The lineshape of the compact fully heavy tetraquark

Hadrons and their distributions are the most direct observables in experiment, which would shed light on the non-perturbative mystery of quantum chromodynamics (QCD). As the result, any new hadron will challenge our current knowlege on the one hand, and provide additional inputs on the other hand. The fully heavy $cc\bar{c}\bar{c}$ system observed by LHCb recently opens a new era for hadron physics. We first extract the internal structure of the fully heavy tetraquarks directly from the experimental data, within the compact tetraquark picture. By fitting to the di-$J/\psi$ lineshape, we find that the $X(6900)$ is only cusp effect from the $J/\psi\psi(3770)$ channel. In addition, there is also a cusp slightly below $6.8~\mathrm{GeV}$ stemming from the $J/\psi\psi^\prime$ channel. The two $0^{++}$ tetraquarks behave as two resonances above the di-$\eta_c$ and di-$J/\psi$ threshold, respectively. The $2^{++}$ state is a bound state below the di-$J/\psi$ threshold. Furthermore, we find that the $X_{0^{++}}(6035)$ shows a significant structure in the di-$\eta_c$ lineshape even after the coupled channel effect. This is an unique feature which can distinguish compact $cc\bar{c}\bar{c}$ tetraquark from the loosely hadronic molecules.