Deeply-bound $K^{-}pp$ state in the ${}^3$He(in-flight $K^{-}$, $n$) spectrum and its moving pole near the $\ddot{I}€\hat{I}\pounds N$ threshold

Abstract

The formation of a deeply-bound $K^{-}pp$ state with $I=1/2$, $J^{\ddot{I}}€=0^{-}$ by the ${}^3$He(in-flight $K^{-}$, $n$) reaction is theoretically investigated in a distorted-wave impulse approximation using the Green's function method. The expected inclusive and semi-exclusive spectra at $p_{K^{-}}=1.0$ GeV/c and $\hat{I}{¸}_{\mathrm{lab}}=0^{\circ }$ are calculated for the forthcoming J-PARC E15 experiment. We demonstrate these spectra with several types of phenomenological $K^{-}$-``$pp$'' optical potentials $U^{\mathrm{opt}}(E)$ which have an energy-dependent imaginary part multiplied by a phase space suppression factor, fitting to recent theoretical predictions or experimental candidates of the $K^{-}pp$ bound state. The results show that a cusp-like peak at the $\ddot{I}€\hat{I}\pounds N$ threshold is an unique signal for the $K^{-}pp$ bound state in the spectrum including the [$K^{-}pp$] $\to$ $Y+N$ decay process from the two-nucleon $K^{-}$ absorption, as well as a distinct peak of the $K^{-}pp$ bound state. The shape of the spectrum is explained by a trajectory of a moving pole of the $K^{-}pp$ bound state in the complex energy plane. The importance of the spectrum with [$K^{-}pp$] $\to$ $Y+N$ from the two-nucleon $K^{-}$ absorption is emphasized in order to extract clear evidence of the $K^{-}pp$ bound state.

41 pages, 14 figures, accepted version for publication in Phys. Rev. C