Radially excited axial mesons and the enigmatic $Z_c$ and $Z_b$ in a coupled-channel model

TL;DR

This paper models the charged exotic states $Z_c$ and $Z_b$ as radially excited quark-antiquark pairs coupled to decay channels, successfully reproducing their masses and widths with minimal parameters and providing decay predictions.

Contribution

It introduces a coupled-channel Schrödinger model incorporating radially excited quark-antiquark pairs to explain the properties of $Z_c$ and $Z_b$ states, matching experimental data with only two free parameters.

Findings

Poles match experimental masses and widths.

Wave-function analysis estimates component probabilities.

Predictions for decay fractions among open-charm and open-bottom channels.

Abstract

The enigmatic charged states $Z_c(3900)$, $Z_c(4020)$, $Z_c(4050)$, $Z_b(10610)$, and $Z_b(10650)$ are studied within a coupled-channel Schr\"odinger model, where radially excited quark-antiquark pairs, with the same angular momenta and isospin as the $a_1(1260)$ and $b_1(1235)$, are strongly coupled to their Okubo-Zweig-Iizuka - allowed decay channels $D\bar{D}^*+\bar{D}D^*$ and $D^*\bar{D}^*$, or $B\bar{B}^*+\bar{B}B^*$ and $B^*\bar{B}^*$, in $S$ and $D$-wave. Poles, matching the experimental mass and width of all the above states, are found by varying only two free parameters. From the wave-function analysis of each resonance, the probability of each of the components contributing to the coupled system is estimated, and predictions can be made for the relative decay fractions among the coupled open-charm or open-bottom decay channels.