Impact of JLab data on the determination of GPDs at zero skewness and new insights from transition form factors $N\to \mathrm{\Delta }$

It is well-established now that the generalized parton distributions (GPDs) at zero skewness are playing important roles in some physical process such as elastic electron-nucleon scattering, elastic (anti)neutrino-nucleon scattering, and wide-angle Compton scattering (WACS) via various types of form factors (FFs). In this study, we are going to utilize the recent JLab measurements of the elastic electron-nucleon scattering reduced cross section, namely GMp12, as a touchstone to unravel the tension observed between the measurements of the WACS cross section and the data of the proton magnetic FF $G_M^p$. We also investigate the impact of GMp12 data on valence unpolarized GPDs $H_v^q$ and $E_v^q$ at zero skewness by performing some ${\chi }^2$ analyses of the related experimental data. By calculating the electric and scalar quadrupole ratios, $R_{\mathrm{EM}}$ and $R_{\mathrm{SM}}$, and magnetic transition FF $G_M^{*}/3G_D$ related to the nucleon-to-delta ($N\to \mathrm{\Delta }$) transition using the extracted GPDs and comparing the results with corresponding experimental measurements, we show that our results are in an excellent consistency with experiments, indicating the universality property of GPDs. We emphasize that the inclusion of these data in the future analysis of GPDs can significantly affect the extracted GPDs especially their uncertainties at smaller values of $Q^2$.

Figure 1

A comparison between the experimental data from the GMp12 measurements [73] for the reduced cross section of Eq. (4) and the corresponding theoretical predictions obtained using Set 2 and Set 3 of GPDs taken from Ref. [32].

Figure 2

Same as Fig. 1, but for GPD Set 11 and Set 12.

Figure 3

A comparison between the results of three analyses performed in Sec. 3c for the valence unpolarized GPD $x{H}_v^u(x)$ as the ratio to the Base Fit at four $t$ values shown in panels (a) $t=-3$, (b) $t=-6$, (c) $t=-9$, and (d) $t=-12{\mathrm{GeV}}^2$.

Figure 4

Same as Fig. 3, but for valence unpolarized GPD $x{H}_v^d(x)$.

Figure 5

Same as Fig. 3, but for valence unpolarized GPD $x{E}_v^u(x)$.

Figure 6

Same as Fig. 3 but for valence unpolarized GPD $x{E}_v^d(x)$.

Figure 7

A comparison between our results for $R_{\mathrm{EM}}$ and $R_{\mathrm{SM}}$ (expressed in percent) obtained using the set of GPDs named GMp12 and the corresponding experimental measurements from MAMI [108, 109, 110, 111], CLAS (2002) [112], CLAS (2006) [113, 114], CLAS (2009) [115], Hall C [116, 117], Hall A [118], and Blomberg (2016) [119]. The other experimental data denoted as “Other sources” have been gathered from Refs. [120, 121, 122, 123].

Figure 8

A comparison between our result for $G_M^{*}/3G_D$ obtained using the set of GPDs named GMp12 and the corresponding experimental measurements from CLAS (2006) [113, 114], CLAS (2009) [115], and Hall C [116, 117] as well as the pure theoretical calculations from the LFRQM [124, 125] and the Dyson-Schwinger equation [126].