Investigation of magnetic moment of (4338) and (4459) Pentaquark States

In this study, we discuss the magnetic moment of ${P}_{cs}\left(4338\right)$ and ${P}_{cs}\left(4459\right)$ hidden-charmed pentaquarks, which are closely related to their substructures. The magnetic moments of these states are calculated with the help of the QCD light-cone sum rules method with quantum numbers $I\left({J}^{P}\right)=0\left(1/{2}^{-}\right)$ and $I\left({J}^{P}\right)=0\left(3/{2}^{-}\right)$ for ${P}_{cs}\left(4338\right)$ and ${P}_{cs}\left(4459\right)$, respectively. Our predictions for the magnetic moment ${\mu }_{{P}_{cs}}=0.34±0.12\phantom{\rule{0.25em}{0ex}}{\mu }_{N}$ for the ${P}_{cs}\left(4338\right)$ state, and ${\mu }_{{P}_{cs}}=-1.67±0.58\phantom{\rule{0.25em}{0ex}}{\mu }_{N}$ for the ${P}_{cs}\left(4459\right)$ state. As a by-product, the magnetic moments of the isospin−1 partners of these states have also been obtained. The magnetic moments are obtained as ${\mu }_{{P}_{cs}}=0.63±0.21\phantom{\rule{0.25em}{0ex}}{\mu }_{N}$ and ${\mu }_{{P}_{cs}}=-3.33±1.04\phantom{\rule{0.25em}{0ex}}{\mu }_{N}$ for the isospin-1 partners of the ${P}_{cs}\left(4338\right)$ and ${P}_{cs}\left(4459\right)$ states, respectively. Our results regarding the magnetic moments of these color singlet-singlet type pentaquark states are compared with the results in the literature.