Analysis of the hidden-charm pentaquark states based on magnetic moment and transition magnetic moment

In this work, we calculate the magnetic moments of the $P^{N^{0}}_{\psi}$ states and $P^{\Delta^{0}}_{\psi}$ states with valence quark content $\bar{c}cudd $ in molecular model, diquark-diquark-antiquark model and diquark-triquark model, as well as the transition magnetic moments in the molecular model. At the same time, we also calculate magnetic moments and transition magnetic moments of $P^{\Delta^{++}}_{\psi}$ states and $P^{\Delta^{-}}_{\psi}$ states in the molecular model as additional products. Our results show that in the diquark-diquark-antiquark model, the magnetic moments of $ \lambda $ excitation state are usually larger than the magnetic moments of $ \rho $ excitation state. We find some interesting proportional relationships between the expressions of transition magnetic moments. The results provide important insights for future experimental observation of hidden-charm pentaquark states and help to distinguish their inner structures. With these efforts, our understanding of the properties for the hidden-charm pentaquark states will become more abundant.