Masses of doubly heavy tetraquarks $T_{Q{Q}^{\mathrm{\prime }}}$ in a relativized quark model

In the present work, the mass spectra of doubly heavy tetraquarks $T_{Q{Q}^{\mathrm{\prime }}}$ are systematically investigated in a relativized quark model. The four-body systems including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved within the variational method. Our results suggest that the $I{J}^P={01}^{+}$ $bb\bar{u}\bar{d}$ state is 54 MeV below the relevant $\bar{B}\bar{B}$ and $\bar{B}{\bar{B}}^{\ast }$ thresholds, which indicates that both strong and electromagnetic decays are forbidden, and thus this state can be a stable one. Its large hidden color component and small root mean square radius demonstrate that it is a compact tetraquark rather than a loosely bound molecule or point-like diquark-antidiquark structure. Our predictions of the doubly heavy tetraquarks may provide valuable information for future experimental searches.