Resolving the puzzling decay patterns of charged $Z_c$ and $Z_b$ states

TL;DR

This paper uses a quark interchange model to analyze decay patterns of charged $Z_c$ and $Z_b$ states, finding that they favor decay into radially excited states and aligning well with experimental data, thus supporting their molecular interpretations.

Contribution

It provides a detailed theoretical analysis of decay ratios of exotic charged states, supporting their molecular nature and predicting new ratios for future experimental verification.

Findings

Decay ratios favor radially excited states over ground states.

Predicted ratios match well with existing experimental measurements.

Proposes new ratios for unmeasured states to guide future experiments.

Abstract

We investigate the ratio of the branching fractions of the molecular candidates decaying into the ground and radially excited states within the quark interchange model. Our numerical results suggest that these molecular candidates are more likely to decay into the radially excited states than into ground states. Especially, the ratio $\Gamma[Z_c(4430)\to \pi\psi(2S)]$/$\Gamma[Z_c(4430)\to \pi J/\psi]\sim 9.8$ is close to the experimental measurement, which supports the interpretation of $Z_c(4430)$ as the $\bar{D}D^*(2S)$ molecular state. The ratios of the branching fractions of $Z_b(10610)$ and $Z_b(10650)$ to $\pi\Upsilon(2S, 3S)$ and $\pi\Upsilon(1S)$ agrees very well with Belle's measurement. We also predict the similar ratios for $Z_c(3900)$, $Z_c(4020)$, $R_{Z_c(3900)}$$\approx$1.3 and $R_{Z_c(4020)}$$\approx$$4.7$. Hopefully the $\pi\psi(2S)$ mode, and ratios $R_{Z_c(3900)}$ and $R_{Z_c(4020)}$ will be measured by the BESIII and Belle collaborations in the near future, which shall be very helpful to understand the underlying dynamics of these exotic states.