Photon Energy Spectrum in $B \to X_s γ$ and Comparison with Data

A comparison of the inclusive photon energy spectrum in the radiative decay $\BGAMAXS$, measured recently by the CLEO collaboration, with the standard model is presented, using a $B$-meson wave function model and improving earlier perturbative QCD-based computations of the same. The dependence of the photon energy spectrum on the non-perturbative model parameters, $p_F$, the $b$-quark Fermi momentum in the $B$ hadron, and $m_q$, the spectator quark mass, is explicitly shown, allowing a comparison of these parameters with the ones obtained from the analysis of the lepton energy spectrum in semileptonic $B$ decays. Taking into account present uncertainties, we estimate $\BBGAMAXS = (2.55 \pm 1.28) \times 10^{-4}$ in the standard model, assuming $\absvts/\absvcb= 1.0$. Comparing this with the CLEO measurement $\BBGAMAXS = (2.32 \pm 0.67) \times 10^{-4}$ implies $\absvts/\absvcb= 1.1 \pm 0.43$, in agreement with the CKM unitarity.