Doubly-charmed pentaquark states in a mass splitting model

Concentrating on the mass differences relative to $P_{\psi}^{N}(4312)^+$, we systematically investigate the spectra of doubly-charmed pentaquark states in the compact $ccqq\bar{q}$ ($q=u, d, s$) configuration. The assumption that the observed $P_{\psi}^{N}(4312)^+$ is a compact hidden-charm pentaquark with $I(J^P)=\frac12(\frac32^-)$ is adopted. We also study the properties of strong decays within a simple rearrangement scheme. The results indicate that the $I(J^P)=\frac12(\frac12^-)$ $ccnn\bar{n}$ with $I_{nn}=0$ where $n$ denotes $u$ or $d$ quark, $I(J^P)=0(\frac12^-)$ $ccnn\bar{s}$, and $I(J^P)=0(\frac12^-)$ $ccns\bar{n}$ ground states should be stable.