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$_perp$, at two Q$^2$ values of qsquaredaveragedlow (GeV/c)$^2$ and qsquaredaveragedhighII (GeV/c)$^2$ and a scattering angle of $30^circ < theta_e < 40^circ$. The measured transverse asymmetries are A$_{perp}$(Q$^2$ = qsquaredaveragedlow (GeV/c)$^2$) = (experimentalasymmetry alulowcorr $pm$ statisticalerrorlow$_{rm stat}$ $pm$ combinedsyspolerrorlowalucor$_{rm sys}$) $times$ 10$^{-6}$ and A$_{perp}$(Q$^2$ = qsquaredaveragedhighII (GeV/c)$^2$) = (experimentalasymme tryaluhighcorr $pm$ statisticalerrorhigh$_{rm stat}$ $pm$ combinedsyspolerrorhighalucor$_{rm sys}$) $times$ 10$^{-6}$. The first errors denotes the statistical error and the second the systematic uncertainties. A$_perp$ arises from the imaginary part of the two-photon exchange amplitude and is zero in the one-photon exchange approximation. From comparison with theoretical estimates of A$_perp$ we conclude that $pi$N-intermediate states give a substantial contribution to the imaginary part of the two-photon amplitude. The contribution from the ground state proton to the imaginary part of the two-photon exchange can be neglected. 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.