The hard scattering amplitude for the higher helicity components of the pion form factor

For obtaining the spin space wave function of the pion meson in the light-cone formalism from the naive quark model, it is necessary to take into account Wigner rotation. Consequently there are higher helicity ($\lambda_1+\lambda_2=\pm 1$) components in the light-cone spin space wave function of the pion besides the usual helicity ($\lambda_1+\lambda_2=0$) components. For the pion electromagnetic form factor, we calculate the hard-scattering amplitude for the higher helicity components in the light-cone perturbation theory. It is found that the hard-scattering amplitude for the higher helicity components is of order $1/Q^4$, which is vanishingly small compared to that of the ordinary helicity component at very high $Q^2$ but should be considered in the $Q^2$ region where experimental data are available.