Coupling of ${\overline{K}}^{*}N$ to the Λ(1520)

We study the coupling of the $\Lambda (1520)\equiv {\Lambda }^{*}$ resonance to the ${\overline{K}}^{*}$ vector meson and nucleon. This coupling is not directly measured from the resonance decay, but is expected to be important in hyperon production reactions, in particular for the exotic ${\Theta }^{+}$ production. We compute the coupling in two different schemes, one in the chiral unitary model where the ${\Lambda }^{*}$ is dominated by the quasibound state of mesons and baryons, and the other in the quark model where the resonance is a p-wave excitation in the three valence quarks. Although it is possible to construct both models such that they reproduce the $\overline{K}N$ and $\pi \Sigma$ decays, there is a significant difference between the ${\Lambda }^{*}{\overline{K}}^{*}N$ couplings in the two models. In the chiral unitary model $\left|g_{{\Lambda }^{*}{\overline{K}}^{*}N}\right|~1.5$, while in the quark model $\left|g_{{\Lambda }^{*}{\overline{K}}^{*}N}\right|~10$. The difference of the results stems from the different structure of the ${\Lambda }^{*}$ in both models, and hence, an experimental determination of this coupling would shed light on the nature of the resonance.

Figure 1

Diagrams for the microscopic mechanism of ${\overline{K}}^{*}N\to {\Lambda }^{*}\to \pi {\Sigma }^{*}$ calculated in the chiral unitary model.

Figure 2

Diagram for the resonance dominance model of ${\overline{K}}^{*}N\to {\Lambda }^{*}\to \pi {\Sigma }^{*}$.

Figure 3

Momentum assignment for the diagram (b) in Fig. 1.

Figure 4

Momentum and spin indices assignment for the loop diagram in (d) in Fig. 1.

Figure 5

(Color online) Upper: Numerical results for the ${\Lambda }^{*}{\overline{K}}^{*}N$ coupling constant as a function of $K^{*}$ momentum $\left|\mathit{k}\right|$ in the chiral unitary model. Thick solid line, thin solid line, and dashed line represent absolute value, real part, and imaginary part of the coupling constant, respectively. Lower: Energy of the $K^{*}$ as a function of $\left|\mathit{k}\right|$, assuming the nucleon is on-shell.

Figure 6

Numerical result for the ${\Lambda }^{*}{\overline{K}}^{*}N$ coupling constant as a function of $K^{*}$ momentum k in the quark model, for different mixing angles θ.