The photon spectrum in $B\to X_s\gamma$ decay, where $X_s$ is any strange hadronic state, is studied using a data sample of $88.5\times {10}^6$ $e^{+}{e}^{-}\to \mathit{{\rm Y}}(4S)\to B\overline{B}$ decays collected by the BABAR experiment at the Stanford Linear Accelerator Center. The partial branching fraction, $\Delta \mathcal{B}(B\to X_s\gamma )=(3.67\pm 0.29(\mathrm{stat})\pm 0.34(\mathrm{syst})\pm 0.29(\mathrm{model}))\times {10}^{-4}$, the first moment $⟨E_{\gamma }⟩=2.288\pm 0.025\pm 0.017\pm 0.015\mathrm{GeV}$, and the second moment $⟨E_{\gamma }^2⟩=0.0328\pm 0.0040\pm 0.0023\pm 0.0036{\mathrm{GeV}}^2$ are measured for the photon energy range $1.9\mathrm{GeV}<E_{\gamma }<2.7\mathrm{GeV}$. They are also measured for narrower $E_{\gamma }$ ranges. The moments are then fit to recent theoretical calculations to extract the heavy quark expansion parameters $m_b$ and ${\mu }_{\pi }^2$ and to extrapolate the partial branching fraction to $E_{\gamma }>1.6\mathrm{GeV}$. In addition, the direct $CP$ asymmetry $A_{CP}(B\to X_{s+d}\gamma )$ is measured to be $-0.110\pm 0.115(\mathrm{stat})\pm 0.017(\mathrm{syst})$.

• Received 26 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.171803