Missing-Mass Measurement of the 12C(K-, K+) Reaction at 1.8 GeV/c with the Superconducting Kaon Spectrometer

Abstract 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.