In this work I present new extractions of the proton's conventional charge $\langle r_E\rangle$ and magnetic $\langle r_M\rangle$ root-mean-square radii using two-photon-exchange corrected electric $G_E^p\left(Q^2\right)$ and magnetic $G_M^p\left(Q^2\right)$ form factor data 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)] covering the range of 0.0155 $<Q^2<$ 1.00 ${\mathrm{GeV}}^2$. The radii were extracted following two different approaches. In the first approach both form factors were fitted separately within a finite and extended $Q^2$ range utilizing several rational functional forms of different orders and number of fitting parameters, and the radii were extracted based on the $G_{(E,M)}^p Q^2$ slope at $Q^2=0$. In the second approach, I investigated possible coupling of both radii through the slope of the form factor ratio $R_p=G_E^p/G_M^p$ at $Q^2$ = 0 and extracted $\langle r_E\rangle$ ($\langle r_M\rangle$) using the extracted values of $\langle r_M\rangle$ ($\langle r_E\rangle$) along with their associated statistical uncertainties as obtained from the first approach. For the first approach, I obtain $\langle r_E\rangle =0.854\pm 0.{002}_{\text{(stat.)}}\pm 0.{003}_{\text{(sys.)}}$ (fm) and $\langle r_M\rangle =0.831\pm 0.{001}_{\text{(stat.)}}\pm 0.{001}_{\text{(sys.)}}$ (fm). For the second approach, I obtain $\langle r_E\rangle =0.851\pm 0.{001}_{\text{(stat.)}}\pm 0.{001}_{\text{(sys.)}}$ (fm) and $\langle r_M\rangle =0.834\pm 0.{002}_{\text{(stat.)}}\pm 0.{003}_{\text{(sys.)}}$ (fm). Both approaches yield consistent results suggesting that the proton's charge and magnetic radii are very close to each other but not exactly the same. My extracted $\langle r_E\rangle$ values are also consistent with previous extractions based on the slope of the Dirac flavor-separated $F_1^{(u,d)}\left(Q^2\right)$ form factors at $Q^2=$ 0 and the ultrahigh precise muonic hydrogen μH Lamb shift and PRad I Collaboration measurements but in strong disagreement with the Mainz A1 Collaboration results. For $\langle r_M\rangle$ my results are in very good agreement with several recent extractions based on combined dispersion analyses, but they are in stark contrast with the conflicting range of results obtained by the Mainz A1 Collaboration. I also extracted the proton's transverse charge and magnetization ${\langle b^2\rangle }_{(1,2)}^p$ and the 3D Dirac and Pauli ${\langle r^2\rangle }_{(1,2)}^p$ radii, and compared the results to previous extractions and theoretical calculations based on dispersively improved chiral effective field theory ($\mathrm{DI}\chi \mathrm{EFT}$).

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• Form factors
• Lepton induced nuclear reactions
• Nuclear radii
• Particle interactions
• Polarization phenomena
• QCD in nuclear reactions