  Combining the up-to-date experimental information on $B\to\pi K, \pi
K^{\ast}$ and $\rho K$ decays, we revisit the decay rates and CP asymmetries of
these decays within the framework of QCD factorization. Using an infrared
finite gluon propagator of Cornwall prescription, we find that the time-like
annihilation amplitude could contribute a large strong phase, while the
space-like hard spectator scattering amplitude is real. Numerically, we find
that all the branching ratios and most of the direct CP violations, except
$A_{CP}(B^{\pm}\to K^{\pm}\pi^{0})$, agree with the current experimental data
with an effective gluon mass $m_g\simeq0.5 {\rm GeV}$. Taking the unmatched
difference in direct CP violations between $B\to\pi^{0} K^{\pm}$ and
$\pi^{\mp}K^{\pm}$ decays as a hint of new physics, we perform a
model-independent analysis of new physics contributions with a set of
$\bar{s}(1+\gamma_{5})b\otimes\bar{q}(1+\gamma_{5})q$ (q=u,d) operators. Detail
analyses of the relative impacts of the operators are presented in five cases.
Fitting the twelve decay modes, parameter spaces are found generally with
nontrivial weak phases. Our results may indicate that both strong phase from
annihilation amplitude and new weak phase from new physics are needed to
resolve the $\pi K$ puzzle. To further test the new physics hypothesis, the
mixing-induced CP violations in $B\to\pi^{0}K_{S}$ and $\rho^{0}K_{S}$ are
discussed and good agreements with the recent experimental data are found.
