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

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.