Remarks on the $P_c$ structures and triangle singularities

Abstract

It was proposed that the narrow $P_c(4450)$ structure observed by the LHCb Collaboration in the reaction ${\Lambda }_b\to J/\psi pK$ might be due to a triangle singularity around the ${\chi }_{c1}$--proton threshold at 4.45~GeV. We discuss the occurrence of a similar triangle singularity in the $J/\psi p$ invariant mass distribution for the decay ${\Lambda }_b\to J/\psi p\pi$, which could explain the bump around 4.45~GeV in the data. More precise measurements of this process would provide valuable information towards an understanding of the $P_c$ structures.

Comments: 8 pages, 5 figures, version accepted for publication in European Physical Journal A