Magnetic dipole moments of the hidden-charm pentaquark states: ${P}_{c}\left(4440\right)$ , ${P}_{c}\left(4457\right)$ and ${P}_{\mathrm{cs}}\left(4459\right)$

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