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

Understand

Assuming four-quark structure for the $X$ resonances in low-lying region, we calculate their masses using the color-spin interaction.

• In specific, 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 $J^{PC}=0^{++}, 1^{+-},2^{++}$.