Abstract
We study the hidden-charm pentaquark states $udsc\bar{c}$ with spins 1/2, 3/2, and 5/2 within the QCD sum-rule approach. First, we construct the currents for the particular configuration of pentaquark states that consist of the flavor singlet three-quark cluster $uds$ of spins 1/2 and 3/2 and the two-quark cluster $\bar cc$ of spin 1, where both clusters are in a color-octet state. From the QCD sum rules obtained by the operator product expansion up to dimension-10 condensates, the extracted masses for the pentaquark states $uds$-$\bar{c}c$ are about 4.6 GeV (5.6 GeV) for spin 1/2$^\pm$, about 5.1 GeV (6.0 GeV) for spin 3/2$^\pm$, about 6.1 GeV (5.9 GeV) for spin 5/2$^\pm$, where the masses of the positive parity states are given in parentheses. Additionally, based on the flavor singlet pentaquark states, it is also shown that other pentaquark states of clusters like $udc$-$\bar{c}s$ and $usc$-$\bar cd$ lead to masses similar to the $uds$-$\bar cc$ case within error bars. Furthermore, in order to see whether any of the states, observed by the LHCb Collaboration, could be understood as the pentaquark of two clusters in the color-octet state, we study the pentaquark formed by the two clusters $udc$-$\bar cu$, where the three-quark cluster is assumed to have the same flavor structure as the above $uds$ cluster. We come to the conclusion that if the observed pentaquark will be found to have spin 1/2 and negative parity, then it could be described as a state of two color-octet clusters.
Highlights
Since the observation of the two exotic hidden-charm pentaquark Pþc states of the quark content uudccwith the spins 3=2 and 5=2 through the decay Λ0b → J=ψK−p by LHCb collaboration [1], many studies on these states and other expected hidden-charm pentaquark states have been performed
From the QCD sum rules obtained by the operator product expansion up to dimension-10 condensates, the extracted masses for the pentaquark states uds-cc are about 4.6 GeV (5.6 GeV) for spin 1=2Æ, about 5.1 GeV (6.0 GeV) for spin 3=2Æ, about 6.1 GeV (5.9 GeV) for spin 5=2Æ, where the masses of the positive parity states are given in parentheses
We discuss the results obtained in the previous sections on the basis of the constructed QCD sum rules (SRs) for pentaquark states
Summary
Since the observation of the two exotic hidden-charm pentaquark Pþc states of the quark content uudccwith the spins 3=2 and 5=2 through the decay Λ0b → J=ψK−p by LHCb collaboration [1], many studies on these states and other expected hidden-charm pentaquark states have been performed. Considering the interpolating current to a pentaquark state for analysis within the QCD sum rules (SRs), the clustering in the color, flavor and spin space is inevitable due to the absence of the invariant rank-5 tensors for the color, flavor and spin subspaces. The flavor singlet hidden-charm pentaquark was analyzed as the bound state of a three-quark and two-quark parts both in color octets, and the stable result was got for the total spin 1=2 in [8]. We assume that all quarks are in an S-wave, the colors of both clusters are color octets, and the two-quark cluster has spin 1 since it has been shown in [8] that such clusters of uds and cc yielded the most stable result To check this assumption, we consider the pentaquark states containing a scalar two-quark cluster and find that such states lead to higher masses than those obtained from pentaquarks with a two-quark cluster of spin 1.
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