The decay width of the $Z_c(3900)$ as an axialvector tetraquark state in solid quark-hadron duality

TL;DR

This paper investigates the decay width of the $Z_c(3900)$, supporting its interpretation as an axialvector tetraquark state through QCD sum rule calculations of hadronic couplings and decay channels.

Contribution

It provides a detailed QCD sum rule analysis including both connected and disconnected diagrams to support the tetraquark assignment of $Z_c(3900)$.

Findings

Supports $Z_c(3900)$ as a diquark-antidiquark axialvector tetraquark.

Calculates decay widths consistent with experimental data.

Distinguishes $Z_c(3900)$ from a molecular state.

Abstract

In this article, we tentatively assign the $Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, study the hadronic coupling constants $G_{Z_cJ/\psi\pi}$, $G_{Z_c\eta_c\rho}$, $G_{Z_cD \bar{D}^{*}}$ with the QCD sum rules in details. We take into account both the connected and disconnected Feynman diagrams in carrying out the operator product expansion, as the connected Feynman diagrams alone cannot do the work. Special attentions are paid to matching the hadron side of the correlation functions with the QCD side of the correlation functions to obtain solid duality, the routine can be applied to study other hadronic couplings directly. We study the two-body strong decays $Z_c^+(3900)\to J/\psi\pi^+$, $\eta_c\rho^+$, $D^+ \bar{D}^{*0}$, $\bar{D}^0 D^{*+}$ and obtain the total width of the $Z_c^\pm(3900)$. The numerical results support assigning the $Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, and assigning the $Z_c^\pm(3885)$ to be the meson-meson type axialvector molecular state.