  Using results on soft-collinear factorization for inclusive B-meson decay
distributions, a systematic study of the partial $B\to X_s\gamma$ decay rate
with a cut $E_\gamma > E_0$ on photon energy is performed. For values of $E_0$
below about 1.9 GeV, the rate can be calculated without reference to shape
functions using a multi-scale operator product expansion (MSOPE). The
transition from the shape-function region to the MSOPE region is studied
analytically. The resulting prediction for the $B\to X_s\gamma$ branching ratio
depends on three large scales: $m_b$, $\sqrt{m_b\Delta}$, and
$\Delta=m_b-2E_0$. Logarithms associated with these scales are resummed at
next-to-next-to-leading logarithmic order. While power corrections in
$\Lambda_{QCD}/\Delta$ turn out to be small, the sensitivity to the scale
$\Delta\approx 1.1$ GeV (for $E_0\approx 1.8$ GeV) introduces significant
perturbative uncertainties, which so far have been ignored. The new theoretical
prediction for the $B\to X_s\gamma$ branching ratio with $E_\gamma\ge 1.8$ GeV
is $Br(B\to X_s\gamma)=(3.38_{-0.42-0.30}^{+0.31+0.32})\times 10^{-4}$, where
the first error is an estimate of perturbative uncertainties and the second one
reflects uncertainties in input parameters. With this cut $(89_{-7}^{+6}\pm
1)%$ of all events are contained. The implications of larger theory
uncertainties for New Physics searches are briefly explored with the example of
the type-II two-Higgs-doublet model, for which the lower bound on the
charged-Higgs mass is reduced compared with previous estimates to approximately
200 GeV at 95% confidence level.
