Study of |Vtd/Vts| Using a Sum of Exclusive B → X Gamma Final States Reconstructed With the BaBar Detector

Experimental data collected with the BABAR detector consisting of 470.9 ± 2.8 million BB events are used to measure the sum of seven exclusive B → Xd(s) γ transitions, where Xd(s) is any non-strange (strange) charmless hadronic state. For each transition avour, measurements are made in the hadronic mass ranges 0.5 ≤ mX < 1.0 GeV=c2 and 1.0 ≤ mX ≤ 2.0 GeV=c2. These are extrapolated and combined in a model-dependent way to obtain the ratio of the total branching fractions, B(B→ Xdγ )=B(B→ Xsγ ) = 0.0456 ± 0.0110 ± 0.0097 where the first error is statistical and the second error is systematic. This is interpreted as a measurement of the ratio of CKM matrix elements |Vtd/Vts| = 0.211 ± 0.023 ± 0.022 ± 0.001 where the final error is due to theoretical uncertainty.