Study of $X(6900)$ with unitarized coupled channel scattering amplitudes

Abstract

In this paper, we study the resonant state $X(6900)$. The scattering amplitudes of coupled channels, $J/\psi J/\psi$-$J/\psi \psi (2S)$-$J/\psi \psi (3770)$, are constructed with the interaction of four vector mesons described by effective Lagrangians. The amplitudes are calculated up to one loop, decomposed by partial wave projection, and unitarized by Pad$\acute{e}$ approximation. These amplitudes are fitted to the latest experimental data sets of di-$J/\psi$ and $J/\psi \psi (2S)$ invariant mass spectra of LHCb, CMS, and ATLAS. High-quality solutions are obtained. With these partial wave amplitudes, we extract the pole parameters of the $X(6900)$. Its quantum number is likely to be $0^{++}$. According to the pole counting rule as well as analysis of the phase shifts of the partial waves, it supports our previous conclusion that the $X(6900)$ prefers to be a compact tetra-quark.

arXiv comment23 pages, 4 figures, add a few discussions

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• Exploring fully heavy scalar tetraquarks $QQ\overline{Q}\overline{Q}$
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• Fully heavy tetraquark states with a diquark-antidiquark configuration
• Possible bound states in the triple-${\eta }_c$ and triple-$J/\psi$ systems
• ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ scatterings from lattice QCD