We perform a precision computation of hybrid static potentials with quantum numbers Λ η ε = Σ g ? , Σ u + , Σ u ? , Π g , Π u , Δ g , Δ u using SU(3) lattice gauge theory. The resulting potentials are used to estimate masses of heavy c ˉ c and b ˉ b hybrid mesons in the Born-Oppenheimer approximation. Part of the lattice gauge theory computation, which we discuss in detail, is an extensive optimization of hybrid static potential creation operators. The resulting optimized operators are expected to be essential for future projects concerning the computation of three-point functions as e.g., needed to study spin corrections, decays or the gluon distribution of heavy hybrid mesons.
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