Partonic Calculation of the Two-Photon Exchange Contribution to Elastic Electron-Proton Scattering at Large Momentum Transfer

We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer through the scattering off a parton in the proton. We relate the two-photon exchange amplitude to the generalized parton distributions which appear in hard exclusive processes. We find that when taking the polarization transfer determinations of the form factors as input, adding in the 2-photon correction does reproduce the Rosenbluth cross sections.

Figure 1

Handbag diagram for the elastic lepton-nucleon scattering at large momentum transfers. In the hard scattering process $H$, the lepton scatters from quarks with momenta $p_q$ and $p_q^{\prime }$. The lower blob represents the GPDs of the nucleon.

Figure 2

Direct and crossed box diagrams for $H$ in Fig. 1.

Figure 3

Rosenbluth plots for elastic $ep$ scattering: ${\sigma }_R$ divided by $({\mu }_p{G}_D{)}^2$, with $G_D=(1+Q^2/0.71{)}^{-2}$. Dotted curves: Born approximation using $G_{Ep}/G_{Mp}$ from polarization data [4, 5]. Dashed curves: results when adding the GPD calculation for the hard $2\gamma$ exchange correction, for the kinematical range $s,-u>M^2$. Full curves are the total results including, in addition, the soft $2\gamma$ exchange correction relative to Mo and Tsai. The data are from Ref. 3.

Figure 4

Proton normal spin asymmetry for elastic $ep$ scattering as function of the center of mass ($c.m.$) scattering angle. The GPD calculation is shown by the solid curve, bounded by the kinematic range where $-u,Q^2>M^2$. For comparison, the elastic contribution is shown by the dotted curve [8].