Proton charge radius from a dispersive analysis of the experimental data over the space- and time-like regions

TL;DR

This paper performs a comprehensive dispersive analysis of nucleon electromagnetic form factors across space- and time-like regions, accurately determining the proton charge radius consistent with previous measurements and reducing uncertainties.

Contribution

It introduces a dispersive analysis method that combines space- and time-like data to precisely extract nucleon form factors and the proton charge radius.

Findings

Proton charge radius found to be 0.840 fm with high precision.

Form factors and radius estimated with bootstrap and spectral function variations.

Results align with previous spacelike and muonic Lamb shift measurements.

Abstract

We present a dispersion theoretical analysis of the experimental data on the electromagnetic form factors of the nucleon covering both the space- and time-like regions. The nucleon form factors over the full range of momentum transfers and the nucleon radius are extracted with high precision. The statistical uncertainties of the extracted form factors and radius are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. For the proton charge radius, we find $r_E^p = 0.840^{+0.003}_{-0.002}{}^{+0.002}_{-0.002}$~fm, in line with previous analyses of spacelike data alone and also the muonic Lamb shift determination.