  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 spatio-temporal 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.
