Exact results for scattering on ultrashort plane wave backgrounds

Abstract

We give exact results for the emission spectra of both nonlinear Breit-Wheeler pair production and nonlinear Compton scattering in ultra-intense, ultra-short duration plane wave backgrounds, modelled as delta-function pulses. This includes closed form expressions for total scattering probabilities. We show explicitly that these probabilities do not exhibit the power-law scaling with intensity associated with the conjectured breakdown of (Furry picture) perturbation theory, instead scaling logarithmically in the high-intensity limit. I. INTRODUCTIONThe coupling of matter to a background field can be arbitrarily strong, requiring non-perturbative methods in the calculation of scattering amplitudes on the background. Highly symmetric backgrounds such as electromagnetic plane waves [1][2][3], widely used as a first model of intense laser fields [4][5][6][7], may be treated exactly for arbitrarily high field strength, allowing a great deal of analytic progress to be made in the calculation of scattering amplitudes.However, the evaluation of observables still requires intense numerical integration. While various results have been found which allow more efficient calculation [8][9][10], it would be desirable to have exact results when confronting questions of a fundamental nature, such as the limits of perturbation theory in the high intensity regime; it has been conjectured that (Furry picture [11]) perturbation theory in strong fields breaks down for sufficiently high field strengths, due to a power-law scaling of higher loop processes [12][13][14][15][16]. If true, this would invalidate current perturbative or semi-perturabtive approaches to QED in strong backgrounds [17,18].Here we have two objectives. The first is to provide some exact results for scattering on ultra-short plane wave pulses. This includes closed-form expressions for total probabilities. Our second objective is to investigate the highintensity scaling of these results in light of the conjectured high-intensity breakdown. The model on which this conjecture is based, and the starting point for many investigations of laser-matter interactions, assumes the laser fields may be treated as constant and homogeneous [4]. We consider here the opposite limit in which the field is of infinitely short duration, being modelled as a sequence of delta function pulses. This will allow us to provide exact results: see also [19] for the use of delta pulses, in combination with constant fields, to Schwinger pair production, where exact results are also obtained.This paper is organised as follows. In Sect. I A we review some necessary structures of QED scattering in plane wave backgrounds. In Sect. II we consider stimulated pair production in a delta-function pulse. Both the differential emission spectra and the total pair creation probability are obtained in closed form, with all integrals performed. We show that the high-intensity scaling of the probability is logarithmic, not power law. We then consider the case of two delta function pulses modelling an oscillating f...

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“…However, the spin can also change in a nonradiative way, through quantum loop effects [20][21][22]. (See [23][24][25][26][27][28][29][30], also [31][32][33][34], for investigations of higher loop orders in strong fields, which has recently seen renewed interest.) It has been suggested to include nonradiative spin changes in numerical codes, using the Bargmann-Michel-Telegdi (BMT) equation [35][36][37].…”

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“…The conjecture is based on the special case of a constant "laser" field, and it is known that the associated scaling does not appear for general fields [25], nor does it hold at high energy [26,27].…”

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