Determination of the moments of the proton charge density

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 \cite{Hob20}. 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: $\langle r^2 \rangle$=0.682(02)$_{Sta.}$(11)$_{Sys.}$~fm$^2$, $\langle r^3 \rangle$=0.797(10)$_{Sta.}$(58)$_{Sys.}$~fm$^3$, and $\langle r^4 \rangle$=1.02(05)$_{Sta.}$(31)$_{Sys.}$~fm$^4$. This analysis leads to the proton charge radius 0.8459(12)$_{Sta.}$(76)$_{Sys.}$~fm once relativistic effects are taken into account.Comment: 10 pages, 3 figure