Measurement of the branching fractions of the radiative charm decays D^{0}→K[over ¯]^{*0}γ and D^{0}→ϕγ

We present a measurement of the branching fractions for the Cabibbo-favored radiative decay D0→K̅ *0γ and the Cabibbo-suppressed radiative decay D0→ϕγ. These measurements are based on a data sample corresponding to an integrated luminosity of 387.1  fb-1 and 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 D0→K-π+ and find B(D0→K̅ *0γ)/B(D0→K-π+)=(8.43±0.51±0.70)×10-3 and B(D0→ϕγ)/B(D0→K-π+)=(7.15±0.78±0.69)×10-4, where the first error is statistical and the second is systematic. This is the first observation of the decay mode D0→K̅ *0γ.