Search for effects beyond the Born approximation in polarization transfer observables in $\vec{e}p$ elastic scattering

Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, $G_E\mathrm{/}{G}_M$, obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange (TPEX) contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic $H(\vec{e},e^{\mathrm{\prime }}\vec{p})$ reaction for three different beam energies at a fixed squared momentum transfer $Q^2=2.5$ GeV${}^2$, spanning a wide range of the virtual photon polarization parameter, $ϵ$. From these measured polarization observables, we have obtained separately the ratio $R$, which equals ${\mu }_p{G}_E\mathrm{/}{G}_M$ in the Born approximation, and the longitudinal polarization transfer component $P_{\mathrm{\ell }}$, with statistical and systematic uncertainties of $\Delta R \approx \pm 0.01 \mbox{(stat)} \pm 0.013 \mbox{(syst)}$and$\Delta P_\ell/P^{Born}_{\ell} \approx \pm 0.006 \mbox{(stat)}\pm 0.01 \mbox{(syst)}$\mathrm{.}Theratio$R$ is found to be independent of $ϵ$ at the 1.5% level, while the $ϵ$ dependence of $P_{\mathrm{\ell }}$ shows an enhancement of $(2.3\pm 0.6)$ relative to the Born approximation at large $ϵ$.