$P_{c\bar cs}(4459)^{0}$, $P_{c\bar c s}(4338)^0$ and mass spectrum of strange hidden-charm pentaquarks

Abstract

Strange hidden-charm pentaquark states have been systematically investigated within a diquark-triquark model. Through a Gaussian expansion method, masses of some diquarks, triquarks and strange hidden-charmed pentaquark states from S-wave to P-wave excitations have been calculated with the non-relativistic Semay and Silvestre-Brac potentials in terms of the same parameters employed for tetraquark states. Masses of pentaquark states in S-wave excitations are found between $4200$ MeV and $4590$ MeV, while masses of all P-wave excitations are found above $4600$ MeV. Mass splittings between the S-wave and P-wave pentaquark states are about $350-570$ MeV. In comparison to the experimental data, $P_{c\bar cs}(4459)^{0}$ observed by LHCb in decay channel $\Xi_{b}^{-}\rightarrow J/\psi \Lambda K^-$ is assumed as the $|1; 0, 1/2; 3/2, 0\rangle_{3/2}$ $[sq][\bar{c}cq]$ pentaquark state with $J^P={3\over 2}^-$, while $P_{c\bar c s}(4338)^0$ observed in the decay channel $B^{-}\rightarrow J/\psi \Lambda \bar{p}$ is very possibly the $|0; 1, 1/2; 1/2, 0\rangle_{1/2}$ $[cq][\bar{c}sq]$ pentaquark state with $J^P={1\over 2}^-$. We predict a lowest strange hidden-charm pentaquark state with $J^P={1\over 2}^-$ around $4200$ MeV.