The transverse charge density in the pion can be represented as a dispersion integral of the imaginary part of the pion form factor in the timelike region. This formulation incorporates information from $e^{+}{e}^{-}$ annihilation experiments and allows one to reconstruct the transverse density much more accurately than from the spacelike pion form factor data alone. We calculate the transverse density using an empirical parametrization of the timelike pion form factor and estimate that it is determined to an accuracy of $\sim 10\%$ at a distance $b\sim 0.1\mathrm{fm}$, and significantly better at larger distances. The density is found to be close to that obtained from a zero-width $\rho$ meson pole over a wide range and shows a pronounced rise at small distances. The resulting two-dimensional image of the fast-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 center requires a substantial presence of pointlike configurations in the pion’s partonic wave function, which can be probed in other high-momentum transfer processes.

• Received 9 December 2010

DOI:https://doi.org/10.1103/PhysRevD.83.013006