First Measurement of the $K^-$ Escape Cross Section in the ${}^{12}{\rm C}(K^{-},p)$ Reaction
We investigated the $\bar{K}$-nucleus interaction through the simultaneous measurement of the inclusive $^{12}{\rm C}(K^-, p)$ and exclusive $K^-$-escape $^{12}{\rm C}(K^-, p K^-_{esc})$ reactions at $1.8$ GeV/$c$ at J-PARC. The present measurement explicitly focuses on the $K^-$ escape process for the first time, successfully accomplishing a direct experimental determination of the imaginary part of the $K^-$ optical potential. The differential cross section for the $K^-$-escape reaction was determined to be $436 \pm 6\:(\text{stat.}) \pm 44\:(\text{syst.})~μ\text{b/sr}$. A simultaneous likelihood fit yielded real and imaginary potential strengths of $V_0 = -72\:^{+3}_{-5}\:(\text{stat.})\:^{+0}_{-8}\:(\text{syst.})~\text{MeV}$ and $W_0 = -100\:^{+7}_{-1}\:(\text{stat.})\:^{+0}_{-16}\:(\text{syst.})~\text{MeV}$ at the nuclear center, respectively. The derived $W_0$ is significantly stronger than that predicted by theoretical models based on one-nucleon processes, suggesting possible contribution of multi-nucleon involving processes.