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We report a measurement of the inclusive $B\to X_{s+d} \gamma$ and $B\toX_{s} \gamma$ branching fractions using a data set of $(772 \pm 11)\times 10^6$$B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belledetector at the KEKB asymmetric-energy $e^+e^-$ collider. Results are presentedfor photon energy thresholds between 1.7 to 2.0 GeV. For the 1.8 GeV thresholdwe find $\mathcal{B}_{s\gamma} = (3.01 \pm 0.10~\text{(stat)} \pm0.18~\text{(syst)} \pm 0.08~\text{(model)})\times 10^{-4}$. The Heavy QuarkExpansion parameters that best fit the spectrum in the shape-function schemeare $m_{b} = (4.626 \pm 0.028) \text{GeV}$ and $ \mu_{\pi}^{2} = (0.301\pm0.063) \text{GeV}^2$.

Measurement of the inclusive $B\to X_{s+d} \gamma$ branching fraction, photon energy spectrum and HQE parameters