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We performed a measurement of the inclusive missing-mass spectrum of the |$^{12}$| C |$(K^-, K^+)$| reaction at an incident beam momentum of 1.8 GeV/ c. This measurement was carried out by using the Superconducting Kaon Spectrometer (SKS) and the K1.8 beamline spectrometer at the Hadron Experimental Facility in J-PARC. From the missing-mass of the |$^{12}$| C |$(K^-, K^+)$| reaction, the binding energy of a |$\Xi ^-$| hyperon in a core |$^{11}$| B nucleus, |$B_{\Xi ^-}$|⁠ , can be calculated. Our experimental setup yielded a good energy resolution of 8.2 MeV (full width at half maximum), which allowed us to observe significant enhancements in the proximity of the |$^{12}_{\Xi }$| Be production threshold region. In order to extract information from the missing-mass spectrum, we employed several fitting parameters assumptions. A good agreement with the spectrum shape was obtained by adding two Gaussian functions, with the constant experimental resolution for the |$\Xi$| -hypernuclear states, to the background distribution. The peak positions were obtained to be |$B_{\Xi ^-} = 8.9 \pm 1.4$| (stat.) |$^{+3.8}_{-3.1}$| (syst.) MeV and |$B_{\Xi ^-} = -2.4 \pm 1.3$| (stat.) |$^{+2.8}_{-1.2}$| (syst.) MeV. Another model assumption, one Breit–Wigner function with |$B_{\Xi ^-} = -2.7 \pm 2.2$| (stat.) |$^{+0.5}_{-0.7}$| (syst.) MeV and |$\Gamma = 4.1 \pm 2.1$| (stat.) |$^{+1.2}_{-0.7}$| (syst.) MeV, also yielded a similar |$\chi ^2$| value. [ABSTRACT FROM AUTHOR]

We have measured, for the first time, the inclusive missing-mass spectrum of the |$^{12}$| C |$(K^-, p)$| reaction at an incident kaon momentum of 1.8 GeV/ |$c$| at the J-PARC K1.8 beamline. We observed a prominent quasi-elastic peak (⁠|$K^-p \rightarrow K^-p$|⁠) in this spectrum. In the quasi-elastic peak region, the effect of secondary interaction is apparently observed as a peak shift, and the peak exhibits a tail in the bound region. We compared the spectrum with a theoretical calculation based on the Green's function method by assuming different values of the parameters for the |$\bar{K}$| –nucleus optical potential. We found that the spectrum shape in the binding-energy region |$-300 \, \text{MeV} < B_{K} < 40$|  MeV is best reproduced with the potential depths |$V_0 = -80$|  MeV (real part) and |$W_0 = -40$|  MeV (imaginary part). On the other hand, we observed a significant event excess in the deeply bound region around |$B_{K} \sim 100$|  MeV, where the major decay channel of |$K^- NN \to \pi\Sigma N$| is energetically closed, and the non-mesonic decay modes (⁠|$K^- NN \to \Lambda N$| and |$\Sigma N$|⁠) should mainly contribute. The enhancement is fitted well by a Breit–Wigner function with a kaon-binding energy of 90 MeV and width 100 MeV. A possible interpretation is a deeply bound state of a |$Y^{*}$| -nucleus system. [ABSTRACT FROM AUTHOR]