  We examine the dielectron invariant mass spectrum and the variation of the
polarization asymmetry as a function of that mass in the event generator of the
five-dimensional Bethe-Heitler differential cross section of the conversion of
linearly polarized photons that we have implemented recently as a Geant4
Physics Model. We compare the results obtained with simulated samples to
analytical expressions.
  Studies of $b \to s \gamma$ decays at LHC and Belle II experiments could
provide hints of physics beyond the standard model in flavor-changing neutral
current processes; issues have been reported in the simulation of the
properties of the background induced by genuine $\gamma$-ray conversions in
their detectors. Our results demonstrate that using the five-dimensional model
would help solve these issues.
