$P_c(4312{)}^{+}$, $P_c(4380{)}^{+}$, 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.

8 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

References in corpus (19)

• Multiquark Resonances
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Exotics: Heavy Pentaquarks and Tetraquarks
• Emergence of a complete heavy-quark spin symmetry multiplet: seven molecular pentaquarks in light of the latest LHCb analysis
• Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks
• Study of $P_c(4457)$, $P_c(4440)$, and $P_c(4312)$ in a quasipotential Bethe-Salpeter equation approach
• Heavy quark spin symmetric molecular states from ${\bar{D}}^{(\ast )}{\Sigma }_c^{(\ast )}$ and other coupled channels in the light of the recent LHCb pentaquarks
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• Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum
• Isospin breaking decays as a diagnosis of the hadronic molecular structure of the $P_c(4457)$
• Interpretation of the Narrow $J/\psi p$ Peaks in ${\Lambda }_b\to J/\psi p{K}^{-}$ Decay in the Compact Diquark Model
• Hidden-charm and hidden-bottom molecular pentaquarks in chiral perturbation theory
• Revisiting the nature of the $P_c$ pentaquarks
• Studying the P_c(4450) resonance in J/psi photoproduction off protons
• Possibility to study pentaquark states $P_c(4312),P_c(4440)$, and $P_c(4457)$ in $\gamma p\to J/\psi p$ reaction
• Structure and decays of hidden heavy pentaquarks
• Heavy pentaquark spectroscopy in the diquark model
• How to reveal the nature of three or more pentaquark states?

Cited by in corpus (24)

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• Strong Interaction Physics at the Luminosity Frontier with 22 GeV Electrons at Jefferson Lab
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• Three-body molecules $\bar{D}{\bar{D}}^{\ast }{\Sigma }_c$- understanding the nature of $T_{cc}$, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• $P_c$ states and their open-charm decays with the complex scaling method
• Prompt production of the hidden charm pentaquarks in the LHC
• Photo- and electro-production of narrow exotic states: from light quarks to charm and up to bottom
• Observation of the ${\Lambda }_{\text{b}}^0$ $\to$ J/$\psi {\Xi }^{-}$K${}^{+}$ decay
• Unravelling Pentaquarks with Born--Oppenheimer effective theory
• Molecular pentaquark states with open charm and bottom flavors
• $X$ structures in $B^{+}\to J/\psi \varphi K^{+}$ as one-loop and double-triangle threshold cusps
• Studying triangle singularity through spin observables
• Towards modeling the short-range interactions of hidden/open charm pentaquark molecular states
• Strong decays of $P_{\psi }^N(4440{)}^{+}$ and $P_{\psi }^N(4457{)}^{+}$ within the Bethe-Salpeter framework
• Observation of the ${\Lambda }_b^0\to J/\psi {\Xi }^{-}{K}^{+}$ and ${\Xi }_b^0\to J/\psi {\Xi }^{-}{\pi }^{+}$ decays
• Analysis of the hidden-charm pentaquark candidates in the $J/\psi p$ mass spectrum with QCD sum rules
• Exotic hadrons associated with $b$-quark
• Box Singularity Conditions in Box Diagrams of Decay Processes