  In the framework of QCD factorization, we study $B^{+(0)} \to \eta' K^{+(0)}$
decays. In order to more reliably determine the phenomenological parameters
$X_H$ and $X_A$ arising from end-point divergences in the hard spectator
scattering and weak annihilation contributions, we use the global analysis for
twelve $B \to PP$ and $VP$ decay modes, such as $B \to \pi \pi$, $\pi K$, $\rho
\pi$, $\rho K$, etc, but excluding the modes whose (dominant) internal
quark-level process is $b \to s \bar s s$. Based on the global analysis, we
critically investigate possible magnitudes of $X_{H,A}$ and find that both
large and small $X_{H,A}$ terms are allowed by the global fit. In the case of
the large $X_{H,A}$ effects, the standard model (SM) prediction of the
branching ratios (BRs) for $B^{+(0)} \to \eta' K^{+(0)}$ is large and well
consistent with the experimental results. In contrast, in the case of the small
$X_{H,A}$ effects, the SM prediction for these BRs is smaller than the
experimental data. Motivated by the recent Belle measurement of $\sin
(2\phi_1)$ through $B^0 \to \phi K_s$, if we take into account possible new
physics effects on the quark-level process $b \to s \bar s s$, we can
explicitly show that these large BRs can be understood even in the small
$X_{H,A}$ case. Specifically, we present two new physics scenarios: R-parity
violating SUSY and R-parity conserving SUSY.
