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 Padacute{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.
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