The role of the triangle singularity in $\Lambda (1405)$ production in the ${\pi }^{-}p\to K^0\pi \Sigma$ and $pp\to p{K}^{+}\pi \Sigma$ processes

Abstract

We have investigated the cross section for the ${\pi }^{-}p\to K^0\pi \Sigma$ and $pp\to p{K}^{+}\pi \Sigma$ reactions paying attention to a mechanism that develops a triangle singularity. The triangle diagram is realized by the decay of a $N^{\ast }$ to $K^{\ast }\Sigma$ and the $K^{\ast }$ decay into $\pi K$, and the $\pi \Sigma$ finally merges into $\Lambda (1405)$. The mechanism is expected to produce a peak around $2140$ MeV in the $K\Lambda (1405)$ invariant mass. We found that a clear peak appears around $2100$ MeV in the $K\Lambda (1405)$ invariant mass which is about $40$ MeV lower than the expectation, and that is due to the resonance peak of a $N^{\ast }$ resonance which plays a crucial role in the $K^{\ast }\Sigma$ production. The mechanism studied produces the peak of the $\Lambda (1405)$ around or below 1400 MeV, as is seen in the $pp\to p{K}^{+}\pi \Sigma$ HADES experiment.

Comments: 12 pages, 9 figures