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We consider rare semileptonic decays of a heavy $D$-meson into a light vectormeson in the framework of QCD factorization. In contrast to the corresponding$B$-meson decays, the naive factorization hypothesis does not even serve as afirst approximation. Rather, the decay amplitudes appear to be dominated bynon-factorizable dynamics, e.g. through annihilation topologies, which areparticularly sensitive to long-distance hadronic contributions. We thereforepay particular attention to intermediate vector-meson resonances appearing inquark-loop and annihilation topologies. Compared to the analogous $B$-mesondecays, we identify a number of effects that result in very large theoreticaluncertainties for differential decay rates. Some of these effects are found tocancel in the ratio of partially integrated decay rates for transversely andlongitudinally polarized $\rho$ mesons. On the phenomenological side thisimplies a very limited potential to constrain physics beyond the Standard Modelby means of these decays.

$D \to \rho \,\ell^+\ell^-$ Decays in the QCD Factorization Approach