Measurement of the Transverse Beam Spin Asymmetry in Elastic Electron-Proton Scattering and the Inelastic Contribution to the Imaginary Part of the Two-Photon Exchange Amplitude

We report on a measurement of the asymmetry in the scattering of transversely polarized electrons off unpolarized protons, A_⊥, at two Q² values of 0.106 and 0.230 (GeV/c)² and a scattering angle of 30^∘<θₑ<40^∘. The measured transverse asymmetries are ${A}_{{⊥}}({Q}²=0.106 (GeV/c{)}²)=({-}8.59±{}{0.89}ₛₜₐₜ±{}{0.75}syst)×{}{10}^{{-}6}$ and ${A}_{{⊥}}({Q}²=0.230 (GeV/c{)}²)=({-}8.52±{}{2.31}ₛₜₐₜ±{}{0.87}syst)×{}{10}^{{-}6}$. The first errors denote the statistical error and the second the systematic uncertainties. From comparison with theoretical estimates of ${A}_{{⊥}}$ we conclude that ${π}N$-intermediate states give a substantial contribution to the imaginary part of the two-photon amplitude. There is no obvious reason why this should be different for the real part of the two-photon amplitude, which enters into the radiative corrections for the Rosenbluth separation measurements of the electric form factor of the proton.