Formation spectra of light kaonic nuclei by in-flight(K¯,N)reactions with a chiral unitary amplitude

Abstract

We study theoretically the in-flight $({K}^{\ensuremath{-}},N)$ reactions for the formation of light kaonic nuclear systems to get deeper physical insights on the spectra and to investigate the formation spectra of the reaction that will be observed at new facilities like the Japan Proton Accelerator Research Complex (J-PARC). We show the expected spectra for the formation of the ${K}^{\ensuremath{-}}\mathit{pp}$, ${K}^{\ensuremath{-}}\mathit{pn}$, ${K}^{\ensuremath{-}}\mathit{nn}$, and ${K}^{\ensuremath{-}}$-$^{11}\mathrm{B}$ systems that are accessible by the $({K}^{\ensuremath{-}},N)$ experiments. By considering the conversion part of the Green's function, we show the missing mass spectra of the $({K}^{\ensuremath{-}},N)$ reactions in coincident with the particle emissions due to $\overline{K}$ absorption. To calculate the cross sections, we use the so-called $T\ensuremath{\rho}$ approximation to evaluate the optical potential. As for the amplitude $T$, we adopt the chiral unitary amplitude of $\overline{K}N$ channel in vacuum for simplicity. The effects of the $p$-wave optical potential of $\ensuremath{\Sigma}(1385)$ channel and the contributions from ${\overline{K}}^{0}$ mixing in $^{3}\mathrm{He}$$({K}^{\ensuremath{-}},n)$ reaction are also evaluated numerically. We also study the behavior of the poles of kaon Green's function in nuclear matter. We conclude that $^{3}\mathrm{He}$$({K}^{\ensuremath{-}},n)$ and $^{3}\mathrm{He}$$({K}^{\ensuremath{-}},p)$ reaction spectra in coincident with the $\ensuremath{\pi}\ensuremath{\Sigma}$ emission may show the structure in the kaon bound region indicating the existence of the unstable kaonic nuclear states. As for the $^{12}\mathrm{C}$$({K}^{\ensuremath{-}},p)$ spectra with the $\ensuremath{\pi}\ensuremath{\Sigma}$ emission, we may also observe the structure in the bound region, however, we need to evaluate the medium effects carefully for larger nuclei.