Abstract

We study the nonlinear QED signature of x-ray vacuum diffraction in the head-on collision of optical high-intensity and x-ray free-electron laser pulses at finite spatiotemporal offsets between the laser foci. The high-intensity laser driven scattering of signal photons outside the forward cone of the x-ray probe constitutes a prospective experimental signature of quantum vacuum nonlinearity. Resorting to a simplified phenomenological ad hoc model, it was recently argued that the angular distribution of the signal in the far-field is sensitive to the wavefront curvature of the probe beam in the interaction region with the high-intensity pump. In this work, we model both the pump and probe fields as pulsed paraxial Gaussian beams and reanalyze this effect from first principles. We focus on vacuum diffraction both as an individual signature of quantum vacuum nonlinearity and as a potential means to improve the signal-to-background separation in vacuum birefringence experiments.

Highlights

  • The fluctuation of virtual particles supplements classicalMaxwell theory in vacuo with effective nonlinear couplings of electromagnetic fields

  • Focusing on slowly varying fields characterized by typical frequencies much smaller than me, quantum vacuum nonlinearities can be reliably studied on the basis of the leading contribution to the Heisenberg-Euler effective Lagrangian LHE [1,2,3,4,5]

  • We study x-ray vacuum diffraction at large offsets between the foci of the pump and probe beams [54]

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Summary

Introduction

Maxwell theory in vacuo with effective nonlinear couplings of electromagnetic fields. Within quantum electrodynamics (QED), the leading nonlinear interaction couples four electromagnetic fields; cf Fig. 1. ÐeħÞ ≃ 1.3 × 1018 V=m and Bcr 1⁄4 Ecr=c ≃ 4 × 109 T, with electron mass me ≃ 511 keV, serve as reference scales for the applied electromagnetic fields. Focusing on slowly varying fields characterized by typical frequencies much smaller than me, quantum vacuum nonlinearities can be reliably studied on the basis of the leading contribution to the Heisenberg-Euler effective Lagrangian LHE [1,2,3,4,5]. In the Heaviside-Lorentz system with units where c 1⁄4 ħ 1⁄4 ε0 1⁄4 1, we have LHE 1⁄4 LMW þ Lint, with classical

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