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

TL;DR

This paper proposes that certain pentaquark signals observed in LHCb data are due to double triangle cusp mechanisms, offering an alternative explanation to the traditional hadron molecule or compact pentaquark models.

Contribution

It introduces a novel double triangle cusp mechanism to explain pentaquark signals, challenging previous interpretations and providing a unified explanation for various experimental observations.

Findings

Double triangle cusps reproduce pentaquark peaks in LHCb data.

Only the P_c(4440)^+ is identified as a true resonance.

The model explains absence of signals in some processes.

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 $\Sigma_c^{(*)}\bar{D}^{(*)}$ 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.