Employing the relativized quark model and the quark-interchange model, we investigate the decay of the charged heavy quarkonium-like states Z c (3900), Z c (4020), Z c (4430), Z b (10610) and Z b (10650) into the ground and radially excited heavy quarkonia via emitting a pion meson. The Z c and Z b states are assumed to be hadronic molecules composed of open-flavor heavy mesons. The calculated decay ratios can be compared with the experimental data, which are useful in judging whether the molecule state assignment for the corresponding Z c or Z b state is reasonable or not. The theoretical framework constructed in this work will be helpful in revealing the underlying structures of some exotic hadrons. Yan-Rui Liu, Jia-Jun Wu, and Yuan Song. We also thank Prof. Ulf-G. Meißner for a careful reading and helpful suggestions.

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. In particular, the ratio Γ½Z c ð4430Þ → πψð2SÞ=Γ½Z c ð4430Þ → πJ=ψ ∼ 9.9 is close to the experimental measurement, which supports the interpretation of Z c ð4430Þ as theDD Ã ð2SÞ molecular state. The ratios of the branching fractions of Z b ð10610Þ and Z b ð10650Þ to πϒð2S; 3SÞ and πϒð1SÞ agrees very well with the Belle Collaboration's measurement. We also predict the similar ratios for Z c ð3900Þ, Z c ð4020Þ, R Z c ð3900Þ ≈ 1.4, and R Z c ð4020Þ ≈ 4.8. Hopefully, the πψð2SÞ mode and the ratios R Z c ð3900Þ and R Z c ð4020Þ will be measured by the BESIII and Belle collaborations in the near future, which shall be very helpful for understanding the underlying dynamics of these exotic states.

The magnetic moment of a baryon state is an equally important dynamical observable as its mass, which encodes crucial information of its underlying structure. According to the different color-flavor structure, we have calculated the magnetic moments of the hidden-charm pentaquark states with the isospin (I, I 3 ) = ( + in the molecular model, the diquark-triquark model, and the diquark-diquark-antiquark model, respectively. Although a good description for the pentaquark mass spectrum and decay patterns has been obtained in all three models, different color-flavor structures lead to different magnetic moments, which can be used to pin down their inner structures and distinguish various models.