Extraction of elastic scattering cross-section ratio $R_{e^{+}{e}^{-}}$ from $ep$ elastic scattering experimental data

In this work, we present a new prediction of the positron-proton to electron-proton elastic scattering cross sections ratio $R_{e^{+}{e}^{-}}$. While many phenomenological studies extracted the ratio $R_{e^{+}{e}^{-}}$ using proposed, model-independent parametrizations of the hard two-photon exchange (TPE) corrections to electron-proton ($\text{ep}$) elastic scattering cross section ${\sigma }_R$, we do not assume prior knowledge of the functional form of the hard TPE corrections to ${\sigma }_R$, and use combined unpolarized, and polarized $\text{ep}$ elastic scattering experimental data to extract the TPE contributions. We provide a simple parametrization of the TPE corrections to ${\sigma }_R$, along with the uncertainties associated with the model dependence of the extractions, and use our TPE parametrization to predict the ratio $R_{e^{+}{e}^{-}}$. We compare our prediction of $R_{e^{+}{e}^{-}}$ to several previous phenomenological extractions, TPE-hadronic calculations, and world's data with emphasis mainly on the kinematics range of the recent precise direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments.

Figure 1

The ratio $R_{e^{+}{e}^{-}}$ as a function of $\varepsilon$ as extracted using Eq. (12) for a sample of low- and high-$Q^2$ data points from the data of Refs. [13, 14, 17]. Also shown is our fit (solid black line).

Figure 2

The TPE coefficient ${\alpha }_1\left(Q^2\right)$ as obtained for all data sets from Refs. [12, 13, 14, 15, 17, 105, 106, 107] (open dark-green squares). The bottom plot is on a smaller vertical scale for clarity. Also shown are the simple parametrization of our results (solid red line), and curves representing ${\alpha }_1\left(Q^2\right)$ as determined using TPE-hadronic calculations from Ref. [26] “BMT Correction” (dashed-dotted magenta line), Ref. [108] “AMT Correction” (dashed-dotted black line), and previous analyzes “QAA1” [78] (dashed red line), “QAA2” [82] (long-dashed blue line), and “Bernauer Spline” [17] (large-dashed magenta line). Note that we do not show extractions of ${\alpha }_1\left(Q^2\right)$ for the TPE-hadronic calculations and “Bernauer Spline” at very low $Q^2$, as the $\varepsilon$ dependence is quite different in our parametrization when the cross sections are dominated by the electric FF $G_E$.

Figure 3

The ratio $R_{e^{+}{e}^{-}}$ as a function of $\varepsilon$ as extracted from this work (solid red line), along with its error band (long-dashed dark-green line), at the $Q^2$ values listed in the figure. Also shown are previous TPE hadronic calculations “AMT-Hadronic” [108] (dashed-dotted black line), and several previous phenomenological extractions: “QAA1” [78] (dashed red line), and “QAA2” [82] (long-dashed blue line). The data points are direct measurements of $R_{e^{+}{e}^{-}}$ from Refs. [100, 101, 102, 103]. For the world's data, the measurement and the $Q^2$ value(s) are given in ${(\mathrm{GeV}/c)}^2$.