  Applying the dispersion approach we compute perturbative QCD corrections to
the power suppressed soft contribution of $B \to \gamma \ell \nu$ at leading
twist. QCD factorization for the $B \to \gamma^{\ast}$ form factors is
demonstrated explicitly for the hard-collinear transverse polarized photon at
one loop, with the aid of the method of regions. While the one-loop hard
function is identical to the matching coefficient of the QCD weak current $\bar
u \, \gamma_{\mu \perp} \, (1- \gamma_5) \, b$ in soft-collinear effective
theory, the jet function from integrating out the hard-collinear fluctuations
differs from the corresponding one entering the factorization formula of $B \to
\gamma \ell \nu$. Furthermore, we evaluate the sub-leading power contribution
to the $B \to \gamma$ form factors from the three-particle $B$-meson
distribution amplitudes (DAs) at tree level. The soft contribution to the $B
\to \gamma$ form factors from the three-particle $B$-meson DAs is shown to be
of the same power compared with the corresponding hard correction, in contrast
to the two-particle counterparts. Numerically the next-to-leading-order QCD
correction to the soft two-particle contribution in $B \to \gamma$ form factors
will induce an approximately $\left (10 \sim 20 \right) \%$ shift to the
tree-level contribution at $\lambda_B(\mu_0)=354 \, {\rm MeV}$. Albeit of power
suppression parametrically, the soft two-particle correction can decrease the
leading power predictions for the $B \to \gamma$ form factors by an amount of
$\left (10 \sim 30 \right) \%$ with the same value of $\lambda_B(\mu_0)$.
Employing the phenomenological model of the three-particle $B$-meson DAs
inspired by a QCD sum rule analysis, the three-particle contribution to the $B
\to \gamma$ form factors is predicted to be of ${\cal O} (1 \%)$, at leading
order in $\alpha_s$, with the default theory inputs.
