In this letter, we perform partial wave decomposition on coupled channel
scattering amplitudes, J/ฯJ/ฯ-J/ฯฯ(2S)-J/ฯฯ(3770),
to study the resonance appears in these processes. Effective Lagrangians are
used to describe the interactions of four charmed vector mesons, and the
scattering amplitudes are calculated up to the next-to-leading order. Partial
wave projections are performed, and unitarization is implemented by Pad\'e
approximation. Then we fit the amplitudes to the J/ฯJ/ฯ invariant mass
spectra measured by LHCb and determine the unknown couplings. The pole
parameters of the X(6900) are extracted as M=6861.0โ8.8+6.3โ~MeV and
ฮ=129.0โ3.4+5.6โ~MeV. Our analysis implies that its quantum number
prefers to be 0++. The pole counting rule and phase shifts show that it is
a normal Breit-Wigner resonance and hence should be a compact tetraquark.Comment: 6 pages, 4 figure