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 $I(J^P)=\frac{1}{2}({\frac{3}{2}}^{-})$ is adopted. We also study the properties of strong decays within a simple rearrangement scheme. The results indicate that the $I(J^P)=\frac{1}{2}({\frac{1}{2}}^{-})$ $ccnn\bar{n}$ with $I_{nn}=0$ where $n$ denotes $u$ or $d$ quark, $I(J^P)=0({\frac{1}{2}}^{-})$ $ccnn\bar{s}$, and $I(J^P)=0({\frac{1}{2}}^{-})$ $ccns\bar{n}$ ground states should be stable.