Charge and longitudinal momentum distributions in transverse coordinate space

We investigate the charge distributions for the $u$ and $d$ quarks in transverse coordinate space in a light-front quark-diquark model for the nucleons using the overlaps of the wave functions constructed from the soft-wall AdS/QCD prediction. We have also obtained the charge distributions for proton and neutron in transverse coordinate space and compared it with the distributions obtained in impact-parameter space. Further, we study the longitudinal momentum distributions using the wave functions in the transverse coordinate space. We have also shown the explicit fermionic and bosonic contributions for different struck $u$ and $d$ quarks.

Figure 1

Charge distributions $P^q({\mathbf{r}}_{\perp })$ and ${\rho }_{ch}^q({\mathbf{b}}_{\perp })$ in the transverse coordinate and impact-parameter spaces respectively for the (a) $u$ quarks and (b) $d$ quarks, where $r=|{\mathbf{r}}_{\perp }|$ and $b=|{\mathbf{b}}_{\perp }|$. The blue solid lines represent the quark-diquark model in AdS/QCD (this work) and the red dashed lines represent the phenomenological model [46]. The bands in the plots represent the errors in the model predictions. For $u$ quark the bands are very small.

Figure 2

Charge distribution $P^{p,n}({\mathbf{r}}_{\perp })$ and ${\rho }_{ch}^{p,n}({\mathbf{b}}_{\perp })$ in the transverse coordinate and impact-parameter spaces respectively for the (a) proton and (b) neutron. The blue solid lines represent the quark-diquark model in AdS/QCD (this work) and the red dashed lines represent the phenomenological model [46]. The bands in the plots represent the errors in the model predictions.

Figure 3

Charge distribution (a) $P^u(x,{\mathbf{r}}_{\perp })$ and (b) $P^d(x,{\mathbf{r}}_{\perp })$ in the transverse coordinate space as a function of ${\mathbf{r}}_{\perp }$ and $x$.

Figure 4

Charge distribution (a) $P^p(x,{\mathbf{r}}_{\perp })$ and (b) $P^n(x,{\mathbf{r}}_{\perp })$ in the transverse coordinate space as a function of ${\mathbf{r}}_{\perp }$ and $x$.

Figure 5

Longitudinal momentum distributions (a) $P_L^{f/b}$ for struck $u$ quark, (b) $P_L^{f/b}$ for struck $d$ quark $d$ and (c) $P_L^p$ for proton when struck quarks are $u$ and $d$. The blue solid lines represent the quark-diquark model in AdS/QCD (this work) and the red dashed lines represent the phenomenological model [46]. The error bands shown in the plots are estimated from the errors in the model parameters.

Figure 6

Longitudinal momentum distributions $P_{Lq}^f(x,{\mathbf{r}}_{\perp })$ and $P_{Lq}^b(x,{\mathbf{r}}_{\perp })$ as a function of ${\mathbf{r}}_{\perp }$ and $x$. Left panel: when the struck flavor is $u$ and the diquark is $ud$; right panel: when the struck flavor is $d$ and the diquark is $uu$.

Figure 7

Longitudinal momentum distributions $P_{Lq}(x,{\mathbf{r}}_{\perp })$ for proton as a function of ${\mathbf{r}}_{\perp }$ and $x$, (a) for struck flavor $u$ and (b) for struck flavor $d$.