$\Lambda (1405)$-induced non-mesonic decay in kaonic nuclei

The non-mesonic decay of kaonic nuclei is studied under the $\Lambda (1405)$-doorway picture, in which the $\bar{K}$ absorption to the nuclei takes place through the $\Lambda (1405)$ resonance, owing to the presence of the $\Lambda (1405)$ just below the $\bar{K} N$ threshold. For the study of the $\Lambda (1405)$-doorway non-mesonic decay of kaonic nuclei, we calculate the $\Lambda (1405) N \to Y N$ transition in uniform nuclear matter using one-meson exchange model. In the present calculation we find that the non-mesonic decay ratio $\Gamma _{\Lambda N} / \Gamma _{\Sigma^{0} N}$ depends strongly on the ratio of the couplings $\Lambda (1405) $-$\bar{K} N$ and $\Lambda (1405) $-$\pi \Sigma$. Especially a larger $\Lambda (1405)$-$\bar{K} N$ coupling leads to enhancement of the decay to $\Lambda N$. Using the chiral unitary approach for description of the $\bar{K} N$ amplitudes, we obtain $\Gamma _{\Lambda N} / \Gamma _{\Sigma^{0} N} \approx 1.2$ almost independently of the nucleon density, and find the total two-nucleon absorption of the $\bar{K}$ in uniform nuclear matter to be 22 MeV at the normal density. We also show the two-nucleon absorption stpectrum of the $(K^{-} , \, N)$ reaction in our approach.