Constraints on $\Xi^-$ nuclear interactions from capture events in emulsion

Five $\Xi^- p\to \Lambda\Lambda$ two-body capture events in $^{12}$C and $^{14}$N emulsion nuclei, in which a pair of single-$\Lambda$ hypernuclei is formed and identified by their weak decay, have been observed in $(K^-,K^+)$ emulsion exposures at KEK and J-PARC. Applying a $\Xi^-$-nucleus optical potential methodology to study atomic and nuclear transitions, we confirm that these capture events occur from Coulomb assisted $1p_{\Xi^-}$ nuclear states. Long-range $\Xi N$ shell-model correlations are found essential to achieve consistency between the $^{12}$C and $^{14}$N events. The resulting $\Xi$-nuclear interaction is strongly attractive, with $\Xi$ potential depth in nuclear matter $V_{\Xi}\gtrsim 20$ MeV. Implications to multi-strangeness features of dense matter are outlined.