Measurements of the $B\to X_s\gamma$ branching fraction and photon spectrum from a sum of exclusive final states

Using 88.9 million $B\overline{B}$ events collected by the BABAR detector at the $\mathit{{\rm Y}}(4S)$, we measure the branching fraction for the radiative penguin process $B\to X_s\gamma$ from the sum of 38 exclusive final states. The inclusive branching fraction above a minimum photon energy $E_{\gamma }>1.9\mathrm{GeV}$ is $\mathcal{B}(b\to s\gamma )=(3.27\pm 0.18(\mathrm{stat}{)}_{-0.40}^{+0.55}(\mathrm{syst}{)}_{-0.09}^{+0.04}(\mathrm{theory}))\times {10}^{-4}$. We also measure the isospin asymmetry between $B^{-}\to X_{s\overline{u}}\gamma$ and ${\overline{B}}^0\to X_{s\overline{d}}\gamma$ to be ${\Delta }_{0-}=-0.006\pm 0.058(\mathrm{stat})\pm 0.009(\mathrm{syst})\pm 0.024({\overline{B}}^0/B^{-})$. The photon energy spectrum is measured in the $B$ rest frame, from which moments are derived for different values of the minimum photon energy. We present fits to the photon spectrum and moments which give the heavy-quark parameters $m_b$ and ${\mu }_{\pi }^2$. The fitted parameters are consistent with those obtained from semileptonic $B\to X_c\ell \nu$ decays, and are useful inputs for the extraction of $|V_{ub}|$ from measurements of semileptonic $B\to X_u\ell \nu$ decays.

Figure 1

Efficiency for correctly reconstructing a signal event in one of the 38 final states as a function of hadronic mass. Note that this efficiency does not include the missing fractions of $B\to X_s\gamma$ final states.

Figure 2

Fits to the $M(X_s)=1.4–1.5\mathrm{GeV}$ bin for (a) correctly reconstructed signal Monte Carlo events; (b) simulated continuum background; (c) simulated cross-feed and hadronic $B$ decay backgrounds, where the contributions from the peaking (dotted) and combinatorial (dashed) backgrounds are shown separately; (d) on-peak data, where the contributions from the signal (dotted-dashed), continuum background (dotted), peaking $B$ background (long-dashed), and combinatorial $B$ background (dashed) are shown separately.

Figure 3

On-peak data fit to the full $M(X_s)$ range, $M(X_s)=0.6–2.8\mathrm{GeV}$ bin, where the contributions from the signal shape (dotted-dashed), fixed continuum ARGUS shape (dotted), peaking background shape (long-dashed), and combinatorial $B\overline{B}$ background shape (dashed) are shown separately.

Figure 4

Missing fractions with systematic errors as a function of the hadronic mass.

Figure 5

The hadronic mass spectrum (a), and the photon energy spectrum (b). The data points are compared to theoretical predictions (histograms) obtained using the shape function (solid line) and kinetic (dashed line) schemes.

Figure 6

Error ellipses corresponding to $\Delta {\chi }^2=1$ from the fit to the spectrum in the shape function scheme using the exponential (solid line), hyperbolic (dotted-dashed) and Gaussian (dashed line) models of the shape function. Both statistical and systematic errors have been taken into account.

Figure 7

First (a), and second (b) moments as a function of the minimum photon energy. The dotted lines show the predicted central values based on fits to the $b\to c\ell \nu$ moments [21], and the solid lines the theoretical uncertainties from the kinetic scheme [20, 40].