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