Reexamination of proton rms radii from low-$q$ power expansions

Several recent publications claim that the proton charge rms radius resulting from the analysis of electron-scattering data restricted to low-momentum transfer agrees with the radius determined from muonic hydrogen, in contrast to the radius resulting from analyses of the full ($e,e$) data set which is 0.04 fm larger. Here we show why these publications erroneously arrive at the low radii.

Figure 1

Sensitivity (arbitrary units) to the moments $\langle r^2\rangle$ and $\langle r^4\rangle$ obtained from fits of the world data.

Figure 2

The solid curves show the relative contribution (in percentages) of the $q^{2n}$ terms to the FSE in $G_e\left(q\right)$. The dashed curve shows the relative contribution of a 0.2% uncertainty of the experimental $G_e\left(q\right)$. For comparison: The $q_{max}$ of the fits linear in $q^2$ (dipole) of Refs. [9, 10] ([11]) amount to 0.72, 0.90, and $1.6{\mathrm{fm}}^{-1}$, respectively.