The photon polarization in radiative $D$ decays, phenomenologically

We work out the phenomenology of untagged time-dependent analysis with radiative $D^0$-decays into CP eigenstates, which allows to probe the photon polarization by means of the charm mesons' finite width difference. We show that $D^0 \to \phi \gamma$ or $D^0 \to \bar K^{0 *} \gamma$ decays, which are SM-dominated, or SM-like, respectively, together with U-spin allow to obtain chirality-predictions for radiative decay amplitudes. The order of magnitude of wrong-chirality contributions in the SM can be cross-checked with an up-down asymmetry in $D^0 \to \bar K_1^0 (\to \bar K \pi \pi) \gamma$. We explore the sensitivity to new physics in $|\Delta c|=|\Delta u|=1$ dipole couplings in the decays $D^0 \to \rho^0 \gamma$. We point out the possibility to test the SM with $D_s \to K_1^+( \to K \pi \pi) \gamma$ decays.