Determination of the generalized parton distributions through the analysis of the world electron scattering data considering two-photon exchange corrections

We determine the valence generalized parton distributions (GPDs) $H_v^q$ and $E_v^q$ with their uncertainties at zero skewness by performing a ${\chi }^2$ analysis of the world electron scattering data considering two-photon exchange corrections. The data include a wide and updated range of the electric and magnetic form factors (FFs) of the proton and neutron. As a result, we find that there are not enough constraints on GPDs $E_v^q$ from FFs data solely though $H_v^q$ are well constrained. By including the new data of the charge and magnetic radius of the nucleon in the analysis, we show that they put new constraints on the final GPDs, especially on $E_v^q$. Moreover, we calculate the gravitational FF $M_2$ and the total angular momentum $J^q$ using the extracted GPDs and compare them with the FFs obtained from the light-cone QCD sum rules (LCSR) and lattice QCD. We show that our results are interestingly in a good consistency with the pure theoretical predictions.

Figure 1

A comparison between our results for GPD $x{H}_v^u(x)$ obtained from three analyses described in Sec. 4a and the corresponding one from the analysis of DK13 [24] at four $t$ values shown in panel (a) $t=0$, (b) $t=-1$, (c) $t=-3$, and (d) $t=-6{\mathrm{G}\mathrm{e}\mathrm{V}}^2$.

Figure 2

Same as Fig. 1 but for GPD $x{H}_v^d(x)$.

Figure 3

Same as Fig. 1 but for GPD $x{E}_v^u(x)$.

Figure 4

Same as Fig. 1 but for GPD $x{E}_v^d(x)$.

Figure 5

A comparison between our results for GPD $x{H}_v^u(x)$ obtained from two analyses described in Sec. 4b and the corresponding ones from the analysis of DK13 [24] at four $t$ values: (a) $t=0$, (b) $t=-1$, (c) $t=-3$, and (d) $t=-6{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The results of the RSM [47] have also been shown for $t=0,-1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$.

Figure 6

Same as Fig. 5 but for GPD $x{H}_v^d(x)$.

Figure 7

Same as Fig. 5 but for GPD $x{E}_v^u(x)$.

Figure 8

Same as Fig. 5 but for GPD $x{E}_v^d(x)$.

Figure 9

A comparison between our results obtained for $M_2(t)$ using Set 4 and Set 5 of GPDs and the corresponding one calculated using LCSR [52].

Figure 10

Same as Fig. 9, but in the interval $0<-t<1.3{\mathrm{GeV}}^2$ and including also the lattice results taken from Table 15 of Ref. [53].

Figure 11

A comparison between our predictions for $J_v^u$ and $J_v^d$ at limit $t=0$ and $\mu =2\mathrm{GeV}$ obtained using Set 4 and Set 5 and the corresponding ones from PRC88 [55], LHPC [56], Thomas [57], TMD [58], and DK13 [24].

Figure 12

Same as Fig. 9, but for the proton total angular momentum $J^q$ of Eq. (20).

Figure 13

Same as Fig. 12, but in the interval $0<-t<1.3{\mathrm{GeV}}^2$ and including also the lattice results taken from Table 15 of Ref. [53].