Pion transverse charge density from e+e− annihilation data and logarithmic dispersion relations

The transverse charge density of the pion is extracted from a dispersive analysis of the e + e − → π + π − exclusive annihilation data. A logarithmic dispersion relation is used to compute the unknown phase of the timelike pion form factor from the modulus obtained from the annihilation cross section. The method is model-independent and permits quantitative uncertainty estimates. The density is obtained with few-percent accuracy down to b ∼ 0.1 fm; at smaller distances it depends qualitatively on the assumed high-energy behavior of the timelike form factor. Implications for pion structure and the relevance of pQCD asymptotics are discussed.