# Treating $Z_c(3900)$ and $Z(4430)$ as the ground-state and first radially excited tetraquarks

## TL;DR

This paper models the $Z_c(3900)$ and $Z(4430)$ as the ground state and first radial excitation of tetraquarks, calculating their properties and decay widths using QCD sum rules to compare with experimental data.

## Contribution

It introduces a novel interpretation of $Z_c(3900)$ and $Z(4430)$ as related tetraquark states and computes their masses, couplings, and decay widths within this framework.

## Key findings

- Masses and couplings of $Z_c(3900)$ and $Z(4430)$ are consistent with experimental data.
- Calculated decay widths align with observed resonance behaviors.
- Supports tetraquark interpretation of these resonances.

## Abstract

Exploration of the resonances $Z_c(3900)$ and $Z(4430)$ are performed by assuming that they are ground-state and first radial excitation of the same tetraquark with $J^{P}=1^{+}$. The mass and current coupling of the $ Z_c(3900)$ and $Z(4430)$ states are calculated using QCD two-point sum rule method by taking into account vacuum condensates up to eight dimensions. We investigate the vertices $Z_cM_hM_l$ and $ZM_hM_l$, with $M_h$ and $M_l $ being the heavy and light mesons, and evaluate the strong couplings $ g_{Z_cM_hM_l}$ and $g_{ZM_hM_l}$ using QCD sum rule on the light cone. The extracted couplings allow us to find the partial width of the decays $ Z_c(3900) \to J/\psi \pi; \,\psi^{\prime} \pi;\, \eta_c \rho$ and $Z(4430) \to \psi^{\prime} \pi;\, J/\psi \pi;\, \eta_c^{\prime}\rho;\, \eta_c\rho$, which may help in comprehensive investigation of these resonances. We compare width of the decays of $Z_c(3900)$ and $Z(4430)$ resonances with available experimental data as well as existing theoretical predictions.