The paper describes a precise measurement of electron scattering off the proton at momentum transfers of $0.003 lesssim Q^2 lesssim 1$ GeV$^2$. The average point-to-point error of the cross sections in this experiment is $sim$ 0.37%. These data are u
sed for a coherent new analysis together with all world data of unpolarized and polarized electron scattering from the very smallest to the highest momentum transfers so far measured. The extracted electric and magnetic form factors provide new insight into their exact shape, deviating from the classical dipole form, and of structure on top of this gross shape. The data reaching very low $Q^2$ values are used for a new determination of the electric and magnetic radii. An empirical determination of the Two-Photon-Exchange (TPE) correction is presented. The implications of this correction on the radii and the question of a directly visible signal of the pion cloud are addressed.
In arXiv:1108.3058v1 [nucl-ex], Arrington criticizes the Coulomb corrections we applied in the analysis of high precision form factor data (see Phys.Rev.Lett.105:242001, 2010, arXiv:1007.5076v3 [nucl-ex]). We show, by comparing different calculations
cited in the Comment, that the criticism of the Comment neglects the large uncertainty of more modern TPE corrections. This uncertainty has also been seen in recent polarized measurements. We rerun our analysis using one of these calculations. The results show that the Comment exaggerates the quantitative effect at small Q^2.
New precise results of a measurement of the elastic electron-proton scattering cross section performed at the Mainz Microtron MAMI are presented. About 1400 cross sections were measured with negative four-momentum transfers squared up to Q^2=1 (GeV/c
)^2 with statistical errors below 0.2%. The electric and magnetic form factors of the proton were extracted by fits of a large variety of form factor models directly to the cross sections. The form factors show some features at the scale of the pion cloud. The charge and magnetic radii are determined to be r_E=0.879(5)(stat.)(4)(syst.)(2)(model)(4)(group) fm and r_M=0.777(13)(stat.)(9)(syst.)(5)(model)(2)(group) fm.
