New phenomenological extraction of the nucleon charge size scale: The baryonic core and quark-antiquark meson cloud radii

In this work, I present new extractions of the proton's $\ensuremath{\langle}{r}_{Ep}\ensuremath{\rangle}$ and neutron's $\ensuremath{\langle}{r}_{En}^{2}\ensuremath{\rangle}$ conventional charge radii. This analysis is based on two-photon-exchange (TPE) corrected elastic electron-proton cross section ${\ensuremath{\sigma}}_{R}$ data from the Mainz experiment, covering the range $0.0155\ensuremath{\le}{Q}^{2}\ensuremath{\le}1.0\phantom{\rule{0.28em}{0ex}}{\mathrm{GeV}}^{2}$, and updated neutron electric ${G}_{E}^{n}({Q}^{2})$ data spanning $0.00973\ensuremath{\le}{Q}^{2}\ensuremath{\le}3.410\phantom{\rule{0.28em}{0ex}}{\mathrm{GeV}}^{2}$. Both ${G}_{E}^{(p,n)}({Q}^{2})$ form factors were fit independently using various functional forms and parametrizations that enforce proper low-${Q}^{2}$ constraints. Charge radii were extracted from fits over multiple ${Q}^{2}$ intervals, with final values obtained from statistically stable regions. The resulting proton charge radius $\ensuremath{\langle}{r}_{Ep}\ensuremath{\rangle}=0.853\ifmmode\pm\else\textpm\fi{}0.{001}_{\text{(stat.)}}\ifmmode\pm\else\textpm\fi{}0.{001}_{\text{(sys.)}}\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$ is consistent with both PRad I and muonic hydrogen results, and falls within the range of values reported in recent reanalyses. The neutron charge radius $\ensuremath{\langle}{r}_{En}^{2}\ensuremath{\rangle}=\ensuremath{-}0.106\ifmmode\pm\else\textpm\fi{}0.{003}_{\text{(stat.)}}\ifmmode\pm\else\textpm\fi{}0.{002}_{\text{(sys.)}} {\mathrm{fm}}^{2}$ also agrees with modern determinations. Additionally, the charge radii of the baryonic core (three valence quarks) and quark-antiquark meson cloud components of the nucleon are extracted. My results support the $1/2$-fermi size scale of the baryonic core, and $0.617\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$ of the mesonic cloud of the nucleon, in good agreement with lattice QCD calculations based on dispersion relations and the functional spectral analysis approach. The flavor-separated mean-squared transverse charge distributions of the up- and down-quark $\ensuremath{\langle}{b}_{(u,d)}^{2}\ensuremath{\rangle}$ radii are also studied, revealing subtle but non-negligible differences in their spatial extent.