Two-particle contributions and nonlocal effects in the QCD sum rules for the axialvector tetraquark candidate $Z_c(3900)$

Abstract

In this article, we study the $Z_c(3900)$ with the QCD sum rules in details by including the two-particle scattering state contributions and nonlocal effects between the diquark and antidiquark constituents. The two-particle scattering state contributions cannot saturate the QCD sum rules at the hadron side, the contribution of the $Z_c(3900)$ plays an un-substitutable role, we can saturate the QCD sum rules with or without the two-particle scattering state contributions. If there exists a barrier or spatial separation between the diquark and antidiquark constituents, the Feynman diagrams can be divided into the factorizable and nonfactorizable diagrams. The factorizable diagrams consist of two colored clusters and lead to a stable tetraquark state. The nonfactorizable Feynman diagrams correspond to the tunnelling effects, which play a minor important role in the QCD sum rules, and are consistent with the small width of the $Z_c(3900)$. It is feasible to apply the QCD sum rules to study the tetraquark states, which begin to receive contributions at the order $\mathcal{O}({\alpha }_s^0)$, not at the order $\mathcal{O}({\alpha }_s^2)$.

arXiv comment23 pages, 24 figures

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Cited by in corpus (17)

• Analysis of the doubly-charmed tetraquark molecular states with the QCD sum rules
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• Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules
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• Revisit the tetraquark candidates in the $J/\psi J/\psi$ mass spectrum
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• The singly-charmed pentaquark molecular states via the QCD sum rules
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• Magnetic moments of the vector hidden-charmed tetraquark states
• Electromagnetic properties of the $D{\bar{D}}^{\ast }K$ molecular hexaquark state
• Analysis of the hidden-charm pentaquark candidates in the $J/\psi \Lambda$ mass spectrum via the QCD sum rules
• Structural dissection of hadronic molecules: The $D^{(\ast )}{\bar{K}}^{(\ast )}$ family under QCD light-cone sum rules
• Analysis of the $X(4475/4710)$, $X(4500/4700)$, $Z_c(4600)$, $Z_{\bar{c}\bar{s}}(4600)$ and related tetraquark states with the QCD sum rules