Analysis of the $Z(4430)$ as the first radial excitation of the $Z_c(3900)$

Abstract

In this article, we take the $Z_c(3900)$ and $Z(4430)$ as the ground state and the first radial excited state of the axial-vector tetraquark states with $J^{PC}=1^{+-}$, respectively, and study their masses and pole residues with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion. The numerical result favors assigning the $Z_c(3900)$ and $Z(4430)$ as the ground state and first radial excited state of the axial-vector tetraquark states, respectively.

11 pages, 4 figures

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• Line Shapes of the Z(4430)
• Bottomed Analog of Z+(4433)
• Mass spectrum of the axial-vector hidden charmed and hidden bottom tetraquark states
• $Z^{+}(4430)$ as a resonance in the $D_1(D_1^{\prime })D^{\ast }$ channel
• Interpreting Z(3900)

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• Treating $Z_c(3900)$ and $Z(4430)$ as the ground-state and first radially excited tetraquarks
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• Analysis of the $Z_{cs}(3985)$ as the axialvector tetraquark state
• Z_c -like spectra from QCD Laplace sum rules at NLO
• The decay width of the $Z_c(3900)$ as an axialvector tetraquark state in solid quark-hadron duality
• Analysis of the mass and width of the $Y(4274)$ as axialvector molecule-like state
• Exploring fully heavy scalar tetraquarks $QQ\overline{Q}\overline{Q}$
• Strong decays of the $Y(4660)$ as a vector tetraquark state in solid quark-hadron duality
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• Revisit the tetraquark candidates in the $J/\psi J/\psi$ mass spectrum
• Analysis of the vector tetraquark states with P-waves between the diquarks and antidiquarks via the QCD sum rules
• Reanalysis of the $X(3915)$, $X(4500)$ and $X(4700)$ with QCD sum rules
• A family of double-beauty tetraquarks: Axial-vector state $T_{bb;\bar{u}\bar{s}}^{-}$
• Settling the $Z_c(4600)$ in the charged charmonium-like family
• Analysis of the 1S and 2S states of the ${\Lambda }_Q$ and ${\Xi }_Q$ with the QCD sum rules
• Assignments of the $X(4140)$, $X(4500)$, $X(4630)$ and $X(4685)$ based on the QCD sum rules
• Reanalysis of the $X(4140)$ as axialvector tetraquark state with QCD sum rules
• Analysis of the scalar doubly charmed hexaquark state with QCD sum rules
• Analysis of the pseudoscalar hidden-charm tetraquark states with the QCD sum rules
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• Analysis of the hidden-charm-hidden-strange tetraquark mass spectrum via the QCD sum rules
• Analysis of the vector hidden-charm-hidden-strange tetraquark states with implicit P-waves
• Triply-charmed hexaquark states with the QCD sum rules
• Analysis of the possible $D{\bar{D}}_{s0}^{\ast }(2317)$ and $D^{\ast }{\bar{D}}_{s1}^{\ast }(2460)$ molecules with QCD sum rules
• The ground states and the first radially excited states of D-wave vector $\rho$ and $\varphi$ mesons
• Analysis of the ${\overline{\Xi }}_{cc}{\Xi }_{cc}$ hexaquark molecular state with the QCD sum rules
• Masses of tetraquark states in the hidden charm sector above $D-D^{\ast }$ threshold
• Modifications on parameters of $Z(4430)$ in a dense medium
• Analysis of the $D{\bar{D}}^{\ast }K$ system with QCD sum rules
• Does vacuum saturation work for the higher dimensional vacuum condensates in the QCD sum rules?
• The ground states and first radial excitations of the vector tetraquark states with explicit P-waves via the QCD sum rules
• The strong coupling $g_{XJ/\psi \varphi }$ of $X(4700)\to J/\psi \varphi$ in the light-cone sum rules
• Analysis of the tensor-tensor type scalar tetraquark states with QCD sum rules
• Tests of the Z_c-like Laplace Sum Rule (LSR) results using FESR at NLO
• Exotic hadrons associated with $b$-quark
• Observation and investigation of the $T_{c\bar{c}1}(4430{)}^{+}$ structure in $B^{+}\to \psi (2S)K_{\text{S}}^0{\pi }^{+}$ decays
• 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
• Hadronic molecule model for the doubly charmed state $T_{cc}^{+}$
• Analysis of the vector hidden-charm tetraquark states without explicit P-waves via the QCD sum rules