Polynomial fits and the proton radius puzzle

The proton radius puzzle refers to the $\ensuremath{\approx}7\ensuremath{\sigma}$ discrepancy that exists between the proton charge radius determined from muonic hydrogen and that determined from electronic hydrogen spectroscopy and electron-proton scattering. One possible partial resolution to the puzzle includes errors in the extraction of the proton radius from $ep$ elastic scattering data. This possibility is made plausible by certain fits that extract a smaller proton radius from the scattering data consistent with that determined from muonic hydrogen. The reliability of some of these fits that yield a smaller proton radius was studied. We found that fits of form factor data with a truncated polynomial fit are unreliable and systematically give values for the proton radius that are too small. Additionally, a polynomial fit with a ${\ensuremath{\chi}}_{\text{reduced}}^{2}\ensuremath{\approx}1$ is not a sufficient indication for a reliable result.