Insight into the nature of the $P_{c}(4457)$ and related pentaquarks

We systematically study the electromagnetic properties of pentaquark states from different perspectives to better understand their nature, internal structure, and quantum numbers, determine their hadronization processes, and shed light on their true nature. The present study examines the magnetic moments of the $P_{c}(4457)$ and related hidden-charm pentaquark states with and without strangeness ($[d d][u c] \bar c$, $[u u][s c] \bar c$, $[dd ][s c] \bar c$, $[s s][u c] \bar c$ and $[s s][d c] \bar c$), employing a comprehensive analysis that encompasses both the compact pentaquark configuration and $J^P = \frac{3}{2}^-$ quantum numbers. The present study compares the results regarding the magnetic moment of the $P_{c}(4457)$ pentaquark state with those reported in the existing literature. The numerical results obtained in this study, when considered alongside existing literature, indicate that the magnetic moments of hidden-charm pentaquark states may offer insights into their underlying structures, which in turn can inform the distinction between their spin-parity quantum numbers. It seems that for the future experimental search of the family of hidden-charm pentaquark states, studying the electromagnetic properties of the hidden-charm pentaquark states can provide valuable information.