Study of $B\to X\gamma$ decays and determination of $|V_{td}/V_{ts}|$

Using a sample of $471\times {10}^6$ $B\overline{B}$ events collected with the BABAR detector, we study the sum of seven exclusive final states $B\to X_{s(d)}\gamma$, where $X_{s(d)}$ is a strange (nonstrange) hadronic system with a mass of up to $2.0\mathrm{GeV}/c^2$. After correcting for unobserved decay modes, we obtain a branching fraction for $b\to d\gamma$ of $(9.2\pm 2.0(\mathrm{stat})\pm 2.3(\mathrm{syst}))\times {10}^{-6}$ in this mass range, and a branching fraction for $b\to s\gamma$ of $(23.0\pm 0.8(\mathrm{stat})\pm 3.0(\mathrm{syst}))\times {10}^{-5}$ in the same mass range. We find $\frac{\mathcal{B}(b\to d\gamma )}{\mathcal{B}(b\to s\gamma )}=0.040\pm 0.009(\mathrm{stat})\pm 0.010(\mathrm{syst})$, from which we determine $|V_{td}/V_{ts}|=0.199\pm 0.022(\mathrm{stat})\pm 0.024(\mathrm{syst})\pm 0.002(\mathrm{th})$.

Figure 1

Projections of $\Delta E$ with $5.275<m_{\mathrm{ES}}<5.286\mathrm{GeV}/c^2$ for (a) $B\to X_s\gamma$ and (c) $B\to X_d\gamma$, and of $m_{\mathrm{ES}}$ with $-0.1<\Delta E<0.05\mathrm{GeV}$ for (b) $B\to X_s\gamma$ and (d) $B\to X_d\gamma$ in the mass range $0.5–1.0\mathrm{GeV}/c^2$. Data points are compared with the sum of all the fit contributions (solid line). The jagged line is an artifact of the fit projection over the sum of several binned histograms. The dashed line shows the signal component.

Figure 2

Projections of $\Delta E$ with $5.275<m_{\mathrm{ES}}<5.286\mathrm{GeV}/c^2$ for (a) $B\to X_s\gamma$ and (c) $B\to X_d\gamma$, and of $m_{\mathrm{ES}}$ with $-0.1<\Delta E<0.05\mathrm{GeV}$ for (b) $B\to X_s\gamma$ and (d) $B\to X_d\gamma$ in the mass range $1.0–2.0\mathrm{GeV}/c^2$. Data points are compared with the sum of all the fit contributions (solid line). The jagged line is an artifact of the fit projection over the sum of several binned histograms. The dashed line shows the signal component.