Testing the tetraquark structure for the X resonances in the low-lying region

Assuming the four-quark structure for the X resonances in the low-lying region, we calculate their masses using the color-spin interaction. Specifically, the hyperfine masses of the color-spin interaction are calculated for the possible states in spin-0, spin-1, spin-2 channels. The two states in spin-0 channel as well as the two states in spin-1 channel are diagonalized in order to generate the physical hyperfine masses. By matching the difference in hyperfine masses with the splitting in corresponding hadron masses and using the X(3872) mass as an input, we estimate the masses corresponding to the states $ J^{PC}=0^{++}$ , $ 1^{+-}$ , $ 2^{++}$ . We find that the masses of two states in $ 1^{+-}$ are close to those of X(3823) , X(3900) , and the mass of the $ 2^{++}$ state is close to that of X(3940) . For them, the discrepancies are about $\sim 10$ MeV. This may suggest that the quantum numbers of the controversial states are $ X(3823)=1^{+-}$ , $ X(3900)=1^{+-}$ , $ X(3940)=2^{++}$ . In this work, we use the same inputs parameters, the constituent quark masses and the strength of the color-spin interaction, that have been adopted in the previous work on the D - or B -meson excited states. There, it was shown that the four-quark structure can be manifested in their excited states. Thus, our results in this work provide a consistent treatment on open- and hidden-charm mesons as far as the four-quark model is concerned