Abstract
We investigate $\Xi(1690)^-$ production from the $K^-p\to K^+K^-\Lambda$ reaction within the effective Lagrangian approach at the tree-level Born approximation. We consider the $s$- and $u$-channel $\Sigma/\Lambda$ ground states and resonances for the $\Xi$-pole contributions, in addition to the $s$-channel $\Lambda$, $u$-channel nucleon pole, and $t$-channel $K^-$-exchange for the $\phi$-pole contributions. The $\Xi$-pole includes $\Xi(1320)$, $\Xi(1535)$, $\Xi(1690)(J^p=1/2^-)$,and $\Xi(1820)(J^p=3/2^-)$. We calculate the Dalitz plot density of $(d^2\sigma/dM_{K^+K^-}dM_{K^-\Lambda}$ at 4.2 GeV$/c$) and the total cross sections for the $K^-p\to K^+K^-\Lambda$ reaction near the threshold. The calculation results are in good agreement with previously acquired experimental data. Using the parameters from the fit, we present the total and differential cross sections for the two-body $K^-p\to K^+\Xi(1690)^-$ reaction near the threshold. In our calculation, a strong enhancement at backward $K^+$ angles is predicted because of the dominant $u$-channel contribution. We also demonstrate that the Dalitz plot analysis for $p_{K^-}=1.915 -- 2.065$ GeV/c enables us to access direct information regarding $\Xi(1690)^-$ production, which can be tested by future $K^-$ beam experiments. The possible spin-parity states of $\Xi(1690)^-$ are briefly discussed as well.
Highlights
While most low-lying baryons fit primarily into SU(3) multiplets, the Ξ spectrum is still far from being established
We demonstrate that the Dalitz plot analysis for pK− 1⁄4 1.915–2.065 GeV=c enables us to access direct information regarding Ξð1690Þ− production, which can be tested by future K− beam experiments
The calculated Dalitz plot for the double differential cross section d2σ= dMKþK− dMK−Λ at pK− 1⁄4 4.2 GeV=c (Ecm 1⁄4 3.01 GeV) is represented in Fig. 2(a), where the ΞÃð1690Þ and Ξð1820Þ resonances appear as vertical bands, while φð1020Þ appears as a horizontal band in the bottom side
Summary
While most low-lying baryons fit primarily into SU(3) multiplets, the Ξ spectrum is still far from being established. The phase in the interference between the two resonances could change the spin analysis result In this respect, it is necessary to carry out a Ξð1690Þ− production experiment using the ðK−; KþÞ reaction near the threshold. Schlein et al [14] reported the first measurement of the K−p → KþK−Λ reaction using a 1.95 GeV=c K− beam with a 72-in hydrogen bubble chamber. The highest statistics data are available from the K−p experiment at 4.2 GeV=c, involving 2935 events from a 2-m hydrogen bubble chamber [17]. It is crucial to perform a high-statistics experiment involving ΞÃ production with a high-intensity K− beam and its decay distribution measurement to firmly determine their spin and parity; this type of experiment is possible at the. The double-polarization asymmetry turns out to be essential for determining the spin and parity quantum numbers of Ξð1690Þ− via experiments
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