The decay of ${\mathrm{\Lambda }}_c^{+}$ into ${\pi }^{+}{\pi }^0\mathrm{\Lambda }(1405)$ with the $\mathrm{\Lambda }(1405)$ decay into ${\pi }^0{\mathrm{\Sigma }}^0$ through a triangle diagram is studied. This process is initiated by ${\mathrm{\Lambda }}_c^{+}\to {\pi }^{+}{\overline{K}}^{*}N$, and then the ${\overline{K}}^{*}$ decays into $\overline{K}\pi$ and $\overline{K}N$ produce the $\mathrm{\Lambda }(1405)$ through a triangle loop containing ${\overline{K}}^{*}N\overline{K}$ which develops a singularity around 1890 MeV. This process is prohibited by the isospin symmetry, but the decay into this channel is enhanced by the contribution of the triangle diagram, which is sensitive to the mass of the internal particles. We find a narrow peak in the ${\pi }^0{\mathrm{\Sigma }}^0$ invariant mass distribution, which originates from the $\mathrm{\Lambda }(1405)$ amplitude, but is tied to the mass differences between the charged and neutral $\overline{K}$ or $N$ states. The observation of the unavoidable peak of the triangle singularity in the isospin-violating $\mathrm{\Lambda }(1405)$ production would provide further support for the hadronic molecular picture of the $\mathrm{\Lambda }(1405)$ and further information on the $\overline{K}N$ interaction.

• Received 6 April 2018

DOI:https://doi.org/10.1103/PhysRevD.97.116004

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Published by the American Physical Society