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Bound-systems of $\Xi^-$--$^{14}_{}{\rm N}$ are studied via $\Xi^-$ captureat rest followed by emission of a twin single-$\Lambda$ hypernucleus in theemulsion detectors. Two events forming extremely deep $\Xi^-$ bound states wereobtained by analysis of a hybrid method in the E07 experiment at J-PARC andreanalysis of the E373 experiment at KEK-PS. The decay mode of one event wasassigned as $\Xi^-+^{14}_{}{\rm N}\to^{5}_{\Lambda}{\rmHe}$+$^{5}_{\Lambda}{\rm He}$+$^{4}_{}{\rm He}$+n. Since there are no excitedstates for daughter particles, the binding energy of the $\Xi^-$ hyperon,$B_{\Xi^-}$, in $^{14}_{}{\rm N}$ nucleus was uniquely determined to be 6.27$\pm$ 0.27 MeV. Another $\Xi^-$--$^{14}_{}{\rm N}$ system via the decay$^{9}_{\Lambda}{\rm Be}$ + $^{5}_{\Lambda}{\rm He}$ + n brings a $B_{\Xi^-}$value, 8.00 $\pm$ 0.77 MeV or 4.96 $\pm$ 0.77 MeV, where the two possiblevalues of $B_{\Xi^-}$ correspond to the ground and the excited states of thedaughter $^{9}_{\Lambda}{\rm Be}$ nucleus, respectively. Because the$B_{\Xi^-}$ values are larger than those of the previously reported events(KISO and IBUKI), which are both interpreted as the nuclear $1p$ state of the$\Xi^-$--$^{14}_{}{\rm N}$ system, these new events give the first indicationof the nuclear $1s$ state of the $\Xi$ hypernucleus, $^{15}_{\Xi}{\rm C}$.

First observation of a nuclear $s$-state of $\Xi$ hypernucleus, $^{15}_{\Xi}{\rm C}$