Tetraquark systems b over line bd over line u in the static limit and lattice QCD

Two hadrons with exotic quark content Z thorn b similar or equal to b over bar bd over bar u were discovered by Belle. We present a lattice study of the b over bar bd over bar u systems with various quantum numbers using static bottom quarks. Only one set of quantum numbers that couples to Zb and pi was explored on the lattice before; these studies found an attractive potential between B and B over bar resulting in a bound state below the threshold. The present study considers the other three sets of quantum numbers. Eigenenergies of the b over bar bd over bar u system are extracted as a function of separation between b and b over bar . The resulting eigenenergies do not show any sizable deviation from noninteracting energies of the systems b over bar b thorn d over bar u and b over bar u thorn d over bar b, so no significant attraction or repulsion is found. A slight exception is a small attraction between B and B over bar at small distance for the quantum number that couples to Zb and eta b rho.