Novel description of $P_c(4312)^+$, $P_c(4380)^+$, and $P_c(4457)^+$ with double triangle cusps

TL;DR

This paper introduces a new explanation for pentaquark peaks in LHCb data, attributing them to double triangle cusp mechanisms rather than traditional molecular or compact pentaquark models, and successfully fits several observed peaks.

Contribution

It proposes a novel double triangle cusp mechanism as an alternative explanation for pentaquark peaks, challenging conventional models and fitting multiple experimental observations.

Findings

Double triangle cusps produce peaks at $P_c$ states.

The model fits $P_c(4312)^+$, $P_c(4380)^+$, and $P_c(4457)^+$ data.

The approach explains absence of signals in some processes.

Abstract

We propose a novel scenario for the peak structures, usually interpreted as hidden charm pentaquark ($P_c$) contributions, in the LHCb's $\Lambda_b^0\to J/\psi p K^-$ data. The key idea is to utilize leading or lower-order singularities from double triangle mechanisms. The singularities cause anomalous threshold cusps, which are significantly more singular than the ordinary ones, at the $\Sigma_c^{(*)}\bar{D}^{(*)}$ threshold. We demonstrate that the double triangle amplitudes interfere with other common mechanisms to create peak structure that fit well the $P_c(4312)^+$, $P_c(4380)^+$, and $P_c(4457)^+$ peaks in the data. This picture is completely different from commonly used ones such as hadron molecules and compact pentaquarks. Meanwhile, $P_c(4440)^+$ is included in the proposed model as a resonance with width and strength significantly smaller than previously estimated. The proposed model can (partly) explain the current data for other processes where $P_c^+$ signals are expected such as: no $P_c^+$ signals in the GlueX $J/\psi$ photoproduction data; a possible signal only from $P_c(4440)^+$ in the LHCb's $\Lambda_b^0\to J/\psi p \pi^-$ data.