Pion Form Factors at Intermediate Momentum Transfer in a Covariant Approach

We study the pion electromagnetic and ${\gamma }^{\ast }+{\pi }^0\to \gamma$ transition form factors at intermediate momentum transfer. We calculate soft, nonperturbative corrections to the leading perturbative amplitudes which arise from the $q\bar{q}$-component of the pion wave function. We work in Minkowski space and use a Lorentz covariant, gauge-invariant generalized perturbative integral representation for the $q\bar{q}$ amplitudes. For the transition form factor we find relative insensitivity to the detailed nonperturbative structure of the wavefunction for $\mathrm{\mid }{q}^2\mathrm{\mid }\text{gsim}10$~GeV${}^2$, whereas considerable sensitivity is found for the electromagnetic form factor.