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

Abstract

A comprehensive study of the $S$-wave heavy tetraquark states with identical quarks and antiquarks, specifically $QQ{\bar{Q}}^{\prime }{\bar{Q}}^{\prime }$ ($Q,Q^{\prime }=c,b$), $QQ\bar{s}\bar{s}$/$\bar{Q}\bar{Q}ss$, and $QQ\bar{q}\bar{q}$/$\bar{Q}\bar{Q}qq$ ($q=u,d$), 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 Schrödinger 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 $QQ\bar{q}\bar{q}$ states with the isospin and spin-parity quantum numbers $I(J^P)=0(1^{+})$: two bound $bb\bar{q}\bar{q}$ states with the binding energies, 153 MeV and 4 MeV below the $B{B}^{\ast }$ threshold, and a shallow $cc\bar{q}\bar{q}$ state at $-15$ MeV from the $D{D}^{\ast }$ threshold. The deeper $bb\bar{q}\bar{q}$ bound state aligns with the lattice QCD predictions, while $cc\bar{q}\bar{q}$ 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 $QQ{\bar{Q}}^{\prime }{\bar{Q}}^{\prime }$, $QQ\bar{s}\bar{s}$ and $QQ\bar{q}\bar{q}$ with $I=1$. Our analysis shows that the bound $QQ{\bar{Q}}^{\prime }{\bar{Q}}^{\prime }$ states are more probable with a larger mass ratio, $m_Q/m_{Q^{\prime }}$. Experimental investigation for these states is desired, which will enrich our understanding of hadron spectroscopy and probe insights into the confinement mechanisms within tetraquarks.

Comments: 38 pages, 18 figures