Measurement of branching fractions and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>and isospin asymmetries for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:math>

The branching fractions of the decays ${B}^{0}\ensuremath{\rightarrow}{K}^{*0}\ensuremath{\gamma}$ and ${B}^{+}\ensuremath{\rightarrow}{K}^{*+}\ensuremath{\gamma}$ are measured using a sample of $88\ifmmode\times\else\texttimes\fi{}{10}^{6}B\overline{B}$ events collected with the BABAR detector at the PEP-II asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. We find $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{K}^{*0}\ensuremath{\gamma})=[3.92\ifmmode\pm\else\textpm\fi{}0.20(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\ifmmode\pm\else\textpm\fi{}0.24(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{K}^{*+}\ensuremath{\gamma})=[3.87\ifmmode\pm\else\textpm\fi{}0.28(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\ifmmode\pm\else\textpm\fi{}0.26(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. Our measurements also constrain the direct $CP$ asymmetry to be $\ensuremath{-}0.074<\mathcal{A}(B\ensuremath{\rightarrow}{K}^{*}\ensuremath{\gamma})<0.049$ and the isospin asymmetry to be $\ensuremath{-}0.046<{\ensuremath{\Delta}}_{0\ensuremath{-}}<0.146$, both at the 90% confidence level.

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