We study tetraquark resonances with lattice QCD potentials computed for a staticbb pair in the presence of two lighter quarks ud, the Born-Oppenheimer approximation and the emergent wave method. As a proof of concept we focus on the system with isospin I = 0, but consider different relative angular momenta l of the heavy quarksbb. For l = 0 a bound state has already been predicted with quantum numbers I(J P ) = 0(1 + ). Exploring various angular momenta we now compute the phase shifts and search for S and T matrix poles in the second Riemann sheet. We predict a tetraquark resonance for l = 1, decaying into two B mesons, with quantum numbers I(J P ) = 0(1 − ), mass m = 10 576 +4 −4 MeV and decay width Γ = 112 +90 −103 MeV.

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We investigate heavy-light four-quark systems udbb with bottom quarks of finite mass which are treated in the framework of NRQCD. We focus on I(J P ) = 0(1 + ), where we recently found evidence for the existence of a tetraquark state using static bottom quarks. Furthermore, we report on an investigation of the udbb four-quark system with quantum numbers I(J P ) = 1(1 + ) again using static bottom quarks.

We investigate BB systems by computing potentials of two static quarks in the presence of two quarks of finite mass using lattice QCD. By solving the Schrödinger equation we check whether these potentials are sufficiently attractive to host bound states. Particular focus is put on the experimentally most promising bottomonium-like tetraquark candidate Z ± b with quantum numbers I(J P ) = 1(1 + ). The bbud four-quark system -qualitative discussion and expectationsThe bbud four-quark system can be characterized by the separation r of the static quark b ≡ Q and the antiquarkb ≡Q, by parity P , total angular momentum J and isospin I. Since we consider static b quarks, i.e. b ≡ Q andb ≡Q, the bb separation is also a quantum number.

We determine Λ (n f =2) MS by fitting perturbative expressions for the quarkantiquark static potential to lattice results for QCD with n f = 2 dynamical quark flavors. To this end we use the perturbative static potential at the presently best known accuracy, i.e. up to O(α 4 s ), in momentum space. The lattice potential is computed on a fine lattice with a ≈ 0.042 fm in position space. To allow for a comparison and matching of both results, the lattice potential is transformed into momentum space by means of a discrete Fourier transform. The value of Λ (n f =2) MS is extracted in momentum space. All sources of statistical and systematic errors are discussed. The uncertainty in the value of Λ (n f =2) MS is found to be smaller than that obtained in a recent position space analysis of the static potential based on the same lattice data.