QCD sum rule study of hidden-charm pentaquarks

We study the mass spectra of hidden-charm pentaquarks having spin $$J = {1\over 2}/{3\over 2}/{5\over 2}$$ and quark contents $$uud c \bar{c}$$. We systematically construct all the relevant local hidden-charm pentaquark currents, and we 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 $$J^P = 1/2^-$$ has the mass $$4.33^{+0.17}_{-0.13}$$ GeV, while the one of $$J^P = 1/2^+$$ is significantly higher, that is, around 4.7–4.9 GeV; (b) the lowest-lying hidden-charm pentaquark state of $$J^P = 3/2^-$$ has the mass $$4.37^{+0.18}_{-0.13}$$ GeV, consistent with the $$P_c(4380)$$ of $$J^P = 3/2^-$$, while the one of $$J^P = 3/2^+$$ is also significantly higher, that is, above 4.6 GeV; (c) the hidden-charm pentaquark state of $$J^P = 5/2^-$$ has a mass around 4.5–4.6 GeV, slightly larger than the $$P_c(4450)$$ of $$J^P = 5/2^+$$