|V_td/V_ts| from QCD Sum Rules on the Light-Cone

The dominant theoretical uncertainty in extracting $|V_{td}/V_{ts}|$ from the ratio of branching ratios $R_{\rho/\omega}\equiv\bar{\cal B}(B\to (\rho,\omega)\gamma)/\bar{\cal B}(B\to K^* \gamma)$ is given by the ratio of form factors $\xi_{\rho}\equiv T_1^{B\to K^*}(0)/T_1^{B\to \rho}(0)$. We find $\xi_{\rho}= 1.17\pm 0.09$ from QCD sum rules on the light-cone. Using QCD factorisation for the branching ratios, including the most dominant power-suppressed effects beyond QCD factorisation, and the current experimental results for $R_{\rho/\omega}$, this translates into $|V_{td}/V_{ts}|_{\rm BaBar} = 0.199^{+0.023}_{-0.025}({\rm exp})\pm 0.014 ({\rm th})$, which corresponds to $\gamma_{\rm BaBar} = (61.0^{+13.5}_{-16.0}({\rm th}){}^{+8.9}_{-9.3}({\rm th}))$, and $|V_{td}/V_{ts}|_{\rm Belle} = 0.207^{+0.028}_{-0.033}({\rm exp}) ^{+0.014}_{-0.015}({\rm th})$, $\gamma_{\rm Belle} = (65.7^{+17.3}_{-20.7}({\rm exp})^{+8.9}_{-9.2}({\rm th}))^\circ$.