The possible members of the $5^1S_0$ meson nonet

TL;DR

This paper investigates the strong decay properties of the $5^1S_0$ meson nonet using the $^3P_0$ model, proposing assignments for certain mesons and predicting properties for the kaon state.

Contribution

It provides a detailed analysis of the $5^1S_0$ meson nonet and suggests specific meson assignments based on decay data, including predictions for the kaon.

Findings

$ ext{pi}(2360)$, $ ext{eta}(2320)$, and $ ext{X}(2500)$ are likely members of the $5^1S_0$ nonet.

The $X(2370)$ is unlikely to be a $5^1S_0$ state due to its width.

Predicted mass and width for the $5^1S_0$ kaon are about 2418 MeV and 163-225 MeV.

Abstract

The strong decays of the $5^1S_0$ $q\bar{q}$ states are evaluated in the $^3P_0$ model with two types of space wave functions. Comparing the model expectations with the experimental data for the $\pi(2360)$, $\eta(2320)$, $X(2370)$, and $X(2500)$, we suggest that the $\pi(2360)$, $\eta(2320)$, and $X(2500)$ can be assigned as the members of the $5^1S_0$ meson nonet, while the $5^1S_0$ assignment for the $X(2370)$ is not favored by its width. The $5^1S_0$ kaon is predicted to have a mass of about 2418 MeV and a width of about 163 MeV or 225 MeV.