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

In this paper, we study the resonant state X (6900). The scattering amplitudes of coupled channels, J / ψ J / ψ - J / ψ ψ ( 2 S ) - J / ψ ψ ( 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 e ´ approximation. These amplitudes are fitted to the latest experimental data sets of di- J / ψ and J / ψ ψ ( 2 S ) 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.