Measurement of $B\to X\gamma$ Decays and Determination of $\mathrm{\mid }{V}_{td}\mathrm{/}{V}_{ts}\mathrm{\mid }$

Using a sample of 383 million $B\bar{B}$ events collected by the $BaBar$ experiment, we measure sums of seven exclusive final states $B\to X_{d(s)}\gamma$,where$X_d$($X_s$) is a non-strange (strange) charmless hadronic system in the mass range $0.6-1.8$ GeV$\mathrm{/}{c}^2$. After correcting for unmeasured decay modes in this mass range, we obtain a branching fraction for $b\to d\gamma$ of $(7.2\pm 2.7(stat\mathrm{.})\pm 2.3(syst\mathrm{.}))\times {10}^{-6}$. Taking the ratio of $X_d$ to $X_s$ we find $\Gamma(b \to d \gamma)/\Gamma(b \to s \gamma) = 0.033 \pm 0.013 (stat.) \pm 0.009 (syst.),$fromwhichwedetermine$|V_{td}/V_{ts}|=0.177\pm 0.043$.