Workshop for young scientists with research interests focused on physics at FAIR

There are several mesons whose $q\bar q$ quark-structure is doubted or even excluded. Therefore it is interesting to look for alternative structures for those candidates. Four-quark systems are a possible explanation. One way to approach four-quark models quantitatively is by means of lattice QCD. We study the heavy-light four-quark system $b\bar b l \bar l$ ($B\bar B$) on the lattice. The heavy (anti-)quarks $b\bar b$ are addressed in the static approximation. We consider the experimentally interesting case of isospin $I_z=+/-1$, i.e. the light (anti-)quarks $l\bar l$ have different flavours. One aim is to investigate whether the attractiveness of the four-quark potentials is sufficient to host a bound state. For that purpose, the potential is plugged into the Schrödinger equation. The energy eigenvalues provide an insight into whether one can find a bound state or not. The crucial task in the process is to ensure that the computed potential is not a bottomonium and a light meson instead of a four-quark system.