Compatibility of recent $\Xi$-nuclear bound state signals

Abstract

J-PARC E05 reported recently a hint of a $\Xi^--{^{11}{\rm B}}$ nuclear state in the ${^{12}}{\rm C}(K^-,K^+){^{12}_{\Xi}}{\rm Be}$ spectrum, bound by $B_{\Xi^-}=8.9\pm 1.4 {^{+3.8}_{-3.1}}$ MeV. Using a density-dependent $\Xi$-nuclear optical potential $V_{\rm opt}^{\Xi}(\rho)$ we explore to what extent a $\Xi^-_{1s}$ assignment of this nuclear state is compatible with $\Xi^-_{1s}$ and $\Xi^-_{1p}$ nuclear-state interpretations of $\Xi^-$ capture events in light emulsion-nuclei experiments. We find that the only acceptable $\Xi^-_{1s}$ assignment at present, barring an abnormally strong repulsive $\rho^2$ component of $V_{\rm opt}^{\Xi}(\rho)$, is that for the $\Xi^--{^{11}{\rm B}}$ signal. This finding supports reassigning $\Xi^-$ capture events in $^{14}$N, originally assigned as $\Xi^-_{1s}-{^{14}{\rm N}}$ nuclear states, to $\Xi^0_{1p}-{^{14}{\rm C}}$ nuclear states. The depth of $V_{\rm opt}^{\Xi}(\rho)$ at nuclear-matter density $\rho_0=0.17$ fm$^{-3}$ is then $-V_{\rm opt}^{\Xi}(\rho_0)\sim 21$ MeV.