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.

12 pages, 9 figures

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• Review of the $\mathbf{\Lambda }$(1405): A curious case of a strange-ness resonance
• QCD and the Strange Baryon Spectrum
• Description of the ${\Xi }_c$ and ${\Xi }_b$ states as molecular states
• Considerations on the Schmid theorem for triangle singularities
• Anomalous enhancement of the isospin-violating $\Lambda (1405)$ production by a triangle singularity in ${\Lambda }_c\to {\pi }^{+}{\pi }^0{\pi }^0{\Sigma }^0$
• $\Lambda (1405)$ production in the process ${\chi }_{c0}(1P)\to \bar{\Lambda }\Sigma \pi$
• Heating triangle singularities in heavy ion collisions
• Pole trajectories of the $\Lambda (1405)$ helps establish its dynamical nature
• Detecting the pure triangle sigularity effect through the $\psi (2S)\to p\bar{p}\eta /p\bar{p}{\pi }^0$ process
• Theoretical study of the Lambda(1405) resonance in Xi_b^0 -> D^0 pi Sigma decay
• The role of triangle singularity in isospin breaking process $J/\psi \to \Lambda \bar{\Lambda }\pi$ and the possible evidence of ${\Sigma }^{\ast }({\frac{1}{2}}^{-})$ states
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• The $\Lambda (1405)$ resonance as a genuine three-quark or molecular state
• Box Singularity Conditions in Box Diagrams of Decay Processes