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We compute the energy of a static hybrid, i.e. of a hybrid quarkonium withstatic quark and antiquark, at short distances in D=4,3 dimensions. The softcontribution to this energy is the static potential of a color octetquark-antiquark pair at short distances, which is known at two loops forarbitrary D. We have checked this expression employing thermal field theorymethods. Using the effective field theory pNRQCD we calculate the ultrasoftcontributions to the hybrid (and singlet) static energy at the two-loop level.We then present new results for the static hybrid energy/potential and thehybrid decay width in three and four dimensions. Finally we comment on themeaning of the perturbative results in two space-time dimensions, where thehybrid does not exist.

The static hybrid potential in D dimensions at short distances