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.

23 pages, 4 figures, add a few discussions

References in corpus (12)

• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Observation of an exotic narrow doubly charmed tetraquark
• Study of the doubly charmed tetraquark $T_{cc}^{+}$
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• Tetraquark state $X(6900)$ and the interaction between diquark and antidiquark
• Two photon couplings of the lightest isoscalars from BELLE data
• Insights into the inner structures of the fully charmed tetraquark state $X(6900)$
• Spectrum of the S-wave fully-heavy tetraquark states
• Pole analysis on the doubly charmed meson in $D^0{D}^0{\pi }^{+}$ mass spectrum
• Pseudoscalar charmonium pair interactions via the Pomeron exchange mechanism
• Nature of the $X(6900)$ in partial wave decomposition of $J/\psi J/\psi$ scattering

Cited by in corpus (5)

• Exploring fully heavy scalar tetraquarks $QQ\overline{Q}\overline{Q}$
• P-wave fully charm and fully bottom tetraquark states
• 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