Lattice perspectives on doubly heavy tetraquarks

Doubly heavy tetraquarks have emerged as new probes to study the heavy hadron spectrum. With the experimental observation of the $J^P=1^{+}$ $T_{cc}^{+}$, they pose a unique opportunity to bring together efforts in experiment, phenomenology, and lattice QCD. In lattice calculations they are accessible as ground states, unlike hidden flavor tetraquarks, and this enables accurate determinations of the scattering parameters alongside the binding energies of these tetraquarks. Today, lattice calculations firmly predict $J^P=1^{+}$ $T_{bb}^{ud}$ and $T_{bb}^{us}$ as QCD bound states, while recent studies approaching the $J^P=1^{+}$ $T_{cc}^{ud}$ find it to be a virtual bound state at slightly non-physical input quark masses. Studies of the $J^P=1^{+}$ $T_{bc}^{ud}$ are ongoing and a new focus area. In light of these developments the evolution of this field until this point is reviewed. Emphasis is put on the methods in lattice spectroscopy that enable a robust evaluation of the lattice studies gathered. They are further reviewed towards their limitations and achievements. Current challenges and opportunities are discussed, including possibilities to approach the left-hand cut in the scattering analysis of the charm candidates and towards understanding the structure of those including two bottom quarks.