Branching Fraction Measurements of $B^{+}\to {\rho }^{+}\gamma$, $B^0\to {\rho }^0\gamma$, and $B^0\to \omega \gamma$

We present a study of the decays $B^{+}\to {\rho }^{+}\gamma$, $B^0\to {\rho }^0\gamma$, and $B^0\to \omega \gamma$. The analysis is based on data containing $347\times {10}^6$ $B\overline{B}$ events recorded with the BABAR detector at the PEP-II asymmetric $B$ factory. We measure the branching fractions $\mathcal{B}(B^{+}\to {\rho }^{+}\gamma )=({1.10}_{-0.33}^{+0.37}\pm 0.09)\times {10}^{-6}$ and $\mathcal{B}(B^0\to {\rho }^0\gamma )=({0.79}_{-0.20}^{+0.22}\pm 0.06)\times {10}^{-6}$, and set a 90% C.L. upper limit $\mathcal{B}(B^0\to \omega \gamma )<0.78\times {10}^{-6}$. We also measure the isospin-averaged branching fraction $\mathcal{B}\mathbf{(}B\to (\rho /\omega )\gamma \mathbf{)}=({1.25}_{-0.24}^{+0.25}\pm 0.09)\times {10}^{-6}$, from which we determine $|V_{\mathrm{td}}/V_{\mathrm{ts}}|={0.200}_{-0.020}^{+0.021}\pm 0.015$, where the first uncertainty is experimental and the second is theoretical.