  The $B$-meson light-cone distribution amplitude (LCDA) is defined as the
matrix element of a quark-antiquark bilocal light-cone operator in the
heavy-quark effective theory (HQET) and is a building block of QCD
factorization formula for exclusive $B$-meson decays. When the corresponding
bilocal HQET operator has a light-like distance $t$ between the quark and
antiquark fields, the scale $\sim 1/t$ separates the UV and IR regions, which
induce the cusp singularity in radiative corrections and the mixing of
multiparticle states in nonperturbative corrections, respectively. We treat the
bilocal HQET operator based on the operator product expansion (OPE),
disentangling the singularities from the IR and UV regions systematically. The
matching at the next-to-leading order $\alpha_s$ is performed in the
$\overline{\rm MS}$ scheme with a complete set of local operators of dimension
$d \le 5$, through a manifestly gauge-invariant calculation organizing all
contributions in the coordinate space. The result exhibits the Wilson
coefficients with Sudakov-type double logarithms and the higher-dimensional
operators with additional gluons. This OPE yields the $B$-meson LCDA for $t$
less than $\sim 1$ GeV$^{-1}$, in terms of $\bar{\Lambda}= m_B - m_b$ and the
two additional HQET parameters as matrix elements of dimension-5 operators. The
impact of these novel HQET parameters on the integral relevant to exclusive $B$
decays, $\lambda_B$, is also discussed.
