Properties of structure functions from helicity components of light quarks and antiquarks in the statistical model

In the quantum statistical parton distribution approach proposed more than one decade ago to describe the parton structure, new properties are now understood; in particular the relation between quarks and antiquarks leads to very specific properties. The simultaneous treatment of unpolarized and polarized parton distribution functions (PDFs) allows a determination of thermodynamical potentials (the master parameters of the model) which drive their behavior and consequently the behavior of the structure functions. The existence of a possible relation between the gluon and a $q\overline{q}$ pair leads to define a toy model for the unpolarized and polarized gluons. In view of forthcoming experimental results in the large-$x$ region, specific predictions made by the model are presented.

Figure 1

BS15 [5] predicted ratios $[\mathrm{\Delta }u(x,Q^2)+\mathrm{\Delta }\overline{u}(x,Q^2)]/[u(x,Q^2+\overline{u}(x,Q^2)]$ and $[\mathrm{\Delta }d(x,Q^2)+\mathrm{\Delta }\overline{d}(x,Q^2)]/\left[\right(d(x,Q^2+\overline{d}(x,Q^2)]$ versus $x$, at $Q^2=1$ (solid), 10 (dashed), 100 (dashed-dotted), and 1000 ${\mathrm{GeV}}^2$ (long-dashed). Experiments data are from the HERMES [7, 8, 9] and Jlab [10, 11] Collaborations.

Figure 2

The ratios $d(x,Q^2)/u(x,Q^2)$ (left) and $\overline{u}(x,Q^2)/\overline{d}(x,Q^2)$ (right) versus $x$ for $Q^2=1$ (solid), 10 (dashed), and 100 ${\mathrm{GeV}}^2$ (dashed-dotted), from BS15 [5].

Figure 3

Left: Comparison of $xG(x,Q^2)$ versus $x$ for $Q^2=1,10,100{\text{GeV}}^2$, computed from BS15 [5] (dashed) and the toy model (solid). Right: Same comparison but for $x\mathrm{\Delta }G(x,Q^2)$.

Figure 4

Comparison of $x\mathrm{\Delta }G(x,Q^2)$ versus $x$ for $Q^2=1,10,100{\text{GeV}}^2$ calculated with the toy DSSV model (solid) and the original one (dashed).

Figure 5

Quark $u$ contribution to the polarized $\mathrm{\Delta }G$ following the toy expression (20).

Figure 6

Left: Inclusive differential cross section for $p+p\to jet+X$ at $\sqrt{s}=200\mathrm{GeV}$ versus jet $p_T$ calculated with the unpolarized toy gluon model (19). Right: The longitudinal double-spin asymmetry $A_{LL}$ in $\vec{p}+\vec{p}\to jet+X$ at $\sqrt{s}=200\mathrm{GeV}$ versus jet $p_T$ calculated with the polarized toy gluon model (20). Data are from the STAR experiment [6].