Polynomial fits and the proton radius puzzle

TL;DR

This paper investigates the reliability of polynomial fits to electron-proton scattering data in the context of the proton radius puzzle, finding that truncated polynomial fits tend to underestimate the proton radius and that a good fit quality does not guarantee accuracy.

Contribution

It demonstrates that certain polynomial fitting methods are unreliable for extracting the proton radius from scattering data, highlighting potential pitfalls in resolving the proton radius puzzle.

Findings

Truncated polynomial fits systematically underestimate the proton radius.

A reduced chi-squared near 1 does not ensure fit reliability.

Polynomial fits can be misleading in proton radius extraction.

Abstract

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