Two-photon exchange contributions to elastic ep scattering in the non-local field formalism

We construct a non-local gauge-invariant Lagrangian to model the electromagnetic interaction of the proton. The Lagrangian includes all allowed operators with dimension up to five. We compute the two-photon exchange contribution to elastic electron–proton scattering using this effective non-local Lagrangian. The one-loop calculation in this model includes the standard box and cross box diagram with the standard on-shell form of the hadron electromagnetic vertices. Besides this we find an extra contribution, which depends on an unknown constant. We use experimentally extracted form factors for our calculation. We find that the correction to the reduced cross section is slightly non-linear as a function of the photon longitudinal polarization ε. The non-linearity seen is within the experimental error bars of the Rosenbluth data. The final result completely explains the difference between the form factor ratio G_E/G_M extracted by Rosenbluth separation technique at SLAC and polarization transfer technique at JLAB.