Suppression of hard two-photon-exchange contributions to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:msub></mml:math> elastic scattering cross-section ratios: A phenomenological approach
I. A. Qattan, Shashikant P. Patole, Ahmad Alsaad
Abstract
We present a new extraction of the positron-proton and electron-proton elastic-scattering cross sections ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ based on a new phenomenological parametrization of the two-photon-exchange (TPE) corrections to electron-proton $(ep)$ elastic-scattering cross section ${\ensuremath{\sigma}}_{R}$. We compare our results to several previous phenomenological extractions, TPE hadronic calculations, and world data on the ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$, including the recent direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments. The ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ as extracted from this work is consistent with unity, and shows little sensitivity to $\ensuremath{\varepsilon}$ and essentially no ${Q}^{2}$ dependence, suggesting a smaller hard-TPE contribution to ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ than that predicted by several previous phenomenological extractions and TPE hadronic calculations. In this work, we show that, under certain assumptions and constraints imposed on the TPE amplitudes ${Y}_{E}$ and ${Y}_{3}$, the proton magnetic form factor squared ${({G}_{M}^{p})}^{2}$, and the proton form factors ratio ${\ensuremath{\mu}}_{p}{R}_{p}={\ensuremath{\mu}}_{p}{G}_{E}^{p}/{G}_{M}^{p}$, the TPE corrections to ${\ensuremath{\sigma}}_{R}$ can be suppressed, yielding a small hard-TPE contribution to ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$. Our results are in agreement with the recent analysis by Bytev and Tomasi-Gustafsson [Phys. Rev. C 99, 025205 (2019)]. We believe that the assumption that hard-TPE corrections could account for the discrepancy in the ratio ${\ensuremath{\mu}}_{p}{R}_{p}$ is still an open question.