Exotic tetraquarks with heavy quarks in lattice QCD

We review all the different direct and indirect approaches that lattice QCD has beenemploying to study multiquarks, focusing in the tetraquarks with heavy quarks. Wealso briefly review the experimental progress in observing tetraquarks, and the mostrepresentative models of tetraquarks, comparing them with the results of lattice QCD.

Since the discovery of quarks and the development of the QCD theory, there has beena large interest in exotic hadrons, initiated by the tetraquark models developed byJaffe in 1974. In the new millennium, this interest exploded with several experimentaldiscoveries of tetraquark resonances with heavy quarks, starting with the $Z_c$ and$Z_b$.

Moreover there is a second class of tetraquarks such as the $T_{bb}$,boundstates in the sense of having no strong decays. Very recently, the narrow$T_{cc}$ tetraquark first predicted with quark models in 1982 Richard et al, wasobserved experimentally. Lattice QCD, being a first principle approach to solve nonperturbative QCD, has been crucial not only to compute precise results, but also tomotivate and inspire research in hadronic physics, with particular interest in exotichadrons.

So far, lattice QCD has not yet been able to comprehend the $Z$ class oftetraquarks, while it predicted the $T$ class of tetraquarks. New methods are beingdeveloped to determine the masses, decay widths and decay processes of tetraquarks.