Compatibility of recent $Ξ$-nuclear bound state signals

Abstract

J-PARC E05 reported recently a hint of a $Ξ^--{^{11}{\rm B}}$ nuclear state in the ${^{12}}{\rm C}(K^-,K^+){^{12}_Ξ}{\rm Be}$ spectrum, bound by $B_{Ξ^-}=8.9\pm 1.4 {^{+3.8}_{-3.1}}$ MeV. Using a density-dependent $Ξ$-nuclear optical potential $V_{\rm opt}^Ξ(ρ)$ we explore to what extent a $Ξ^-_{1s}$ assignment of this nuclear state is compatible with $Ξ^-_{1s}$ and $Ξ^-_{1p}$ nuclear-state interpretations of $Ξ^-$ capture events in light emulsion-nuclei experiments. We find that the only acceptable $Ξ^-_{1s}$ assignment at present, barring an abnormally strong repulsive $ρ^2$ component of $V_{\rm opt}^Ξ(ρ)$, is that for the $Ξ^--{^{11}{\rm B}}$ signal. This finding supports reassigning $Ξ^-$ capture events in $^{14}$N, originally assigned as $Ξ^-_{1s}-{^{14}{\rm N}}$ nuclear states, to $Ξ^0_{1p}-{^{14}{\rm C}}$ nuclear states. The depth of $V_{\rm opt}^Ξ(ρ)$ at nuclear-matter density $ρ_0=0.17$ fm$^{-3}$ is then $-V_{\rm opt}^Ξ(ρ_0)\sim 21$ MeV.