New extraction of the Re+e− elastic scattering cross-section ratio based on a simplified phenomenological hard two-photon-exchange correction approach

Abstract

In this work, we present a prediction of the positron-proton and electron-proton elastic scattering cross-section ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ based on a new phenomenological parametrization of the hard two-photon-exchange (TPE) corrections to electron-proton elastic scattering cross section ${\ensuremath{\sigma}}_{R}$. The TPE parametrization proposed in this work is rather simple, as it only requires the use of suitable global fits of both the Rosenbluth magnetic ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{M}$, and the true magnetic ${G}_{M}$ form factors, or alternatively, the electric form factors ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{E}$ and ${G}_{E}$. We compare our results to recent extractions, and world's data on ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ with emphasis mainly on the kinematics range of the recent direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments. With the proper choice of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{M}$ and ${G}_{M}$ parametrizations, and while our results are in generally good agreement with ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ measurements taken at high $\ensuremath{\varepsilon}$ points and for all ${Q}^{2}$ range, they agree remarkably well, within the error bands of the predictions, with ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ measurements taken at low-$\ensuremath{\varepsilon}$ points for ${Q}^{2}=1.0$ and $1.5\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$, where emphasis should be placed for evidence of hard TPE correction. Finally, we believe that the assumption that hard TPE corrections could account for the discrepancy on the proton's form factors ratio ${\ensuremath{\mu}}_{p}{G}_{E}/{G}_{M}$ is still an open question as more measurements of ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ are clearly needed for ${Q}^{2}>\phantom{\rule{4pt}{0ex}}2.1\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$, in the region where the discrepancy is significant.