Global analysis of proton elastic form factor data with two-photon exchange corrections

We use the world's data on elastic electron-proton scattering and calculations of two-photon exchange effects to extract corrected values of the proton's electric and magnetic form factors over the full $Q^2$ range of the existing data. Our analysis combines the corrected Rosenbluth cross section and polarization transfer data, and is the first extraction of $G_E$ and $G_M$ including explicit two-photon exchange corrections and their associated uncertainties. In addition, we examine the angular dependence of the corrected cross sections to examine the possible nonlinearities of the cross section as a function of ɛ.

Figure 1

Ratio of elastic $e^{+}p$ to $e^{-}p$ cross sections. The data (crosses) are taken from Ref. [53] and references therein. The filled diamonds show the ratio using the TPE calculation of Ref. [22], whereas the open diamonds include the additional contribution in Eq. (10), which modifies the high-$Q^2$ correction at low ɛ.

Figure 2

Ratio ${\mu }_p{G}_E/G_M$ extracted from polarization transfer (filled diamonds) and LT measurements (open circles). The top (bottom) figure shows LT separations without (with) TPE corrections applied to the cross sections.

Figure 3

Extracted values of $G_E$ and $G_M$ from the global analyses. The open circles are the results of the combined analysis of the cross-section data and polarization measurements (Sec. 3c, Table ). The magenta crosses are the extracted values of $G_M$ (Table ) for the high-$Q^2$ region, where $G_E$ cannot be extracted. The solid lines are the fits to TPE-corrected cross-section and polarization data (Sec. 3a). The dotted curves show the results of taking $G_E$ and $G_M$ to be $\sqrt{{\sigma }_L}$ and $\sqrt{{\sigma }_T}$, respectively, from a fit to the TPE-uncorrected reduced cross section (Appendix ), i.e., the value one would obtain using only cross-section data and ignoring TPE.