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Based on the light-cone (LC) framework and the $k_T$ factorization formalism,the transverse momentum effects and the different helicity components'contributions to the pion form factor $F_{\pi}(Q^2)$ are recalculated. Inparticular, the contribution to the pion form factor from the higher helicitycomponents ($\lambda_1+\lambda_2=\pm 1$), which come from the spin-space Wignerrotation, are analyzed in the soft and hard energy regions respectively. Ourresults show that the right power behavior of the hard contribution from thehigher helicity components can only be obtained by fully keeping the $k_T$dependence in the hard amplitude, and that the $k_T$ dependence in LCwavefunction affects the hard and soft contributions substantially. A model forthe twist-3 wavefunction $\psi_p(x,\mathbf{k_\perp})$ of the pion has beenconstructed based on the moment calculation by applying the QCD sum rules,whose distribution amplitude has a better end-point behavior than that of theasymptotic one. With this model wavefunction, the twist-3 contributionsincluding both the usual helicity components ($\lambda_1+\lambda_2=0$) and thehigher helicity components ($\lambda_1+\lambda_2=\pm 1$) to the pion formfactor have been studied within the modified pQCD approach. Our results showthat the twist-3 contribution drops fast and it becomes less than the twist-2contribution at $Q^2\sim 10GeV^2$. The higher helicity components in thetwist-3 wavefunction will give an extra suppression to the pion form factor.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 experimentaldata well at the energy region where pQCD is applicable.Comment: 4 pages, 2 figures, Prepared for International Conference on QCD and  Hadronic Physics, Beijing, China, 16-20 June 200

Pion Electromagnetic Form Factor in the KT Factorization Formulae

Pion Electromagnetic Form Factor in the K_T Factorization Formulae