High spin kaons

The COMPASS Collaboration recently reported the observation of strange-meson spectra in the reaction $K^- + p \to K^- \pi^- \pi^+ + p$ and found $K_3$ and $K_4$ states, with masses of $2119 \pm 13 ^{+45}_{-12}$ MeV and $2210 \pm 40 ^{+80}_{-30}$ MeV, respectively. This discovery has significantly renewed interest, prompting a detailed and systematic study of high-spin kaons. In this work, we analyze the mass spectrum and the Okubo-Zweig-Iizuka-allowed two-body strong decay properties of high-spin kaons having $J^P=3^{\pm}, 4^{\pm}$, and $5^{\pm}$ within the framework of the modified Godfrey-Isgur model and the $^3P_0$ model. Moreover, we identify critical decay channels, which may serve as useful guidance for future experimental studies.