  We investigate the determination of the Higgs-boson propagator poles in the
MSSM. Based upon earlier works, we point out that in case of a large hierarchy
between the electroweak scale and one or more SUSY masses a numerical
determination with $\overline{\text{DR}}$ Higgs field renormalization induces
higher order terms which would cancel in a more complete calculation. The
origin of these terms is the momentum dependence of contributions involving at
least one of the heavy particles. We present two different methods to avoid
their appearance. In the first approach, the poles are determined by expanding
around the one-loop solutions. In the second approach, a "heavy-OS" Higgs field
renormalization is employed in order to absorb the momentum dependence of heavy
contributions. We will find that the first approach leads to an unwanted
behaviour of the Higgs boson mass predictions close to crossing points where
two Higgs bosons that mix with each other are almost mass degenerate. These
problems are avoided in the second approach, which became the default approach
used in the public code FeynHiggs. Despite the discussion being very specific
to the MSSM, the argumentation and the methods presented in this work are
straightforwardly applicable to the determination of propagator poles in other
models involving a large mass hierarchy.
