  The large branching ratios for pure annihilation $\bar{B}_s^0$ $\to$ $\pi^+
\pi^-$ and $\bar{B}_d^0$ $\to$ $K^+ K^-$ decays reported by CDF and LHCb
collaborations recently and the so-called ${\pi}K$ and ${\pi}{\pi}$ puzzles
indicate that spectator scattering and annihilation contributions are important
to the penguin-dominated, color-suppressed tree dominated, and pure
annihilation nonleptonic $B$ decays. Combining the available experimental data
for $B_{u,d}$ ${\to}$ $\pi \pi$, ${\pi}K$ and $K \bar{K}$ decays, we do a
global fit on the spectator scattering and annihilation parameters
$X_H({\rho}_H$, ${\phi}_H)$, $X_A^i({\rho}_A^{i},{\phi}_A^{i})$ and
$X_A^f({\rho}_A^{f},{\phi}_A^{f})$, which are used to parameterize the endpoint
singularity in amplitudes of spectator scattering, nonfactorizable and
factorizable annihilation topologies within the QCD factorization framework, in
three scenarios for different purpose. Numerically, in scenario II, we get
$({\rho}_A^{i},{\phi}_A^{i}[^{\circ}])=(2.88^{+1.52}_{-1.30},-103^{+33}_{-40})$
and
$({\rho}_A^{f},{\phi}_A^{f}[^{\circ}])=(1.21^{+0.22}_{-0.25},-40^{+12}_{-8})$
at the $68\%$ confidence level, which are mainly demanded by resolving ${\pi}K$
puzzle and confirm the presupposition that $X_A^i\neq X_A^f$. In addition,
correspondingly, the $B$-meson wave function parameter $\lambda_B$ is also
fitted to be $0.18^{+0.11}_{-0.08}\, MeV$, which plays an important role for
resolving both ${\pi}K$ and $\pi\pi$ puzzles. With the fitted parameters, the
QCDF results for observables of $B_{u,d}$ $\to$ $\pi \pi$, $\pi K$ and $K
\bar{K}$ decays are in good agreement with experimental measurements. Much more
experimental and theoretical efforts are expected to understand the underlying
QCD dynamics of spectator scattering and annihilation contributions.
