A Model for the Twist-3 Wave Function of the Pion and Its Contribution   to the Pion Form Factor
  A model for the twist-3 wave function $\psi_p(x,\mathbf{k_\perp})$ of the pion has been constructed based on the moment calculation by applying the QCD sum rules, whose distribution amplitude has a better end-point behavior than that of the asymptotic one. With this model wave function, the twist-3 contributions including both the usual helicity components ($\lambda_1+\lambda_2=0$) and the higher helicity components ($\lambda_1+\lambda_2=\pm 1$) to the pion form factor have been studied within the modified pQCD approach. Our results show that the twist-3 contribution drops fast and it becomes less than the twist-2 contribution at $Q^2\sim 10GeV^2$. The higher helicity components in the twist-3 wave function will give an extra suppression to the pion form factor. The model dependence of the twist-3 contribution to the pion form factor has been studied by comparing three different models. When all the power contributions, which include higher order in $\alpha_s$, higher helicities, higher twists in DA and etc., have been taken into account, it is expected that the hard contributions will fit the present experimental data well at the energy region where pQCD is applicable. 
Tao Huang and Xing-Gang Wu