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Measurement of the Branching Fractions of the Radiative Charm Decays $D^{0} \to {\bar K}^{*0} γ$ and $D^{0} \to ϕγ$

We present a measurement of the branching fractions for the Cabibbo-favored radiative decay, $D^{0} \to {\bar K}^{*0} γ$, and the Cabibbo-suppressed radiative decay, $D^{0} \to ϕγ$. These measurements are based on a data sample corresponding to an integrated luminosity of $387.1 fb^{-1}$, recorded with the BaBar detector at the PEP-II $e^+e^-$ asymmetric-energy collider operating at center-of-mass energies 10.58 and 10.54 GeV. We measure the branching fractions relative to the well-studied decay $D^{0} \to K^{-} π^{+}$ and find ${\cal B}(D^{0} \to {\bar K}^{*0} γ)/{\cal B}(D^{0} \to K^{-} π^{+}) = (8.43 \pm 0.51 \pm 0.70) \times 10^{-3}$ and ${\cal B}(D^{0} \to ϕγ)/{\cal B}(D^{0} \to K^{-} π^{+}) = (7.15 \pm 0.78 \pm 0.69) \times 10^{-4}$, where the first error is statistical and the second is systematic. This is the first measurement of ${\cal B}(D^{0} \to {\bar K}^{*0} γ)$.