$Z_c(4430)$, $Z_c(4200)$, $Z_1(4050)$, and $Z_2(4250)$ as triangle singularities

TL;DR

This paper proposes that the observed exotic states Zc(4430), Zc(4200), Z1(4050), and Z2(4250) are not genuine particles but are instead caused by triangle singularities in loop diagrams, offering a kinematic explanation for their properties.

Contribution

The study introduces a novel interpretation that these charged charmonium-like states result from triangle singularities, challenging the traditional four-quark state models.

Findings

Triangle singularities can explain the properties of the observed states.

The model accounts for the presence and absence of certain states in different decay channels.

It provides a natural explanation for asymmetric spectral shapes.

Abstract

$Z_c(4430)$ discovered in $\bar{B}^0\to\psi(2S)K^-\pi^+$, $Z_c(4200)$ found in $\bar{B}^0\to J/\psi K^-\pi^+$, and $Z_1(4050)$ and $Z_2(4250)$ observed in $\bar{B}^0\to\chi_{c1}K^-\pi^+$ are candidates of charged charmonium-like states. All surviving theoretical models interpreted these candidates as four-quark states, until we recently identified a compelling alternative. We discuss that kinematical singularities in triangle loop diagrams induce a resonance-like behavior that can consistently explain the properties (such as spin-parity, mass, width, and Argand plot) of $Z_c(4430)$, $Z_c(4200)$, $Z_1(4050)$ and $Z_2(4250)$ from experiments. In terms of the triangle singularities, we can also naturally understand interesting experimental findings such as the appearance (absence) of $Z_c(4200)$($Z_c(4430)$)-like contribution in $\Lambda_b^0\to J/\psi p\pi^-$, and the highly asymmetric shape of the spectrum bump for $Z_1(4050)$; the other theoretical models have not successfully addressed these points. Although Pakhlov et al. proposed another triangle diagram to generate a $Z_c(4430)$-like bump, we argue that this scenario is very unlikely.