Valence double parton distributions of the nucleon in a simple model

Abstract

Valence double parton distribution functions of the nucleon are evaluated in the framework of a simple model, where the conservation of the longitudinal momentum is taken into account. The leading-order DGLAP QCD evolution from the low quark-model scale to higher renormalization scales is carried out via the Mellin moments of the distributions. Results of the valence quark correlation function show that in general the double distributions cannot be approximated as a product of the single-particle distributions.

Figures (3)

• Figure 1: The valence sPDF of the nucleon (multiplied by $x$) at the scale of $\mu=2$ GeV, plotted as a function of the Bjorken variable $x$. The darker band corresponds to the NNPDF2.3 fit with no LHC data, while the broader light band is the the NNPDF2.3 fit with the collider data only Ball:2012cx. We show sPDF evolved with the dDGLAP equations from the quark-model scale $\mu_0$ to $\mu=2$ GeV. Left: The solid, dashed, and dotted lines correspond to the valon model $|\psi(x)|^2=A x^\alpha$ with $\alpha=1$, $1/2$, and $0$, respectively. Right: The solid and dashed lines correspond to the model $|\psi(x)|^2=A (1-x)^a$ with $a=2$ and $a=1$, respectively.
• Figure 2: Contour plots of the valence dPDF of the nucleon multiplied by $x_1 x_2$, i.e., the quantity $x_1 x_2 D_2(x_1,x_2)$, at the scale $\mu_0$ and evolved to $\mu=2$ GeV and $\mu=1$ TeV with the LO dDGLAP equations. Model with $a=2$ corresponding to $\psi(x)=\sqrt{3}(1-x)$.
• Figure 3: Contour plots of the valence quark correlation function $\rho(x_1,x_2)=D_2(x_1,x_2)/[D_1(x_1)D_1(x_2)]-1$, at the scales $\mu_0$, $\mu=2$ GeV, and $\mu=1$ TeV. Model with $a=2$ corresponding to $\psi(x)=\sqrt{3}(1-x)$.