  In this work, we propose a model by combining the parameterization method and
the QCD factorization to study the $B\to\pi K$ puzzle. The parameterization
introduces twelve parameters, the weak angle $\gamma$ and the other eleven
hadronic parameters. These hadronic parameters are calculated by the QCD
factorization (QCDF). The calculational accuracy of the QCDF is improved by
including the twist-3 three parton tree and one loop corrections. Three
additional nonperturbative strong phases from the gluonic penguin, color
suppressed, and color favored tree diagrams are required to account for the
direct CP asymmetries. The weak angle, three nonperturbative strong phases, and
four scale variables are assumed as fitting parameters. These eight parameters
are determined by a least squares fit to the eight measurements. The fit shows
that the hadronic parameters need to be process-dependent. The
process-dependent hadronic parameters break the isospin symmetry `dynamically'.
A large negative relative phase associated with the internal up quark gluonic
penguin diagram is observed. The weak angle $\gamma$ is found to be
$72.1\pm5.8$ degree, being consistent with the world averaged value,
$72.1\pm5.8$ degree. By a least squares fit to the mixing induced asymmetry
$S(\pi^{0}K_{S})=0.58\pm0.06$, the weak angle $\beta$ is determined to be
$22.9\pm2.1$ degree, which is in a well agreement with the world averaged
value, $22.5\pm4.4\pm0.6$ degree. The model predicts the ratio
$C^{\prime}/T^{\prime}$ (color suppressed/color favored) to be $0.59\pm0.08$.
The above evidences indicate that the model can solve the $B\to\pi K$ puzzle
consistently.
