Prediction of $e^{\pm }$ elastic scattering cross-section ratio based on phenomenological two-photon exchange corrections

I present a prediction of the $e^{\pm }$ elastic scattering cross-section ratio, $R_{e^{+}{e}^{-}}$, as determined using a new parametrization of the two-photon exchange (TPE) corrections to electron-proton elastic scattering cross section ${\sigma }_R$. The extracted ratio is compared to several previous phenomenological extractions, TPE hadronic calculations, and direct measurements from the comparison of electron and positron scattering. The TPE corrections and the ratio $R_{e^{+}{e}^{-}}$ show a clear change of sign at low $Q^2$, which is necessary to explain the high-$Q^2$ form factors discrepancy while being consistent with the known $Q^2\to 0$ limit. While my predictions are in generally good agreement with previous extractions, TPE hadronic calculations, and existing world data including the recent two measurements from the CLAS and VEPP-3 Novosibirsk experiments, they are larger than the new OLYMPUS measurements at larger $Q^2$ values.

Figure 1

The ratio $F(\epsilon ,Q^2)/{\left(G_M^p\right)}^2$ as a function of $\varepsilon$ as extracted from this work (solid black line) for a range of $Q^2$ values listed in the figure. Also shown are previous phenomenological extractions and fits: ABGG [62] (solid red line), Arrington [39] (dashed blue line), Qattan-I [42] (dashed magenta line), Qattan-II [44] (solid magenta line), and Bernauer [48] (dashed-dotted black line).

Figure 2

The ratio $R_{e^{+}{e}^{-}}$ as a function of $\varepsilon$ as extracted from this work (solid black line) for a range of $Q^2$ values listed in the figure. Also shown are previous TPE hadronic calculations AMT [63] (dashed red line) and phenomenological extractions and fits: ABGG [62] (solid red line), Arrington [39] (dashed blue line), Qattan-I [42] (dashed magenta line), Qattan-II [44] (solid magenta line), and Bernauer [48] (dashed-dotted black line).

Figure 3

The ratio $R_{e^{+}{e}^{-}}$ as a function of $\varepsilon$ as extracted from this work (solid black line) at the $Q^2$ values listed in the figure. Also shown are previous TPE hadronic calculations AMT [63] (dashed red line) and several previous phenomenological extractions and fits: ABGG [62] (solid red line), Arrington [39] (dashed blue line), Qattan-I [42] (dashed magenta line), Qattan-II [44] (solid magenta line), and Bernauer [48] (dashed-dotted black line). The data points are direct measurements of $R_{e^{+}{e}^{-}}$ [51, 53, 54, 58, 66, 67, 68, 69, 70, 71, 72, 73, 74]. For the world data, the measurement and the $Q^2$ value(s) are given in ${(\mathrm{GeV}/c)}^2$.