%0 Journal Article %T 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 %A F. E. Maas %A K. Aulenbacher %A S. Baunack %A L. Capozza %A J. Diefenbach %A B. Gl£¿ser %A Y. Imai %A T. Hammel %A D. von Harrach %A E. -M. Kabub %A R. Kothe %A J. H. Lee %A A. Sanchez-Lorente %A E. Schilling %A D. Schwaab %A G. Stephan %A G. Weber %A C. Weinrich %A I. Altarev %A J. Arvieux %A M. Elyakoubi %A R. Frascaria %A R. Kunne %A M. Morlet %A S. Ong %A J. Vandewiele %A S. Kowalski %A R. Suleiman %A S. Taylor %J Physics %D 2004 %I arXiv %R 10.1103/PhysRevLett.94.082001 %X 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. %U http://arxiv.org/abs/nucl-ex/0410013v1