Pion Form Factors at Intermediate Momentum Transfer in a Covariant Approach

We study the pion electromagnetic and $\gamma^* + \pi^0 \to \gamma$ 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 $|q^2|\gsim 10$~GeV$^2$, whereas considerable sensitivity is found for the electromagnetic form factor.