Testing the tetraquark structure for the $X$ resonances in low-lying region

Abstract

Assuming four-quark structure for the $X$ resonances in low-lying region, we calculate their masses using the color-spin interaction. In specific, the hyperfine masses of the color-spin interaction are calculated for the possible states in spin-0, spin-1, spin-2 channels. The two states in spin-0 channel as well as the two states in spin-1 channel are diagonalized in order to generate the physical hyperfine masses. By matching the difference in hyperfine masses with the splitting in corresponding hadron masses and using the $X(3872)$ mass as an input, we estimate the masses corresponding to the states $J^{PC}=0^{++},1^{+-},2^{++}$. We find the masses of two states in $1^{+-}$ are close to those of $X(3823)$, $X(3900)$, and the mass of the $2^{++}$ state is close to that of $X(3940)$. For them, the discrepancies are about $\sim 10$ MeV. This may suggest that the quantum numbers of the controversial states are $X(3823)=1^{+-},X(3900)=1^{+-},X(3940)=2^{++}$. In this work, we use the same inputs parameters, the constituent quark masses and the strength of the color-spin interaction, that have been adopted in the previous work on the $D$ or $B$-meson excited states. There, it was shown that the four-quark structure can be manifested in their excited states. Thus, our results in this work provide a consistent treatment on open- and hidden-charm mesons as far as the four-quark model is concerned.

8 pages, substantially revised, more references are added, the version to be published in EPJA

References in corpus (7)

• Big-Bang Nucleosynthesis
• Observation of a resonance-like structure in the pi^+- psi' mass distribution in exclusive B-->K pi^+- psi' decays
• The Z(4430) and a New Paradigm for Spin Interactions in Tetraquarks
• Stable multiquark states with heavy quarks in a diquark model
• Hidden-Charm Tetraquarks and Charged Zc States
• Testing confining potentials through meson/baryon hyperfine splitting ratio
• Four-quark structure of the excited states of heavy mesons

Cited by in corpus (15)

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• Hexaquark picture for $d^{\ast }(2380)$
• Tetraquark mixing framework for isoscalar resonances in light mesons
• Possible signatures for tetraquarks from the decays of $a_0(980)$, $a_0(1450)$
• Further signatures to support the tetraquark mixing framework for the two light-meson nonets
• Doubly heavy tetraquark states in a mass splitting model
• Testing the tetraquark mixing framework from QCD sum rules for $a_0(980)$
• Spin-1 diquark contributing to the formation of tetraquarks in light mesons
• Tetraquark mixing supported by the partial decay widths of two light-meson nonets
• Hidden-Charm Tetraquarks in a Mixture Model: Coupled-Channel Analysis with $c\bar{c}$ and Hadronic Molecular Components
• An analysis on doubly bottom molecular tetraquarks composed of $H_{(s)}$ and $T_{(s)}$ doublets