Two-photon exchange from intermediate state resonances in elastic electron-proton scattering
Jaseer Ahmed, P. G. Blunden, Wally Melnitchouk
Abstract
We use a recently developed dispersive approach to compute the two-photon exchange (TPE) correction to elastic electron-proton scattering, including contributions from hadronic ${J}^{P}=1/{2}^{\ifmmode\pm\else\textpm\fi{}}$ and $3/{2}^{\ifmmode\pm\else\textpm\fi{}}$ resonant intermediate states below 1.8 GeV. For the transition amplitudes from the proton ground state to the resonant excited states we employ new exclusive meson electroproduction data from CLAS at ${Q}^{2}\ensuremath{\lesssim}5\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$, and we explore the effects of both fixed and dynamic widths for the resonances. Among the resonant states, the $N(1520)\phantom{\rule{0.16em}{0ex}}3/{2}^{\ensuremath{-}}$ becomes dominant for ${Q}^{2}\ensuremath{\gtrsim}2\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$, with a sign opposite to the comparably sized $\mathrm{\ensuremath{\Delta}}(1232)\phantom{\rule{0.16em}{0ex}}3/{2}^{+}$ contribution, leading to an overall increase in the size of the TPE correction to the cross section relative to the nucleon only contribution at higher ${Q}^{2}$ values. The results are in good overall agreement with recent ${e}^{+}p$ to ${e}^{\ensuremath{-}}p$ cross-section ratio and polarization transfer measurements, and provide compelling evidence for a resolution of the electric to magnetic form factor ratio discrepancy.