  With updated experimental data and improved theoretical calculations, several
significant deviations are being observed between the Standard Model
predictions and the experimental measurements of the branching ratios of
$\bar{B}_{(s)}^0\to D_{(s)}^{(*)+} L^-$ decays, where $L$ is a light meson from
the set $\{\pi,\rho,K^{(\ast)}\}$. Especially for the two channels
$\bar{B}^0\to D^{+}K^-$ and $\bar{B}_{s}^0\to D_{s}^{+}\pi^-$, both of which
are free of the weak annihilation contribution, the deviations observed can
even reach 4-5$\sigma$. Here we exploit possible new-physics effects in these
class-I non-leptonic $B$-meson decays within the framework of QCD
factorization. Firstly, we perform a model-independent analysis of the effects
from twenty linearly independent four-quark operators that can contribute,
either directly or through operator mixing, to the quark-level $b\to c\bar{u}
d(s)$ transitions. It is found that, under the combined constraints from the
current experimental data, the deviations observed could be well explained at
the $1\sigma$ level by the new-physics four-quark operators with
$\gamma^{\mu}(1-\gamma_5)\otimes\gamma_{\mu} (1-\gamma_5)$ structure, and also
at the $2\sigma$ level by the operators with $(1+\gamma_5)\otimes(1-\gamma_5)$
and $(1+\gamma_5)\otimes(1+\gamma_5)$ structures. However, the new-physics
four-quark operators with other Dirac structures fail to provide a consistent
interpretation, even at the $2\sigma$ level. Then, as two specific examples of
model-dependent considerations, we discuss the case where the new-physics
four-quark operators are generated by either a colorless charged gauge boson or
a colorless charged scalar, with their masses fixed both at the $1$~TeV.
Constraints on the effective coefficients describing the couplings of these
mediators to the relevant quarks are obtained by fitting to the current
experimental data.
