Investigation of magnetic moment of $P_{cs}(4338)$ and $P_{cs}(4459)$ pentaquark states

Abstract: In this study, we discuss the magnetic moment of $P_{cs}(4338)$ and $P_{cs}(4459)$ 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 $I(J^P) = 0(1/2^-)$ and $I(J^P) = 0(3/2^-)$ for $P_{cs}(4338)$ and $P_{cs}(4459)$, respectively. Our predictions for the magnetic moment $\mu_{P_{cs}} = 0.34 \pm 0.12~\mu_N$ for the $P_{cs}(4338)$ state, and $\mu_{P_{cs}} = -1.67 \pm 0.58~\mu_N $ for the $P_{cs}(4459)$ 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 $\mu_{P_{cs}} = 0.63 \pm 0.21~\mu_N$ and $\mu_{P_{cs}} = -3.33 \pm 1.04 ~\mu_N $ for the isospin-1 partners of the $P_{cs}(4338)$ and $P_{cs}(4459)$ states, respectively. Our results regarding the magnetic moments of these color singlet-singlet type pentaquark states are compared with the results in the literature.