Cross section Measurements for ${}^{12}$C$(K^{-},K^{+}\hat{I}{ž}^{-})$ and ${}^{12}$C$(K^{-},K^{+}\hat{I}›\hat{I}›)$ Reactions at 1.8 GeV$/c$

Abstract

We present a measurement of the production of $\hat{I}{ž}^{-}$ and $\hat{I}›\hat{I}›$ in the ${}^{12}$C$(K^{-},K^{+})$ reaction at an incident beam momentum of 1.8 GeV/$c$, based on high-statistics data from J-PARC E42. The cross section for the ${}^{12}$C$(K^{-},K^{+}\hat{I}{ž}^{-})$ reaction, compared to the inclusive ${}^{12}$C$(K^{-},K^{+})$ reaction cross section, indicates that the $\hat{I}{ž}^{-}$ escaping probability peaks at 70\% in the energy region of $E_{\hat{I}}ž=$100 to 150 MeV above the $\hat{I}{ž}^{-}$ emission threshold. A classical approach using eikonal approximation shows that the total cross sections for $\hat{I}{ž}^{-}$ inelastic scattering ranges between 42 mb and 23 mb in the $\hat{I}{ž}^{-}$ momentum range from 0.4 to 0.6 GeV/c. Furthermore, based on the relative cross section for the ${}^{12}$C$(K^{-},K^{+}\hat{I}›\hat{I}›)$ reaction, the total cross section for $\hat{I}{ž}^{-}p\to \hat{I}›\hat{I}›$ is estimated in the same approach to vary between 2.2 mb and 1.0 mb in the momentum range of 0.40 to 0.65 GeV/c. Specifically, a cross section of 1.0 mb in the momentum range of 0.5 to 0.6 GeV/c imposes a constraint on the upper bound of the decay width of the $\hat{I}{ž}^{-}$ particle in infinite nuclear matter, revealing $\hat{I}{“}_{\hat{I}}ž<\sim 0.6$ MeV.