Possible assignments of the scalar $K_0^{*}(1950)$ and $K_0^{*}(2130)$ within the ${}^3{P}_0$ model

We have evaluated the strong decays of the $K_0^{*}(1950)$ and $K_0^{*}(2130)$ within the ${}^3{P}_0$ model by employing the meson wave functions from the relativized quark model. By comparing with the experimental measurements, the $K_0^{*}(2130)$ could be assigned as $K_0^{*}(3^3{P}_0)$, while the $K_0^{*}(1950)$ is difficult to be explained as the $q\overline{q}$ meson. We also predict that the $K_0^{*}(2^3{P}_0)$ state has a mass of about 1811 MeV and a width of about 656 MeV, while the $K_0^{*}(4^3{P}_0)$ state has a mass of about 2404 MeV and a width of about 180 MeV.

Figure 1

Two-body decay diagrams of $A\to BC$ according to the ${}^3{P}_0$ model, where a pair of quark-antiquark is created to form the final two mesons. Left: meson $B$ is formed by the quark in meson $A$ combined with the created antiquark, and meson $C$ is formed by the antiquark in meson $A$ combined with the created quark. Right: meson $B$ is formed by the antiquark in meson $A$ combined with the created quark, and meson $C$ is formed by the quark in meson $A$ combined with the created antiquark.

Figure 2

The dependence of the total width of $K_0^{*}(3{{}^{3}P}_0)$ on the initial state mass. The experimental total width of the $K_0^{*}(2130)$ is denoted by the dashed line with a green band.

Figure 3

The Regge trajectory of the $K_0^{*}(n{{}^{3}P}_0)$ ($n=1$, 2, 3, 4) states, where $M_n$ is its mass, and the red line is the fitting result.

Figure 4

The dependence of the total width of $K_0^{*}(2{{}^{3}P}_0)$ on the initial state mass.

Figure 5

The dependence of the total width of $K_0^{*}(4{{}^{3}P}_0)$ on the initial state mass.