QCD anatomy of $B\to X_s\gamma$ decays

Abstract.

We present an updated next-to-leading order analysis of the $B\to X_s\gamma$ branching ratio and photon spectrum, including consistently the effects of Fermi motion in the heavy-quark expansion. For the Standard Model, we obtain ${\rm B}(B\to X_s\gamma)=(2.57\pm 0.26_{-0.36}^{+0.31})\times 10^{-4}$ for the integral over the high-energy part of the photon spectrum with $E_\gamma^{\rm lab}> 2.2$ GeV, where the first error reflects the uncertainty in the input parameters, and the second one the uncertainty in the calculation of Fermi motion. This prediction agrees with the CLEO measurement of the same quantity within one standard deviation. From a reanalysis of the CLEO data, we obtain for the total branching ratio ${\rm B}(B\to X_s\gamma)=(2.62\pm 0.60_{\rm exp}\,\mbox{}^{+0.37}_{-0.30\,{\rm th}})\times 10^{-4}$ using the measured rate above 2.2 GeV, and $(2.66\pm 0.56_{\rm exp}\,\mbox{}^{+0.43}_{-0.48\,{\rm th}})\times 10^{-4}$ using a fit to the photon energy spectrum. Both values are consistent with the Standard Model prediction of $(3.29\pm 0.33)\times 10^{-4}$. Our analysis contains an improved discussion of renormalization-scale dependence and QED corrections. We also study the sensitivity of the branching ratio and photon spectrum to hadronic parameters such as the b-quark mass, and to possible contributions from New Physics beyond the Standard Model.