Systematic study of exotic $1^{-+}$ tetraquark spectroscopy
The masses of exotic quantum-number $1^{-+}$ compact tetraquark states are calculated in a constituent quark model, where a Cornell-like potential is employed as the central potential, spin-spin and spin-orbit coupling derived from the Breit-Fermi interaction are treated as hyperfine corrections, and model parameters are taken from previous works. The ground state $1^{-+}$ P-wave tetraquarks are predicted at 1.9, 4.2, and 6.6~GeV for the light, charmonium-like, and fully-charm sectors, respectively. The decay width ratios of $1^{-+}$ tetraquark states are calculated for two-body strong decay channels within the rearrangement mechanism, including $\omega h_1$ and $\eta f_1$ for isospin $I=0$ light tetraquarks, $\rho h_1$ and $\pi f_1$ for isospin $I=1$ light tetraquarks, $\pi/\eta+\chi_{c1}$ and $\rho/\omega + h_c$ for charmonium-like tetraquarks, and $\eta_c \chi_{c1}$ and $J/\psi h_c$ for fully-charm tetraquarks. The theoretical results are compared with the observed exotic $1^{-+}$ states, and promising search channels for $1^{-+}$ tetraquarks are discussed. The work suggests that $\eta_1(1855)$ is unlikely to be a compact tetraquark state.