Singular charge density at the center of the pion?

We relate the three-dimensional infinite momentum frame spatial charge density of the pion to its electromagnetic form factor F_π(Q²). Diverse treatments of the measured form factor data including phenomenological fits, nonrelativistic quark models, the application of perturbative quantum chromodynamics (QCD), QCD sum rules, holographic QCD, and the Nambu--Jona-Lasinio (NJL) model all lead to the result that the charge density at the center of the pion has a logarithmic divergence. Relativistic constituent quark models do not display this singularity. Future measurements planned for larger values of Q² may determine whether or not a singularity actually occurs.