Forward sum rule for the $2\gamma$-exchange correction to the charge-radius extraction from elastic electron scattering

Two-photon-exchange (TPE) contributions to elastic electron-proton scattering in the forward regime in leading logarithmic $\sim tln\left|t\right|$ approximation in the momentum transfer $t$ are considered. The imaginary part of the TPE amplitude in the forward kinematics is related to the total photoabsorption cross section. The real part of the TPE amplitude is obtained from an unsubtracted fixed-$t$ dispersion relation. This allows a clean prediction of the real part of the TPE amplitude at forward angles with the leading term $\sim tln\left|t\right|$. Numerical estimates are comparable with or exceed the experimental precision in extracting the charge radius from the experimental data.

Figure 1

Imaginary part of the $2\gamma$-exchange diagram.

Figure 2

Results for the TPE effect on the reduced cross section $\delta {\sigma }_R(E,t)/\left|t\right|$ for the proton, as a function of $\left|t\right|$ in ${\mathrm{GeV}}^2$ for three values of the laboratory beam energies: 180, 315, and 450 MeV. The experimental sensitivity is also shown.

Figure 3

Same as in Fig. 2 for the deuteron.

Figure 4

Same as in Fig. 2 for the proton and for two values of the laboratory beam energies: 1.1 and 2.2 GeV corre-sponding to the kinematics of the proposed JLab experiment [26].