Insights into the inner structures of the fully charmed tetraquark state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>6900</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
Zhi-Hui Guo, J. A. Oller
Abstract
The recently discovered fully charmed tetraquark candidate $X(6900)$ is analyzed within the frameworks of effective-range expansion, compositeness relation and width saturation, and a coupled multichannel dynamical study. By taking into account constraints from heavy-quark spin symmetry, the coupled-channel amplitude including the $J/\ensuremath{\psi}J/\ensuremath{\psi}$, ${\ensuremath{\chi}}_{c0}{\ensuremath{\chi}}_{c0}$, and ${\ensuremath{\chi}}_{c1}{\ensuremath{\chi}}_{c1}$ is constructed to fit the experimental di-$J/\ensuremath{\psi}$ event distributions around the energy region near 6.9 GeV. Another dynamical two-coupled-channel amplitude with the $J/\ensuremath{\psi}J/\ensuremath{\psi}$ and $\ensuremath{\psi}(3770)J/\ensuremath{\psi}$ is also considered to describe the same datasets. The three different theoretical approaches lead to similar conclusions that the two-meson components do not play dominant roles in the $X(6900)$. Our determinations of the resonance poles in the complex energy plane from the refined coupled-channel study are found to be consistent with the experimental analyses. The coupled-channel amplitudes also have another pole corresponding to a narrow resonance $X(6825)$ that we predict sitting below the ${\ensuremath{\chi}}_{c0}{\ensuremath{\chi}}_{c0}$ threshold and of molecular origin. We give predictions to the line shapes of the ${\ensuremath{\chi}}_{c0}{\ensuremath{\chi}}_{c0}$ and ${\ensuremath{\chi}}_{c1}{\ensuremath{\chi}}_{c1}$ channels, which could provide a useful guide for future experimental measurements.