Pion transverse charge density from timelike form factor data

Understand

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 ~10% at a distance b ~ 0.1 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.