  We report about an ongoing lattice field theory project concerned with the
investigation of heavy hybrid mesons. In particular we discuss our computation
of the structure of hybrid static potential flux tubes in SU(2) lattice
Yang-Mills theory, which is based on the squares of the chromoelectric and
chromomagnetic field strength components. Our flux tube results for hybrid
static potential quantum numbers $\Sigma_g^-$, $\Sigma_u^+$, $\Sigma_u^-$,
$\Pi_g$, $\Pi_u$, $\Delta_g$, $\Delta_u$ are significantly different compared
to the flux tube of the ordinary static potential.
