Pion Form Factors at Intermediate Momentum Transfer in a Covariant Approach

We study the pion electromagnetic and $γ^* + π^0 \to γ$ 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.

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