New Insights into the Nucleon’s Electromagnetic Structure

We present a combined analysis of the electromagnetic form factors of the nucleon in the space- and timelike regions using dispersion theory. Our framework provides a consistent description of the experimental data over the full range of momentum transfer, in line with the strictures from analyticity and unitarity. The statistical uncertainties of the extracted form factors are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. We also perform a high-precision extraction of the nucleon radii and find good agreement with previous analyses of spacelike data alone. For the proton charge radius, we find $r_E^p=0.840_{-0.002}^{+0.003}{}_{-0.002}^{+0.002}\mathrm{fm}$, where the first error is statistical and the second one is systematic. The Zemach radius and third moment are in agreement with Lamb shift measurements and hyperfine splittings. The combined dataset of space- and timelike data disfavors a zero crossing of ${\mu }_p{G}_E^p/G_M^p$ in the spacelike region. Finally, we discuss the status and perspectives of modulus and phase of the form factors in the timelike region in the context of future experiments, as well as the onset of perturbative QCD.

Figure 1

Complete fit to space- and timelike data with bootstrap error (shaded band) compared to data for $|G_{\mathrm{eff}}|$ of the proton (upper) and neutron (lower). Fitted data are depicted by closed symbols; data given by open symbols are shown for comparison only (see Supplemental Material [15] for explicit references).

Figure 2

Complete fit to space- and timelike data with bootstrap error (shaded band) compared to JLab data for ${\mu }_p{G}_E^p/G_M^p$ at spacelike momentum transfer. Fitted data are depicted by closed symbols. The data for $|t|<1{\mathrm{GeV}}^2$ (open symbols, see also the inset) are shown for comparison only. For references to the data, see Supplemental Material [15].

Figure 3

Form factor ratio $|G_{\mathrm{eff}}^p(t)/G_{\mathrm{eff}}^n(t)|$ in the timelike region for the best fit, with the bootstrap uncertainties indicated by the shaded band.

Figure 4

Complete fit to space- and timelike data with bootstrap error (shaded band) compared to proton data for $|G_E/G_M|$ (closed symbols, fitted; open symbols, not fitted) (upper) and our prediction for $\arg (G_E/G_M)$ (lower).