We combine lattice QCD results for the potential of two static antiquarks in the presence of two quarks qq of finite mass and quark model techniques to study possibly existing qqbb tetraquarks. While there is strong indication for a bound four-quark state for qq = (ud − du)/ √ 2, i.e. isospin I = 0, we find clear evidence against the existence of corresponding tetraquarks with qq ∈ {uu, (ud+ du)/ √ 2, dd}, i.e. isospin I = 1, qq = ss and qq = cc.PACS numbers: 12.38. Gc, 13.75.Lb, 14.40.Rt, 14.65.Fy.1 has exotic quantum numbers J P C = 1 −+ or Z ± c and Z ± b masses and decay products strongly suggest hidden cc or bb pairs, while their electrical charge ±1 indicates isospin I = 1. While the evidence for π −+ arXiv:1505.00613v2 [hep-lat] 12 May 2015