Strangeness plus-one ($S=+1$) resonance-state $P_0^{+*}$ via $K^{+}n\to K^{*0}p$

In our current study, we delve into the peak-like structure observed during the reaction process of $K^{+}n\to K^{0}p$ at approximately $\sqrt{s}\approx 2.5$ GeV. Our focus centers on exploring the potential $S=+1$ resonance $P_0^{+*}\equiv P_0^{*}$ as an excited state within the extended vector-meson and baryon ($VB$) antidecuplet. To achieve this aim, we employ the effective Lagrangian method in conjunction with the $(u,t)$-channel Regge approach, operating within the tree-level Born approximation. We thoroughly examine various spin-parity quantum numbers for the resonance, resulting in a compelling description of the data, where $M_{P_0^{*}}\approx 2.5$ GeV and ${\mathrm{\Gamma }}_{P_0^{*}}\approx 100$ MeV. Furthermore, we propose an experimental technique to amplify the signal-to-noise ratio ($S/N$) for accurately measuring the resonance. Notably, our findings reveal that background interference diminishes significantly within the $K^{*}$ forward-scattering region in the center-of-mass frame when the $K^{*}$ is perpendicularly polarized to the reaction plane. Additionally, we explore the recoil-proton spin asymmetry to definitively determine the spin and parity of the resonance. This study stands to serve as a valuable reference for designing experimental setups aimed at investigating and comprehending exotic phenomena in quantum chromodynamics. Specifically, our insights will inform future J-PARC experiments, particularly those employing higher kaon beam energies.

Figure 1

Feynman diagrams pertinent to the process $K^{+}n\to K^{*0}p$ within the tree-level Born approximation are presented.

Figure 2

(a) Total cross sections for the nonresonant contributions as functions of $E_{\mathrm{c}.\mathrm{m}.}$, serving as the background (BKG), including the total (solid line), $\pi$ (dotted line), $\mathrm{\Lambda }\left(1116\right)$ (dashed line), $\mathrm{\Lambda }\left(1670\right)$ (long-dashed line), $\mathrm{\Lambda }\left(1670\right)$ (dot-dashed line), $\mathrm{\Sigma }\left(1192\right)$ (long-short-dashed line), and ${\mathrm{\Sigma }}^{*}\left(1385\right)$ (long-dot-dashed line) components. (b) Total cross sections with four different spin-parity quantum numbers of the $P_0^{*}$: $J^P=1/2^{+}$ (solid line), $J^P=1/2^{-}$ (dotted line), $J^P=3/2^{+}$ (dashed line), and $J^P=3/2^{-}$ (long-dashed line). Experimental data are obtained from various sources, including Refs. [16]. Data points that deviate from the background description are marked with hollow circles.

Figure 3

The differential cross sections for the angular dependence $d\sigma /dcos\theta$ [mb] at $E_{\mathrm{c}.\mathrm{m}.}=(2.0,2.5,3.0)$ GeV are depicted in (a), (b), and (c) as functions of $cos\theta$, illustrating each contribution. Here, $\theta$ represents the scattering angle of the final state $K^{*}$ in the c.m. frame. (d) displays $d\sigma /dcos\theta$ as a function of $E_{\mathrm{c}.\mathrm{m}.}$ and $cos\theta$. In this panel, we exclusively showcase the results for $P_0^{*}(3/2^{-})$, as other quantum-number states exhibit negligible differences.

Figure 4

(a) Differential cross sections $d\sigma /dcos\theta$ for ${\mathit{k}}_K·{\mathit{\epsilon }}_{K^{*}}=0$ for $\theta =0$ (solid line), $\pi /4$ (dotted line), and $\pi /2$ (dashed line) in the c.m. frame. Here, we only present the results for the $P_0^{*}(3/2^{-})$, as other quantum-number states do not significantly differ. (b) The same as (a), plotted as a function of $cos\theta$ and $E_{\mathrm{c}.\mathrm{m}.}$ for ${\mathit{k}}_K·{\mathit{\epsilon }}_{K^{*}}=0$ at $\theta =0$.

Figure 5

(a) Recoil-proton spin asymmetry (RSA) in Eq. (10) as functions of $E_{\mathrm{c}.\mathrm{m}.}$ for different spin-parity quantum numbers of $P^{*}0$, with $\mathit{\epsilon }{K}^{*}$ perpendicular to the reaction plane. (b) ${\mathrm{\Sigma }}_{\perp }$ as functions of $cos\theta$ at $E_{\mathrm{c}.\mathrm{m}.}=2.5$ GeV following the same approach.