Transverse spin structure function $g_2(x,Q^2)$ in the valon model

The spin dependent structure function, $g_2^{ww}$, is calculated in the valon model. A simple approach is given for the determination of the twist-3 part of $\overline{g_2}(x,Q^2)$ in Mellin space, thus enabling us to obtain the full transverse structure function $g_2(x,Q^2)$ for the proton, neutron, and deuteron. In light of the new data, we have further calculated the transversely polarized structure function of $g_2^{{}^3\mathrm{He}}(x,Q^2)$. Our results are checked against the experimental data and nice agreements are observed.

Figure 1

Polarized valon distribution functions for U and D valon types (the helicity distributions for the valons) inside the proton.

Figure 2

Polarized proton (a), neutron (b), and deuteron (c) structure functions $g_1(x,Q^2)$ at $Q^2=5{\text{GeV}}^2$. The results from the valon model are compared with the experimental data [20, 21, 22, 23, 24, 25].

Figure 3

Transverse polarized proton structure functions $g_2^{ww}(x,Q^2)$ at $Q^2=5{\text{GeV}}^2$. We compare our results with the results from other phenomenological models [29, 30].

Figure 4

The twist-3 part of proton transverse spin structure function ${\overline{g}}_2(z,Q^2)$ in the valon, at $Q^2=2,3,5,10{\text{GeV}}^2$.

Figure 5

The twist-3 part of the proton transverse spin structure function ${\overline{g}}_2(z,Q^2)$ in the valon at $Q^2=5{\text{GeV}}^2$ for different $N_c$.

Figure 6

The twist-3 part of proton (a) and deuteron (b) transverse spin structure functions, $x^2{\overline{g}}_2(x,Q^2)$ at $Q^2=5{\text{GeV}}^2$. We compared our results with E143 data [3] and other phenomenological groups [29, 32].

Figure 7

$x{g}_2(x,Q^2)$ for the proton (a), neutron (b), and deuteron (c) at $Q^2=2,3,5,10{\text{GeV}}^2$.

Figure 8

Full transverse polarized structure functions $g_2(x,Q^2)$ for the proton (a), neutron (b), and deuteron (c) at $Q^2=5{\text{GeV}}^2$ from the valon model, compared with experimental data [3, 4, 6].

Figure 9

Full transversely polarized ${}^3\mathrm{He}$ structure function $g_2(x,Q^2)$ at $Q^2=5{\text{GeV}}^2$. The data points are from [38, 39, 40].

Figure 10

$d_2^p$ (a) and $d_2^n$ (b) are calculated in the valon model. Our results are compared with experimental data as well as with results obtained from other phenomenological groups [3, 29, 40, 42, 43, 44, 45, 46].