Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory

We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite Q² with the derivative at Q²=0. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to use the finite-Q² FF data for constraining the radius (up to Q²≈0.5 GeV² and larger) and avoids the difficulties arising in methods relying on the Q²→0 extrapolation. We obtain a radius of 0.844(7) fm, consistent with the high-precision muonic hydrogen results.