Abstract
In this article, we construct the diquark-diquark-antiquark type interpolating currents, and study the masses and pole residues of the $J^P={\frac{3}{2}}^-$ and ${\frac{5}{2}}^+$ hidden-charmed pentaquark states in details with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In calculations, we use the formula $\mu=\sqrt{M^2_{P_c}-(2{\mathbb{M}}_c)^2}$ to determine the energy scales of the QCD spectral densities. The present predictions favor assigning the $P_c(4380)$ and $P_c(4450)$ to be the ${\frac{3}{2}}^-$ and ${\frac{5}{2}}^+$ pentaquark states, respectively.
Highlights
In 1964, Gell-Mann suggested that multiquark states beyond the minimal quark contents qqand qqq maybe exist [1]; a quantitative model for the tetraquark states with the quark contents qqqqwas developed by Jaffe using the MIT bag model in 1976 [2]
We studied the acceptable energy scales of the QCD spectral densities for the hidden charm tetraquark states and molecular states in the QCD sum rules in detail for the first time [16,17,18,19,37,38,39,46,47,48], and suggested the formula μ=
In Refs. [16,17,18,19,37,38,39,46,47,48], we studied the acceptable energy scales of the QCD spectral densities for the hidden charm tetraquark states and molecular states in the QCD sum rules in detail for the first time, and we suggested the formula μ =
Summary
In 1964, Gell-Mann suggested that multiquark states beyond the minimal quark contents qqand qqq maybe exist [1]; a quantitative model for the tetraquark states with the quark contents qqqqwas developed by Jaffe using the MIT bag model in 1976 [2]. We can construct the tetraquark states and pentaquark states according to the diquark–antidiquark model and diquark– diquark–antiquark model, respectively [5,6,7]. Χc p molecular pentaquark states [21,22,23,24,25] (or not the molecular pentaquark states [26]), the diquark–diquark–antiquark type pentaquark states [27,28,29], the diquark–triquark type pentaquark states [30], re-scattering effects [31,32,33], etc We can test their resonant nature by using photoproduction off a proton target [34,35,36]. We construct the molecular pentaquark states according to the routine quark → meson and baryon → molecular
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