [1] which makes the running coupling strength α(s) increasingly with increasing energy/momentum scale s [2]. The Ritus-Narozhny (RN) conjecture [6,7,8,9,10] argues that the effective coupling becomes αχ2/3, meaning that the Furry picture expansion beaks down at αχ2/3 > 1 [11,12,13,14] (for the definition of χ see below) and one enters a genuinely non-perturbative regime The latter requires adequate calculation procedures, as the lattice regularized approaches, which are standard since many years in QCD, e.g. in evaluations of observables in the soft sector where αQCD > 1, cf [15]. The latter requires adequate calculation procedures, as the lattice regularized approaches, which are standard since many years in QCD, e.g. in evaluations of observables in the soft sector where αQCD > 1, cf. [15]. (In QED itself, an analog situation is meet in the Coulomb field of nuclear systems with proton numbers Z > Zcrit ≈ 173: if αZcrit > 1 the QED vacuum beak-down sets in; cf. [16] for the actual status of that field)
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