Abstract
Recently, the Belle Collaboration reported a new exotic state $Y(4620)$ with mass at 4625.9 MeV in the positronium annihilation process. Inspired by experiment, we study the tetraquark system $c\overline{s}s\overline{c}$ with quantum numbers ${J}^{P}={1}^{\ensuremath{-}}$ in the framework of chiral constituent quark model with the help of Gaussian expansion method. Two structures, diquark-antidiquark and meson-meson, with all possible color and spin configurations are considered. The result shows that no bound state can be formed. To investigate the possible resonance states, the real scaling method is employed. Several resonance states with energies 4354, 4408, 4469, 4497, and 4531 MeV are proposed. Taking into account the errors in calculating the $q\overline{q}$ mesons, the system errors in the calculation of four-quark system are around 60--100 MeV. The resonance with energy 4531 MeV is possible the candidate of the newly found state $Y(4620)$.
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