QCD sum rule study of hidden-charm pentaquarks

We study the mass spectra of hidden-charm pentaquarks having spin $J = {1\over2}/{3\over2}/{5\over2}$andquarkcontents$uud c \bar c$. We systematically construct all the relevant local hidden-charm pentaquark currents, and select some of them to perform QCD sum rule analyses. We find that the $P_c(4380)$ and $P_c(4450)$ can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. Besides them, we also find a) the lowest-lying hidden-charm pentaquark state of $J^P=1\mathrm{/}{2}^{-}$ has the mass $4.33_{-0.13}^{+0.17}$ GeV, while the one of $J^P = 1/2^+$issignificantlyhigher,thatisaround$4.7-4.9$ GeV; b) the lowest-lying hidden-charm pentaquark state of $J^P=3\mathrm{/}{2}^{-}$ has the mass $4.37_{-0.13}^{+0.18}$ GeV, consistent with the $P_c(4380)$ of $J^P=3\mathrm{/}{2}^{-}$, while the one of $J^P=3\mathrm{/}{2}^{+}$ is also significantly higher, that is above $4.6$ GeV; c) the hidden-charm pentaquark state of $J^P=5\mathrm{/}{2}^{-}$ has a mass around $4.5-4.6$ GeV, slightly larger than the $P_c(4450)$ of $J^P=5\mathrm{/}{2}^{+}$.