Re-examination of the Perturbative Pion Form Factor with Sudakov Suppression

The perturbative pion form factor with Sudakov suppression is re-examined. Taking into account the multi-gluon exchange in the law $Q^2$ regions, we suggest that the running coupling constant should be frozen at $\alpha_s(t=\sqrt{<{\bf k}_{T}^{2}>})$ and $\sqrt{<{\bf k}_{T}^{2}>}$ is the average transverse momentum which can be determined by the pionic wave function. In addition, we correct the previous calculations about the Sudakov suppression factor which plays an important role in the perturbative predictions for the pion form factor.