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arXiv · 2103.13140

Tetraquark state $X(6900)$ and the interaction between diquark and antidiquark

Hong-Wei Ke·Xin Han·Xiao-Hai Liu·Yan-Liang Shi
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Abstract

Recently LHCb declared a new structure $X(6900)$ in the final state di-$J/\psi$ which is popularly regarded as a $cc$-$\bar c\bar c$ tetraquark state. %popularly. Within the Bethe-Salpeter (B-S) frame we study the possible $cc$-$\bar c\bar c$ bound states and the interaction between diquark ($cc$) and antidiquark ($\bar c\bar c$). In this work $cc$ ($\bar c\bar c$) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of $cc$-$\bar c\bar c$ bound state are $0^+$, $1^+$ and $2^+$. Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for diquark and antidiquark system. Then we deduce the B-S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of $X(6900)$ when we assign appropriate values for parameter $\kappa$ introduced in the interaction (kernel).We also briefly calculate the spectra of $bb$-$\bar b\bar b$ bound states. Future measurement of $bb$-$\bar b\bar b$ state will help us to determine the exact form of effective interaction.

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Hong-Wei Ke, Xin Han, Xiao-Hai Liu, Yan-Liang Shi. 2021-03-24. Tetraquark state $X(6900)$ and the interaction between diquark and antidiquark. https://doi.org/10.1140/epjc%2Fs10052-021-09229-y

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