High spin kaons

TL;DR

This work systematically analyzes high-spin kaons (\(J^P=3^{\pm},4^{\pm},5^{\pm}\)) using Regge trajectories, the modified Godfrey-Isgur (MGI) model for masses and wave functions, and the $^3P_0$ model for OZI-allowed two-body decays. By combining Regge fits with MGI masses, the authors assign COMPASS-observed states \(K_3'(2120)(1F)\) and \(K_4(2210)(1G)\) and compute their decay widths and branching patterns, achieving consistency with experimental data on total widths and key channels. They also predict masses and decays for yet-unobserved high-spin kaons (\(K_3(1F)\), \(K_3'(2F)\), \(K_4'(1G/2G)\), \(K_5(1H)\), \(K_5'(1H)\)) and outline crucial final states to guide experimental searches. Overall, the work demonstrates the efficacy of the MGI and $^3P_0$ frameworks in strange-meson spectroscopy and provides concrete guidance for future kaon studies at facilities like COMPASS, LHCb, and BESIII.

Abstract

The COMPASS Collaboration recently reported the observation of strange-meson spectra in the reaction $K^- + p \to K^- π^- π^+ + p$ 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.

Figures (5)

• Figure 1: The Regge trajectories of the $K_J^*(L=J-1)$, $K_J$, and $K_J^\prime$ families. Open circles denote the theoretical values obtained by Eq. \ref{['rt']}, while filled geometrical shapes represent experimental data. Vertical lines indicate the uncertainties associated with each kaon's mass. For the $K^*$ family, the horizontal axis corresponds to $J-2$, whereas for $K_J^\prime$ family, the horizontal axis represents $J+1$, and for $K_J$ kaons, the horizontal axis corresponds to $J+2$, where and $J$ denotes the angular momentum of the corresponding meson.
• Figure 2: The $\theta$ dependence of the total decay width for $K_3^\prime(2120)$, with the corresponding experimental data COMPASS:2025wkw (represented by a blue band) being presented alongside our theoretical calculation for comparison. The solid line corresponds to the result obtained using the experimental mass, while the dashed line denotes that obtained with the theoretical mass derived from the MGI model.
• Figure 3: The $\theta$ dependence of the total decay width of the $K_3(2320)$, along with the corresponding experimental data ParticleDataGroup:2024cfk (represented by a light green band) which is provided for comparison with our theoretical calculation. The solid line corresponds to the result obtained using the experimental mass, while the dashed line denotes that obtained with the theoretical mass derived from the MGI model.
• Figure 4: The dependence of the total decay width on the mixing angle $\theta$ for the $K_4(2210)$ state, along with corresponding experimental data COMPASS:2025wkw (pink band) for comparison with our theoretical calculation. The solid line corresponds to the result obtained using the experimental mass, while the dashed line denotes that obtained with the theoretical mass derived from the MGI model.
• Figure 5: The $\theta$ dependence of the total decay width of $K_4(2500)$ state, along with the corresponding experimental data ParticleDataGroup:2024cfk (represented as a turquoise blue line) for comparison with our theoretical calculation. The solid line corresponds to the result obtained using the experimental mass, while the dashed line denotes that obtained with the theoretical mass derived from the MGI model.