Magnetic dipole moments of the hidden-charm pentaquark states: $$P_c(4440)$$, $$P_c(4457)$$ and $$P_{cs}(4459)$$

Abstract In this work, we employ the light-cone QCD sum rule to calculate magnetic dipole moments of $$P_c(4440)$$ P c ( 4440 ) , $$P_c(4457)$$ 4457 and $$P_{cs}(4459)$$ cs 4459 pentaquark states by considering them as diquark–diquark–antiquark molecular pictures with quantum numbers $$J^P = \frac{3}{2}^-$$ J = 3 2 - \frac{1}{2}^-$$ 1 respectively. analyses, use form interpolating currents, photon distribution amplitudes obtain moment states. Theoretical examinations on hidden-charm states, are essential their results can help us better figure out substructure dynamics theory strong interaction. As a product, extract electric quadrupole octupole pentaquark. These values show non-spherical charge distribution.