Naive parton picture for kaon color transparency in $A(e,e'K^+)$

Abstract

Nuclear transparency in the electronuclear reaction $A(e,e'K^+)$ is investigated in parallel with our previous study of pion transparency in Phys.\ Rev.\ C {\bf 111}, 064608 (2025). Based on an extended Glauber framework that incorporates shadowing from the initial-state two-step process, kaon color transparency (CT) is analyzed to show that the steeper $Q^2$ dependence observed for kaon CT, compared with the pion case, is more naturally described by the naive parton model (NPM) than by the quantum diffusion model (QDM). The inclusion of initial-state shadowing further reduces the transparency and improves the agreement with the experimental data. The $Q^2$ and $A$ dependences of the kaon transparency are presented up to $Q^2=10$~GeV$^2/c^2$, together with the corresponding $α(Q^2)$ and the supplementary ratio $T_A/T_C$, for comparison with the Jefferson Lab (JLab) data obtained with the 6-GeV electron beam on $^{12}$C, $^{63}$Cu, and $^{197}$Au nuclei.

Figures (5)

• Figure 1: Ratio $\sigma_{KN}^{\rm eff}/\sigma_{KN}$ in Eq. (\ref{['eq:sigmaeff']}) as a function of the propagation distance $z$ at $Q^2=3.0$ GeV$^2/c^2$ and $p_K=2.89$ GeV$/c$. The quadratic behavior from the NPM and the linear behavior from the QDM are shown using the formation lengths obtained from Eqs. (\ref{['eq:lfnpm']}) and (\ref{['eq:lfqdm']}).
• Figure 2: $Q^2$ dependence of the nuclear transparency $T_A$ in $^{12}$C, $^{63}$Cu, and $^{197}$Au. The solid curves show the result of the extended Glauber calculation in Eq. (\ref{['eq:TA']}), where the NPM with $R_K=0.58$ fm is used and the shadowing effect is evaluated with $\sigma_{\phi N}=18$ mb. The dashed curves show the NPM result without shadowing. The dotted curves correspond to the pure Glauber calculation without NPM or shadowing, and the dash-dotted curves indicate the shadowing correction to that baseline. For comparison, panel (a) also shows the QDM predictions for $\Delta M^2=0.3$ GeV$^2$ and $0.7$ GeV$^2$, represented by the dash-dot-dotted and dash-dash-dotted curves, respectively. The data are taken from Ref. Nuruzzaman2011.
• Figure 3: $Q^2$ dependence of the ratio $T_A/T_C$ obtained by normalizing the transparency of each target nucleus to that of $^{12}$C. The solid curves represent the ratio obtained from the extended Glauber calculation including shadowing and the NPM, with the same notation as in Fig. \ref{['fig:fig2']}. The dash-dot-dotted curves show the corresponding result from the extended Glauber calculation including shadowing and the QDM with $\Delta M^2=0.3$ GeV$^2$. The data are taken from Ref. Nuruzzaman2011.
• Figure 4: $A$ dependence of $T_A$ at fixed $Q^2$. From top to bottom, the panels correspond to $Q^2=1.1$, 2.2, and 3.0 GeV$^2/c^2$, respectively. The solid and dashed curves show the calculations with and without shadowing, with the same notation as in Fig. \ref{['fig:fig2']}. For comparison, the QDM prediction at $Q^2=2.2$ GeV$^2/c^2$ is shown by the dash-dot-dotted curve in the middle panel. The data are taken from Ref. Nuruzzaman2011.
• Figure 5: $Q^2$ dependence of $\alpha$ for the nuclear transparency $T_A$. The parameter $\alpha$ is extracted by averaging over the JLab data for the three target nuclei. The dash-dot-dotted curve shows the QDM result for comparison, and the thick dotted line denotes the approximately constant value of $\alpha$ extracted from $K^+$--nucleus scattering carroll. The data are taken from Ref. Nuruzzaman2011.