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

Abstract

J-PARC E05 reported recently a hint of a ${\Xi }^{-}-{}^{11}\mathrm{B}$ nuclear state in the ${}^{12}\mathrm{C}(K^{-},K^{+}){}_{\Xi }^{12}\mathrm{Be}$ spectrum, bound by $B_{{\Xi }^{-}}=8.9\pm 1.4{}_{-3.1}^{+3.8}$ MeV. Using a density-dependent $\Xi$-nuclear optical potential $V_{\mathrm{opt}}^{\Xi }(\rho )$ 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 $V_{\mathrm{opt}}^{\Xi }(\rho )$, is that for the ${\Xi }^{-}-{}^{11}\mathrm{B}$ signal. This finding supports reassigning ${\Xi }^{-}$ capture events in ${}^{14}$N, originally assigned as ${\Xi }_{1s}^{-}-{}^{14}\mathrm{N}$ nuclear states, to ${\Xi }_{1p}^0-{}^{14}\mathrm{C}$ nuclear states. The depth of $V_{\mathrm{opt}}^{\Xi }(\rho )$ at nuclear-matter density ${\rho }_0=0.17$ fm${}^{-3}$ is then $-V_{\mathrm{opt}}^{\Xi }({\rho }_0)\sim 21$ MeV.

v1: 11 pages, 2 figures, 2 tables, to be submitted for publication; v2: 13 pages, 2 figures, 2 tables, to be published in Phys. Lett. B; v3: published version

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