Large-Q2behavior of the pion electromagnetic form factor

We study the large-$Q^2$ behavior of the electromagnetic form factor of the pion, which is viewed as a quark-antiquark bound state in a (nongauge) quantum field theory. When the pion's Bethe-Salpeter wave function is expanded in O(4) partial waves, it is found that the information needed about the partial-wave amplitudes is their scaling behavior at large momentum and the locations of their poles in the complex $J$ plane. This information is determined by using the operator-product expansion, conformal invariance at short distances, and a regularity property that holds at least in the ladder model. The resulting behavior of the form factor is roughly $F\left(Q^2\right)\sim {\left(Q^2\right)}^{-1\mathrm{}}$, with corrections due to anomalous dimensions.