Phenomenological reexamination of two-photon-exchange corrections to the proton recoil-polarization ratio ${\mu }_p{G}_E/G_M$ utilizing electron-proton elastic scattering experimental data

In this work, we have phenomenologically reexamined the $\varepsilon$ dependence of the proton's recoil-polarization ratio $R={\mu }_p{G}_E/G_M$ for possible two-photon-exchange (TPE) corrections beyond the one-photon-exchange (OPE) or Born approximation. High-precision Rosenbluth measurements of ${\sigma }_R(\varepsilon ,Q^2)$ taken at $Q^2=2.64$, 3.20, and $4.10{\mathrm{GeV}}^2$ were used to extract the TPE coefficients needed to provide an estimate of the size of the TPE corrections to the ratio $R$, and construct the two TPE $Y_{(M,E)}(\varepsilon ,Q^2)$ amplitudes. Our results suggest that the ratio $R$ shows very small (negligible) enhancement with $\varepsilon$, less than 0.40% in magnitude, with values consistent with the OPE prediction for the $Q^2$ range studied. We also compare our results to previous phenomenological extractions and several theoretical calculations.

Figure 1

The reduced cross section ${\sigma }_R$ as a function of $\varepsilon$ (solid red squares) from Ref. [10] at the $Q^2$ value listed in the figure. Also shown are our ${\sigma }_R$ Fit based on Eq. (6) (solid black line), and the global fit based on Eq. (3) (long dashed dark-green line) for comparison. The global fit is only performed at $Q^2=2.64{\mathrm{GeV}}^2$.

Figure 2

(a) The ratio $R$ as a function of $\varepsilon$ at $Q^2=2.50{\mathrm{GeV}}^2$ from Ref. [91] (solid dark-green squares) and Ref. [98] (solid red triangle). Also shown are our ${\sigma }_R$ Fit (solid dark line), “Glob. Fit” (long dashed dark-green line) at $Q^2=2.64{\mathrm{GeV}}^2$ along with their uncertainty bands (long dashed black line) and (small dashed dark-green line), respectively, and the Born set value (small dashed-red line) as given by Ref. [69]. (b) The theoretical predictions: “Hadronic” [17] (long dashed-dotted black line), “GPD” [27] (long dashed blue line), pQCD [20] (“COZ” [60] (large dotted cyan line), and “BLW” [43] (long dashed-dotted cyan line), and “SF” [28] (long dashed-dotted blue line).

Figure 3

The $\varepsilon$ dependence of the TPE amplitudes at $Q^2=2.64{\mathrm{GeV}}^2$ from this work: $Y_M$ (top) (solid black line), and $Y_E$ (bottom) (${\sigma }_R$ Fit: solid red line, and Glob. Fit: small dashed dark-green line). In addition, we compare our results to previous phenomenological extractions from Ref. [76] IQ (dashed magenta line), and Ref. [69] Guttmann Fit I (dashed black line) and Guttmann Fit II (long-dashed black line). Also shown are several previous hadronic TPE calculations: BK: elastic [32] (dashed red line), BK: elastic $+\mathrm{\Delta }\left(1232\right)$ [34] (long-dashed red line), BK: elastic $+P_{33}$ [35] (solid magenta line), BK: elastic $+\pi N$ [36] (dashed-dotted dark-green line), and calculations based on QCD factorization within the SCET approach KV [22] (dotted blue line).

Figure 4

The $\varepsilon$ dependence of the TPE amplitudes $Y_{(M,E)}$ as extracted from this work at the $Q^2$ listed in the figure: This Work: $Y_M, Y_E$ solid (black, red), respectively. Also shown are previous phenomenological extractions [76]: IQ: $Y_M, Y_E$ long-dashed (black, red) line, respectively, and hadronic calculations assuming different intermediate states: elastic: $Y_M, Y_E$ (solid, dashed-dotted) cyan line, respectively, from Ref. [32], and elastic $+\pi N$ with spin-1/2 and -3/2 channels labeled as elastic $+\pi N$: $Y_M, Y_E$ dotted (black, red) line, respectively, from Ref. [36].