$\Lambda (1405)$ mediated triangle singularity in the $K^{-}d\to p{\Sigma }^{-}$ reaction

Abstract

We study for the first time the $p{\Sigma }^{-}\to K^{-}d$ and $K^{-}d\to p{\Sigma }^{-}$ reactions close to threshold and show that they are driven by a triangle mechanism, with the $\Lambda (1405)$, a proton and a neutron as intermediate states, which develops a triangle singularity close to the $\bar{K}d$ threshold. We find that a mechanism involving virtual pion exchange and the $K^{-}p\to {\pi }^{+}{\Sigma }^{-}$ amplitude dominates over another one involving kaon exchange and the $K^{-}p\to K^{-}p$ amplitude. Moreover, of the two $\Lambda (1405)$ states, the one with higher mass around $1420$ MeV, gives the largest contribution to the process. We show that the cross section, well within measurable range, is very sensitive to different models that, while reproducing $\bar{K}N$ observables above threshold, provide different extrapolations of the $\bar{K}N$ amplitudes below threshold. The observables of this reaction will provide new constraints on the theoretical models, leading to more reliable extrapolations of the $\bar{K}N$ amplitudes below threshold and to more accurate predictions of the $\Lambda (1405)$ state of lower mass.

Comments: 12 pages and 10 figures