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 rₚ and neutron rₙ² root-mean-square charge radius using the Dirac flavor-separated up- and down-quark F₁(u,d)(Q²) form factors data covering the range 0.0155<Q²<4.250 GeV² 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)(Q²) at Q²=0 through model-independent relations. As the charge radius is extracted in the limit Q²→0 with focus mainly on low-Q² data points, we limit our extraction up to Q²=1.00.16em0exGeV², 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-Q² data points by extending the fitting range up to Q²=4.25 GeV². For the proton, we find rₚ=0.848±0.002(stat.)±0.003(sys.) fm, which is in excellent agreement with the ultra-high precise muonic hydrogen μH 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 rₙ²=-0.089±0.002(stat.)±0.002(sys.) fm², which is ≈23.6% below the value obtained by the recent precise measurements of the neutron GEⁿ(Q²) form factor at low-Q² utilizing the connection between the N→Δ quadrupole transitions and GEⁿ(Q²), and ≈29.4% below the new adjusted rₙ² world data value.