Pole mass determination in presence of heavy particles

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.