Probing CP Violation in $h\rightarrow\gamma\gamma$ with Converted Photons

We study Higgs diphoton decays, in which both photons undergo nuclear conversion to electron- positron pairs. The kinematic distribution of the two electron-positron pairs may be used to probe the CP violating (CPV) coupling of the Higgs to photons, that may be produced by new physics. Detecting CPV in this manner requires interference between the spin-polarized helicity amplitudes for both conversions. We derive leading order, analytic forms for these amplitudes. In turn, we obtain compact, leading-order expressions for the full process rate. While performing experiments involving photon conversions may be challenging, we use the results of our analysis to construct experimental cuts on certain observables that may enhance sensitivity to CPV. We show that there exist regions of phase space on which sensitivity to CPV is of order unity. The statistical sensitivity of these cuts are verified numerically, using dedicated Monte-Carlo simulations.