New extraction of the nucleon charge radius based on its Dirac-flavor-dependent form factors

In this work, we present new extractions of the proton r₏ and neutron r₍^2 root-mean-square charge radius using the Dirac flavor-separated up- and down-quark F₁^ (u, d) (Q^2) form factors data covering the range 0. 0155<Q^2<4. 250 GeV^2 from I. A. Qattan and J. Arrington Phys. Rev. C 86, 065210 (2012) and I. A. Qattan, J. Arrington, and A. Alsaad Phys. Rev. C 91, 065203 (2015). The charge radius values are calculated using the two-dimensional (2D) transverse quark charge distributions based on the slopes of F₁^ (u, d) (Q^2) at Q^2=0 through model-independent relations. As the charge radius is extracted in the limit Q^20 with focus mainly on low-Q^2 data points, we limit our extraction up to Q^2=1. 00. 16em{0ex}GeV^2, and investigate the impact of fitting procedure, data fitting range, and convergence of the fitted functions used on the stability and precision of the extracted charge radius. In addition, we investigate any model dependence of the fits that might be associated with the inclusion of high-Q^2 data points by extending the fitting range up to Q^2=4. 25 GeV^2. For the proton, we find r₏=0. 8480. 002 (stat. ) 0. 003 (sys. ) fm, which is in excellent agreement with the ultra-high precise muonic hydrogen Lamb shift results and PRad I Collaboration measurements, but in disagreement with the Mainz Collaboration extractions and the Particle Data Book (CODATA 2010--2014) results. For the neutron, we find r₍^2=-0. 0890. 002 (stat. ) 0. 002 (sys. ) fm^2, which is 23. 6% below the value obtained by the recent precise measurements of the neutron G₄^n (Q^2) form factor at low-Q^2 utilizing the connection between the N quadrupole transitions and G₄^n (Q^2), and 29. 4% below the new adjusted r₍^2 world data value.