Two photon exchange contributions to elastic $\vec{e}+p\rightarrow e+\vec{p}$ process in the non-local field formalism

Abstract

We compute the two photon exchange contributions to elastic scattering of polarized electrons from target protons. We use a non-local field theory formalism for this calculation. The formalism maintains gauge invariance and provides a systematic procedure for making this calculation. The results depend on one unknown parameter, $\bar{b}$ . We compute the two photon exchange correction to the ratio of electric to magnetic form factors extracted using polarization transfer experiments. The correction is found to be small if $\bar{b}\sim 1$ . However, for larger values of $\bar{b}>3$ , the correction can be quite significant. The correction to the polarization transfer results goes in the right direction to explain their difference with the ratio measured by the Rosenbluth separation method. We find that the difference between the two experimental results can be explained for a wide range of values of the parameter $\bar{b}$ . We also find that the corrections due to two photon exchange depend on the photon longitudinal polarization e. Hence, we predict an e dependence of the form factor ratio extracted using the polarization transfer technique. Finally, we obtain a limit on $\bar{b}$ by requiring that the non-linearity in e dependence of the unpolarized reduced cross section is within experimental errors.