Pionic and hidden-color, six-quark contributions to the deuteron $b_1$ structure function

The $b_1$ structure function is an observable feature of a spin-1 system sensitive to non-nucleonic components of the target nuclear wave function. The contributions of exchanged pions in the deuteron are estimated and found to be of measurable size for values of $x$ of about 0.1. A simple model for a hidden-color, six-quark configuration (with $\sim 0.15\%$ probability to exist in the deuteron) is proposed and found to give substantial contributions for values of $x>0.2$. Good agreement with Hermes data is obtained. Predictions are made for an upcoming JLab experiment. The Close and Kumano sum rule is investigated and found to be a useful guide to understanding various possible effects that may contribute.

Figure 1

Forward Compton scattering diagram for the Sullivan process. The virtual photon ${\gamma }^{*}$ encounters an exchanged pion (dashed line), breaking it up forming a complicated state (blob) which then emits the pion which is absorbed by another nucleon. The imaginary part of this graph is related to the deep inelastic structure functions of the deuteron.

Figure 2

$\delta f_{\pi }\left(y\right)$ of Eq. (19). The results obtained with the Argonne V18 deuteron wave function [20] overlap with those of the Reid '93 potential [47].

Figure 3

Computed values of $b_1^{\pi }$, for different pion structure function at $Q^2=1.17$ GeV${}^2$. Solid lines—full structure function [46],  short-dashed lines (blue)—valence [46], dot dashed lines (red)—full structure function (mode 3) [51], long dashed lines (green) (mode 3) [51].

Figure 4

Computed values of $b_1^{6q}$ from Eq. (26). Sensitivity to parameters is displayed. (a) Solid lines (blue) uses $R=1.2$ fm, $m=338$ MeV, long dashed lines (red) $R$ is decreased by 10%, dotted lines (green) $R$ is increased by 10%. (b) Solid lines (blue) uses $R=1.2$ fm, $m=338$ MeV, long dashed (red) $m$ is increased by 10%, dotted lines (green), $m$ is decreased by 10%.

Figure 5

Computed values of $b_1=b_1^{\pi }+b_1^{6q}$ from Eq. (20) and Eq. (26). The pion structure function is that of [46], model 1.

Figure 6

Computed values of $100(b_1^{\pi }+b_1^{6q})$, for values of $Q^2=$ 1.17, 1.76, 2.12, and 3.25 GeV${}^2$ [46] distributions and for [51] (lowest curve at $x=0.15$). For the other curves, $b_1^{\pi }$ increases as $Q^2$ increases for small values of $x$.