$P_c(4312{)}^{+}$, $P_c(4380{)}^{+}$, and $P_c(4457{)}^{+}$ as double triangle cusps

Abstract

Understanding the nature of the hidden charm pentaquark(like) signals in the LHCb data for ${\Lambda }_b^0\to J/\psi p{K}^{-}$ is a central problem of hadron spectroscopy. We propose a scenario completely different from previous ones such as hadron molecules and compact pentaquarks. We identify relevant double triangle mechanisms with leading or lower-order singularities. The associated anomalous threshold cusps at the ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$ thresholds are significantly more singular than the ordinary ones. Then we demonstrate that the double triangle amplitudes reproduce the peak structures of $P_c(4312{)}^{+}$, $P_c(4380{)}^{+}$, and $P_c(4457{)}^{+}$ in the LHCb data, through an interference with other common mechanisms. Only the $P_c(4440{)}^{+}$ peak is due to a resonance with width and strength significantly smaller than previously estimated. $P_c^{+}$ signals are expected in other processes and the proposed model (partly) explains the current data such as: the GlueX $J/\psi$ photoproduction data with no $P_c^{+}$ signals; the LHCb ${\Lambda }_b^0\to J/\psi p{\pi }^{-}$ data with a possible signal only from $P_c(4440{)}^{+}$. The double triangle singularity is now a possible option to interpret resonancelike structures near thresholds in general.

arXiv comment8 pages, 4 figures, Supplemental material (v2) title changed; references added; figure and discussion added on double triangle singularity (v3) published version; table of parameter values added to supplemental material

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