In-medium properties of ${\Theta }^{+}$ as a KπN structure in relativistic mean field theory

The properties of nuclear matter are discussed with the relativistic mean-field (RMF) theory. Then, we use two models in studying the in-medium properties of ${\Theta }^{+}$: A pointlike ${\Theta }^{+}$ in the usual RMF and a $K\pi N$ structure for the pentaquark. It is found that the in-medium properties of ${\Theta }^{+}$ are dramatically modified by its internal structure. The effective mass of ${\Theta }^{+}$ in medium is, at normal nuclear density, about 1030 MeV in the pointlike model, whereas it is about 1120 MeV in the $K\pi N$ pentaquark model. The nuclear potential depth of ${\Theta }^{+}$ in the $K\pi N$ model is approximately −37.5 MeV, much shallower than −90 MeV in the usual pointlike RMF model.

Figure 1

The scalar meson mean-field value as a function of the scalar density. The straight lines are for the results without nonlinear ${\sigma }_0$ terms, and the curves correspond to the results with nonlinear ${\sigma }_0$ terms. The dotted line and curve is the result for NL3, the solid curve is for the NL-SH parameter set, and the dashed line is for the parameters from Ref. 46.

Figure 2

The scalar density as a function of the nuclear density for three parameter sets NL3, NL-SH, and the parameters in Ref. 46, respectively.

Figure 3

$K^{+}$ energy as a function of the baryon density for the RMF and ChPT models. For the ChPT model, the results with ${\Sigma }_{\mathit{KN}}=270,350$, and 450 MeV are plotted, and for the RMF model, the results with NL3 and Nl-SH plotted.

Figure 4

The effective mass of ${\Theta }^{+}$ with two models in the nuclear medium, one in which ${\Theta }^{+}$ is treated as a pointlike particle (denoted with ${\Theta }^{+}$) and the other in which ${\Theta }^{+}$ is treated as a $K\pi N$ structure (denoted with $K\pi N$). The results with parameter sets NL-SH and NL3 are plotted.

Figure 5

The potentials of ${\Theta }^{+}$ with two models in the nuclear medium, in which one ${\Theta }^{+}$ is treated as a pointlike particle (denoted with ${\Theta }^{+}$) and the other in which ${\Theta }^{+}$ is treated as a $K\pi N$ structure (denoted with $K\pi N$). The results with parameter sets NL-SH and NL3 are plotted.