Mass Spectra of Full-Heavy and Double-Heavy Tetraquark States in the Conventional Quark Model

A comprehensive study of the S-wave heavy tetraquark states with identical quarks and antiquarks, specifically QQ Q' Q' ($Q, Q'=c,b$), QQ s s/Q Q ss, and QQ q q/Q Q qq ($q=u,d$), are studied in a unified constituent quark model. This model contains the one-gluon exchange and confinement potentials. The latter is modeled as the sum of all two-body linear potentials. We employ the Gaussian expansion method to solve the full four-body Schr\"{o}dinger equations, and search bound and resonant states using the complex-scaling method. We then identify $3$ bound and $62$ resonant states. The bound states are all QQ q q states with the isospin and spin-parity quantum numbers I(JP)=0(1⁺): two bound bbq̄q̄ states with the binding energies, 153 MeV and 4 MeV below the BB^* threshold, and a shallow ccq̄q̄ state at $-15$ MeV from the DD^* threshold. The deeper bb q q bound state aligns with the lattice QCD predictions, while cc q q bound state, still has a much larger binding energy than the recently observed T⁺cc by LHCb collaboration. No bound states are identified for the QQ Q' Q', QQ s s and QQ q q with $I=1$. Our analysis shows that the bound QQ Q' Q' states are more probable with a larger mass ratio, mQ/mQ'. Experimental investigation for these states is desired, which will enrich our understanding of hadron spectroscopy and probe insights into the confinement mechanisms within tetraquarks.