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The transverse charge density in the pion can be represented as a dispersionintegral of the imaginary part of the pion form factor in the timelike region.This formulation incorporates information from e+e- annihilation experimentsand allows one to reconstruct the transverse density much more accurately thanfrom the spacelike pion form factor data alone. We calculate the transversedensity using an empirical parametrization of the timelike pion form factor andestimate that it is determined to an accuracy of ~10% at a distance b ~ 0.1 fm,and significantly better at larger distances. The density is found to be closeto that obtained from a zero-width rho meson pole over a wide range and shows apronounced rise at small distances. The resulting two-dimensional image of thefast-moving pion can be interpreted in terms of its partonic structure in QCD.We argue that the singular behavior of the charge density at the centerrequires a substantial presence of pointlike configurations in the pion'spartonic wave function, which can be probed in other high-momentum transferprocesses.

Pion transverse charge density from timelike form factor data