Reanalysis of the $X(3915)$, $X(4500)$ and $X(4700)$ with QCD sum rules

Abstract

In this article, we study the $C{\gamma }_5\otimes {\gamma }_{5}C$ type and $C\otimes C$ type scalar $cs\bar{c}\bar{s}$ tetraquark states with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in a consistent way. The ground state masses $M_{C{\gamma }_5\otimes {\gamma }_{5}C}=3.89\pm 0.05\mathrm{GeV}$ and $M_{C\otimes C}=5.48\pm 0.10\mathrm{GeV}$ support assigning the $X(3915)$ to be the ground state $C{\gamma }_5\otimes {\gamma }_{5}C$ type tetraquark state with $J^{PC}=0^{++}$, but do not support assigning the $X(4700)$ to be the ground state $C\otimes C$ type $cs\bar{c}\bar{s}$ tetraquark state with $J^{PC}=0^{++}$. Then we tentatively assign the $X(3915)$ and $X(4500)$ to be the 1S and 2S $C{\gamma }_5\otimes {\gamma }_{5}C$ type scalar $cs\bar{c}\bar{s}$ tetraquark states respectively, and obtain the 1S mass $M_{1S}=3.85_{-0.17}^{+0.18}\mathrm{GeV}$ and 2S mass $M_{2S}=4.35_{-0.11}^{+0.10}\mathrm{GeV}$ from the QCD sum rules, which support assigning the $X(3915)$ to be the 1S $C{\gamma }_5\otimes {\gamma }_{5}C$ type tetraquark state, but do not support assigning the $X(4500)$ to be the 2S $C{\gamma }_5\otimes {\gamma }_{5}C$ type tetraquark state.

17 pages, 6 figures

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Cited by in corpus (15)

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• Spectrum of the Hidden-Bottom and the Hidden-Charm/Strange Exotics in the Dynamical Diquark Model
• Analysis of the $Z_{cs}(3985)$ as the axialvector tetraquark state
• Analysis of the mass and width of the $X(4140)$ as axialvector tetraquark state
• Analysis of the triply-heavy baryon states with the QCD sum rules
• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
• 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
• Understanding the $0^{++}$ and $2^{++}$ charmonium(-like) states near 3.9 GeV
• Assignments of the $X(4140)$, $X(4500)$, $X(4630)$ and $X(4685)$ based on the QCD sum rules
• Analysis of the scalar doubly charmed hexaquark state with QCD sum rules
• Analysis of the hidden-charm-hidden-strange tetraquark mass spectrum via the QCD sum rules
• $X$ structures in $B^{+}\to J/\psi \varphi K^{+}$ as one-loop and double-triangle threshold cusps
• Analysis of the ${\overline{\Xi }}_{cc}{\Xi }_{cc}$ hexaquark molecular state with the QCD sum rules
• Analysis of the $D{\bar{D}}^{\ast }K$ system with QCD sum rules