Measurement of the $\overline{B}\to X_s\gamma$ branching fraction with a sum of exclusive decays

We use $772\times 10^6$ $B\overline{B}$ meson pairs collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector to measure the branching fraction for $\overline{B}\to X_s\gamma$. Our measurement uses a sum-of-exclusives approach in which 38 of the hadronic final states with strangeness equal to $+1$, denoted by $X_s$, are reconstructed. The inclusive branching fraction for $M_{X_s}<2.8\mathrm{GeV}/c^2$, which corresponds to a minimum photon energy of 1.9 GeV, is measured to be $\mathcal{B}(\overline{B}\to X_s\gamma )=(3.51\pm 0.17\pm 0.33)\times 10^{-4}$, where the first uncertainty is statistical and the second is systematic.

Figure 1

Neural network output classifier (NN classifier) that ranges from $-1$ for the $q\overline{q}$ background-like events to $+1$ for the signal-like events (MC). The signal (one dot-dashed line), the cross-feed (dashed line), the $q\overline{q}$ background (two dot-dashed line) and the $B\overline{B}$ background (solid line) are shown. We select events with the NN classifier above 0.78.

Figure 2

$M_{\text{bc}}$ fits in $M_{X_s}$ bins in $0.6\mathrm{GeV}/c^2<M_{X_s}<1.4\mathrm{GeV}/c^2$. The plot shows the data (black points), and the fit function (blue solid line). The fit components correspond to signal (red thick short dashed line), cross-feed (red thin short dashed line), peaking $B\overline{B}$ background (green thick long dashed line), nonpeaking $B\overline{B}$ background (green thin long dashed line) and $q\overline{q}$ background (blue dot-dashed line). (a) $0.6<M_{X_s}<0.7(\mathrm{GeV}/c^2)$. (b) $0.7<M_{X_s}<0.8(\mathrm{GeV}/c^2)$. (c) $0.8<M_{X_s}<0.9(\mathrm{GeV}/c^2)$. (d) $0.9<M_{X_s}<1.0(\mathrm{GeV}/c^2)$. (e) $1.0<M_{X_s}<1.1(\mathrm{GeV}/c^2)$. (f) $1.1<M_{X_s}<1.2(\mathrm{GeV}/c^2)$. (g) $1.2<M_{X_s}<1.3(\mathrm{GeV}/c^2)$. (h) $1.3<M_{X_s}<1.4(\mathrm{GeV}/c^2)$.

Figure 3

$M_{\text{bc}}$ fits in $M_{X_s}$ bins in $1.4\mathrm{GeV}/c^2<M_{X_s}<2.2\mathrm{GeV}/c^2$. The plot shows the data (black points), and the fit function (blue solid line). The fit components correspond to signal (red thick short dashed line), cross-feed (red thin short dashed line), peaking $B\overline{B}$ background (green thick long dashed line), nonpeaking $B\overline{B}$ background (green thin long dashed line) and $q\overline{q}$ background (blue dot-dashed line). (a) $1.4<M_{X_s}<1.5(\mathrm{GeV}/c^2)$. (b) $1.5<M_{X_s}<1.6(\mathrm{GeV}/c^2)$. (c) $1.6<M_{X_s}<1.7(\mathrm{GeV}/c^2)$. (d) $1.7<M_{X_s}<1.8(\mathrm{GeV}/c^2)$. (e) $1.8<M_{X_s}<1.9(\mathrm{GeV}/c^2)$. (f) $1.9<M_{X_s}<2.0(\mathrm{GeV}/c^2)$. (g) $2.0<M_{X_s}<2.1(\mathrm{GeV}/c^2)$. (h) $2.1<M_{X_s}<2.2(\mathrm{GeV}/c^2)$.

Figure 4

$M_{\text{bc}}$ fits in $M_{X_s}$ bins in $2.2\mathrm{GeV}/c^2<M_{X_s}<2.8\mathrm{GeV}/c^2$. The plot shows the data (black points), and the fit function (blue solid line). The fit components correspond to signal (red thick short dashed line), cross-feed (red thin short dashed line), peaking $B\overline{B}$ background (green thick long dashed line), nonpeaking $B\overline{B}$ background (green thin long dashed line) and $q\overline{q}$ background (blue dot-dashed line). (a) $2.2<M_{X_s}<2.4(\mathrm{GeV}/c^2)$. (b) $2.4<M_{X_s}<2.6(\mathrm{GeV}/c^2)$. (c) $2.6<M_{X_s}<2.8(\mathrm{GeV}/c^2)$.

Figure 5

Partial branching fraction as a function of $M_{X_s}$. The error bars correspond to the statistical (solid) and the quadratic sum of the statistical and systematic (dashed).