Limitations of the paraxial beam model in the study of quantum vacuum signals

Studies of nonlinear quantum vacuum signals often model the driving laser fields as paraxial beams. This in particular holds for analytic approaches. While this allows for reliable predictions in most situations, there are also notable exceptions. A prominent example is the overestimation of the polarization-flipped signal photon yield in the collision of two equally focused, parallel polarized laser beams by a factor of about 6. In the present work, we identify the origin of this deficiency and devise a strategy to obtain accurate closed-form expressions also in cases challenging the conventional (leading order) paraxial beam model. We demonstrate the potential of our approach on the example of two linearly polarized laser pulses colliding at a generic collision angle.