Study of $1^{--}$ P wave charmoniumlike and bottomoniumlike tetraquark spectroscopy

The masses of $1^{--}$ P-wave charmonium-like and bottomonium-like tetraquark states are calculated in a constituent quark model (CQM) where the Cornell-like potential and Breit-Fermi interaction are employed. All model parameters were imported from previous work, and predetermined by studying the low-lying conventional S- and P-wave light, charmed, bottom, charmonium, and bottomonium meson mass spectra. The lowest $1^{--}$ tetraquark mass is predicted to be around 4.15 GeV. The decay widths of $1^{--}$ P-wave tetraquark states are calculated for possible two-body strong decay channels within the rearrangement mechanism, including $ωχ_{cJ}$, $ηJ/ψ$, and $ρJ/ψ$ for charmonium-like tetraquarks, and $ωχ_{bJ}$ for bottomonium-like tetraquarks. The tetraquark theoretical results are compared with the selected exotic states, also known as Y states, and tentative assignments are suggested. This study suggests that $ψ(4230)$, $ψ(4360)$, $ψ(4660)$, and $Υ$(10753) may be P-wave tetraquark states and that multiple states might exist around 4.36 GeV.