Parton densities and structure functions of nucleons and light nuclei based on the modified chiral quark-exchange model

We investigate the structure of the light nuclei based on the modified chiral quark model $\left(\chi \mathrm{QM}\right)$, for the first time. To this end, we first calculate the parton distribution functions (PDFs) of the bounded nucleons using the $\chi \mathrm{QM}$ and then compute those of the light nuclei. For this purpose, it is first needed to obtain the bare quark densities inside the bounded nucleons of the nucleus. These bare distributions are calculated by applying the quark exchange model (QEM) in this article. Finally, we obtain the quark, antiquark, and gluon distributions and also the structure functions (SFs) of the bound state nucleons and the light nuclei at low $Q^2$ scale $(Q^2=0.35{\mathrm{GeV}}^2)$. These distributions can be evolved to the higher scales using DGLAP evolution equations. It is shown that the results of our theoretical framework are in good agreement with the experimental data and they also have appropriate behavior in comparison with the different parametrization models.

Figure 1

The schematic representation of (a) Eqs. (7), (b) (8), (c) (9), (d) (10), in the two-body quark exchange approximation.

Figure 2

(a) The quark $q_i$ fluctuates into a GS boson $\mathcal{B}$ and a constituent quark $q_j$. (b) The gluon emission of the constituent quark $q_i$.

Figure 3

(a) The GS boson $\mathcal{B}$ splits into a quark-antiquark pair $q_k{\overline{q}}_k$. (b) Gluon emits a $q_k{\overline{q}}_k$ pair.

Figure 4

The $u$ and $d$ quark and valence quark distributions of ${}^3\mathrm{He}$ at $Q^2=0.35{\mathrm{GeV}}^2$.

Figure 5

The $s$ quark and light antiquark densities inside ${}^3\mathrm{He}$ at $Q^2=0.35{\mathrm{GeV}}^2$.

Figure 6

The gluon momentum distribution of a helium nucleus at $Q^2=0.35{\mathrm{GeV}}^2$.

Figure 7

The sea quark asymmetries of a helium nucleus: (a) $\overline{d}-\overline{u}$ and (b) $x(s-\overline{s})$ inside ${}^3\mathrm{He}$ at $Q^2=0.35{\mathrm{GeV}}^2$.

Figure 8

The SFs of bounded proton and neutron inside ${}^3\mathrm{He}$ ($F_{2ex}^p,F_{2ex}^n$) and also those of free ones ($F_2^p,F_2^n$) at $Q^2=11.5{\mathrm{GeV}}^2$. The results of the modified chiral quark exchange model for $p$ and $n$ SFs have been compared with NMC [59] and EMC [60] experimental data, respectively.

Figure 9

The ratios of SFs for neutron and proton $(F_2^n/F_2^p)$, and also tritium and helium $(F_2^{{}^3\mathrm{H}}/F_2^{{}^3\mathrm{He}})$ at $Q^2=0.35{\mathrm{GeV}}^2$ and $10{\mathrm{GeV}}^2$. The ratio of neutron and proton SFs have been displayed for bounded nucleons inside ${}^3\mathrm{He} {(F_2^n/F_2^p)}_{ex}$ and also for the free ones.

Figure 10

The $F_2^n/F_2^p$ ratio for both bounded and free nucleons at $Q^2=0.35{\mathrm{GeV}}^2$ and $10{\mathrm{GeV}}^2$, compared with various experimental data. The results are plotted for (a) $x>0.001$, (b) $x>0.1$.

Figure 11

The deuteron and proton SFs ratio compared with NMC [61] data.

Figure 12

Ratio of EMC ratios for ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$ obtained using $\chi \mathrm{QM}$. A comparison with CTEQ [65] and GRV [65, 67] results has been done as well at $Q^2=10{\mathrm{GeV}}^2$.