Consistency of electron scattering data with a small proton radius

We determine the charge radius of the proton by analyzing the published low momentum transfer electron-proton scattering data from Mainz. We note that polynomial expansions of the form factor converge for momentum transfers squared below 4m_π², where m_π is the pion mass. Expansions with enough terms to fit the data, but few enough not to overfit, yield proton radii smaller than the CODATA or Mainz values and in accord with the muonic atom results. We also comment on analyses using a wider range of data, and overall obtain a proton radius RE=0.840(16) fm.