Determination of the moments of the proton charge density

TL;DR

This paper analyzes proton electric form factor data to accurately determine the moments of the proton charge density, addressing systematic errors and providing precise measurements of key spatial moments.

Contribution

It introduces a comprehensive integral method for evaluating proton charge density moments from experimental data, with detailed error analysis and sensitivity to fitting functions.

Findings

Determined the proton charge radius squared as 0.694(09)$_{Sta.}$(16)$_{Sys.}$ fm$^2$

Calculated the third moment of the charge density as 0.870(46)$_{Sta.}$(80)$_{Sys.}$ fm$^3$

Estimated the fourth moment as 1.47(25)$_{Sta.}$(45)$_{Sys.}$ fm$^4$

Abstract

A global analysis of proton electric form factor experimental data from Rosenbluth separation and low squared four-momentum transfer experiments is discussed for the evaluation of the spatial moments of the proton charge density based on the recently published integral method. Specific attention is paid to the evaluation of the systematic errors of the method, particularly the sensitivity to the choice of the mathematical expression of the form factor fitting function. Within this comprehensive analysis of proton electric form factor data, the moments of the proton charge density are determined for integer order moments, particularly: $\langle r^2 \rangle$=0.694(09)$_{Sta.}$(16)$_{Sys.}$~fm$^2$, $\langle r^3 \rangle$=0.870(46)$_{Sta.}$(80)$_{Sys.}$~fm$^3$, and $\langle r^4 \rangle$=1.47(25)$_{Sta.}$(45)$_{Sys.}$~fm$^4$.