Measurement of $B\to X\gamma$ Decays and Determination of $|V_{td}/V_{ts}|$

Using a sample of $383\times {10}^6$ $B\overline{B}$ 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 nonstrange (strange) charmless hadronic system in the mass range $0.6–1.8\mathrm{GeV}/c^2$. After correcting for unmeasured decay modes in this mass range, we obtain a branching fraction for $b\to d\gamma$ of $\mathbf{(}7.2\pm 2.7(\mathrm{stat})\pm 2.3(\mathrm{syst})\mathbf{)}\times {10}^{-6}$. Taking the ratio of $X_d$ to $X_s$ we find $\Gamma (b\to d\gamma )/\Gamma (b\to s\gamma )=0.033\pm 0.013(\mathrm{stat})\pm 0.009(\mathrm{syst})$, from which we determine $|V_{td}/V_{ts}|=0.177\pm 0.043$.

Figure 1

Projections of the fits to data in the hadronic mass range $0.6–1.0\mathrm{GeV}/c^2$ (a)–(d) and $1.0–1.8\mathrm{GeV}/c^2$ (e)–(h). Projections of $\Delta E$ with $5.275<m_{\mathrm{ES}}<5.286\mathrm{GeV}/c^2$ for (a),(e) $B\to X_s\gamma$ and (c),(f) $B\to X_d\gamma$, and of $m_{\mathrm{ES}}$ with $-0.1<\Delta E<0.05\mathrm{GeV}$ for (b),(g) $B\to X_s\gamma$ and (d),(h) $B\to X_d\gamma$. Data (points) are compared with the sum of all the fit contributions (solid curve) including the signal (dashed curve) and the $B\to X_s\gamma$ contribution in the $B\to X_d\gamma$ fit (dotted curve).