Study of Two-Photon Exchange via the Beam Transverse Single Spin Asymmetry in Electron-Proton Elastic Scattering at Forward Angles over a Wide Energy Range

We report on a new measurement of the beam transverse single spin asymmetry in electron-proton elastic scattering, $A_{\perp }^{ep}$, at five beam energies from 315.1 to 1508.4 MeV and at a scattering angle of $30°<\theta <40°$. The covered $Q^2$ values are 0.032, 0.057, 0.082, 0.218, 0.613 $(\mathrm{GeV}/c{)}^2$. The measurement clearly indicates significant inelastic contributions to the two-photon-exchange (TPE) amplitude in the low-$Q^2$ kinematic region. No theoretical calculation is able to reproduce our result. Comparison with a calculation based on unitarity, which only takes into account elastic and $\pi N$ inelastic intermediate states, suggests that there are other inelastic intermediate states such as $\pi \pi N$, $K\mathrm{\Lambda }$, and $\eta N$. Covering a wide energy range, our new high-precision data provide a benchmark to study those intermediate states.

Figure 1

The two-photon-exchange contribution to the elastic electron-proton scattering amplitude. The blob in the lower part represents the doubly virtual Compton scattering (VVCS) amplitude.

Figure 2

The asymmetries $A_{\mathrm{mea}}$ measured in 146 frames of the A4 EMC, presented as a function of the electron azimuthal angle ${\varphi }_e$, fit by $A_{\mathrm{mea}}=-A_{\perp }^{\exp }\cos {\varphi }_e+C$.

Figure 3

$A_{\perp }^{ep}$ as a function of beam energy. Note the data point at 855.2 MeV from Ref. [67] is shifted horizontally for a better view. The bands reflect the dependence of the mean scattering angle on beam energy.