Determining the size of the proton

TL;DR

This paper presents a new method to determine the proton radius using electromagnetic form factors, resulting in a value of 0.831 fm, which contributes to resolving discrepancies in fundamental proton measurements.

Contribution

It introduces a novel approach based on electromagnetic form factors to calculate the proton radius, providing an independent verification of previous measurements.

Findings

Proton radius estimated at 0.831 fm.

New expression for transition energy in muonic hydrogen.

Supports alternative measurement methods for fundamental constants.

Abstract

A measurement of the Lamb shift of 49,881.88(76) GHz in muonic hydrogen in conjunction with theoretical estimates of the proton structure effects was recently used to deduce an accurate but rather small radius of the proton. Such an important shift in the understanding of fundamental values needs reconfirmation. Using a different approach with electromagnetic form factors of the proton, we obtain a new expression for the transition energy, $\Delta = E_{2P_{{3}/{2}}}^{f=2} - E_{2S_{{1}/{2}}}^{f=1}$, in muonic hydrogen and deduce a proton radius, $r_p = 0.831$ fm.