Towards a Resolution of the Proton Form Factor Problem: New Electron and Positron Scattering Data

There is a significant discrepancy between the values of the proton electric form factor, $G_E^p$, extracted using unpolarized and polarized electron scattering. Calculations predict that small two-photon exchange (TPE) contributions can significantly affect the extraction of $G_E^p$ from the unpolarized electron-proton cross sections. We determined the TPE contribution by measuring the ratio of positron-proton to electron-proton elastic scattering cross sections using a simultaneous, tertiary electron-positron beam incident on a liquid hydrogen target and detecting the scattered particles in the Jefferson Lab CLAS detector. This novel technique allowed us to cover a wide range in virtual photon polarization ($ϵ$) and momentum transfer ($Q^2$) simultaneously, as well as to cancel luminosity-related systematic errors. The cross section ratio increases with decreasing $ϵ$ at $Q^2=1.45{\mathrm{GeV}}^2$. This measurement is consistent with the size of the form factor discrepancy at $Q^2\approx 1.75{\mathrm{GeV}}^2$ and with hadronic calculations including nucleon and $\mathrm{\Delta }$ intermediate states, which have been shown to resolve the discrepancy up to $2–3{\mathrm{GeV}}^2$.

Figure 1

Number of events as a function of the four variables, $\mathrm{\Delta }\varphi$, $\mathrm{\Delta }{P}_p$, and $\mathrm{\Delta }{E}^{\pm }$, before (blue dashed) and after (red) applying the other three elastic cuts on each and summed over all kinematics.

Figure 2

The number of $e^{+}p$ elastic scattering events plotted versus $Q^2$ and $ϵ$ for positive torus polarity. The red lines indicate the bin boundaries for the $Q^2\approx 1.45{\mathrm{GeV}}^2$ data. The hole at $ϵ\approx 0.7$ is due to the trigger requirement that at least one of the two particles hits the EC. The holes for other configurations (negative torus polarity or $e^{-}p$ events) are smaller.

Figure 3

Ratio of $e^{+}p/e^{-}p$ cross sections corrected for ${\delta }_{\text{brem}}$ as a function of $ϵ$ at $Q^2=1.45{\mathrm{GeV}}^2$ (top) and as a function of $Q^2$ at $ϵ=0.88$ (bottom). The filled blue circles show the results of this measurement. The inner error bars are the statistical uncertainties and the outer error bars are the statistical, systematic, and radiative-correction uncertainties added in quadrature. The black dotted line at $R^{\prime }=1$ is the limit of no TPE. The almost-identical nucleon-only hadronic calculations are shown by the short-dashed black (Blunden et al. [26]) and solid magenta curves (Zhou and Yang [45]). The long-dashed red curve shows the calculation including $N+\mathrm{\Delta }$ intermediate states [45]. The cyan dot-dashed curve shows the calculation of TPE effects on a structureless point proton [12]. The open green circles show the previous world data at $Q^2\ge 1{\mathrm{GeV}}^2$ (top) and $ϵ\ge 0.8$ (bottom) [34].