Why is the $Z_c(3900)$ absent in the $h_c\pi$ final state?

TL;DR

This paper analyzes the nature of exotic hadronic states like $Z_c(3900)$ using Heavy Quark Spin Symmetry, explaining why $Z_c(3900)$ is absent in the $h_c ext{ extendash}\pi$ final state through differences in HQSS violation.

Contribution

It introduces a comprehensive phenomenological model incorporating HQSS and its violation to explain the selective appearance of exotic states in different decay channels.

Findings

HQSS violation is negligible in bottom sector, leading to similar structures in all decay channels.

Significant HQSS breaking in the charm sector explains the selective presence of $Z_c(3900)$ and $Z_c(4020)$.

The $Z_c(4020)$ likely arises from a threshold cusp effect, indicating a molecular nature.

Abstract

In this work, we perform a comprehensive phenomenological analysis of the exotic hadronic states $Z_c(3900)$, $Z_c(4020)$, $Z_b(10610)$ and $Z_b(10650)$ within the framework of Heavy Quark Spin Symmetry (HQSS) and its violation. By constructing S-wave contact interactions between elastic ($D\bar{D}^*/D^*\bar{D}^*$ or $B\bar{B}^*/B^*\bar{B}^*$) and inelastic ($J/\psi\pi, h_c\pi$ or $\Upsilon\pi$, $h_b\pi$) channels, we solve the Lippmann-Schwinger equation to obtain physical production amplitudes and perform a global fit to experimental invariant-mass spectra. Our results demonstrate a striking difference between the charm and bottom sectors: HQSS violation is negligible in the bottom system, leading to comparable peak structures for both $Z_b$ states in all hidden-bottom decay channels. In contrast, significant HQSS breaking is required to describe the $Z_c$ system, where the violation is predominantly concentrated in the elastic interactions. This explains the observed selectivity: $Z_c(3900)$ appears prominently only in $J/\psi\pi$, while $Z_c(4020)$ appears only in $h_c\pi$. Pole analysis confirms the molecular nature of the states, with the $Z_c(4020)$ likely arising from a threshold cusp effect. The model's robustness is verified against variations of the form factor and cutoff, showing stable results.