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Polynomial fits and the proton radius puzzle

The Proton Radius Puzzle refers to the ~7σ 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 which 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 χ^2_{reduced} ~ 1 is not a sufficient indication for a reliable result.