# Lower bound on the proton charge radius from electron scattering data

## TL;DR

This paper establishes a model-independent lower bound on the proton charge radius using low-$Q^2$ electron-proton scattering data, reaffirming the discrepancy with muonic hydrogen measurements.

## Contribution

It introduces a method to derive a rigorous lower bound on the proton radius directly from finite-$Q^2$ data, avoiding model-dependent extrapolations.

## Key findings

- Lower bound on proton radius: R_E > 0.850(1) fm
- Reaffirms discrepancy between electron scattering and muonic hydrogen results
- Method bypasses assumptions in traditional form-factor extrapolations

## Abstract

The proton charge-radius determinations from the electromagnetic form-factor measurements in electron-proton scattering require an extrapolation to zero momentum transfer ($Q^2=0$) which is prone to model-dependent assumptions. We show that the data at finite momentum transfer can be used to establish a rigorous lower bound on the proton charge radius. Using the available $ep$ data at low $Q^2$, we obtain $R_E > 0.850(1)$ fm as the lower bound on the proton radius. This reaffirms the discrepancy between the $ep$ and muonic-hydrogen values, while bypassing the model-dependent assumptions that go into the fitting and extrapolation of the $ep$ data.