  For the interpretation of the signal discovered in the Higgs searches at the
LHC it will be crucial in particular to discriminate between the minimal Higgs
sector realised in the Standard Model (SM) and its most commonly studied
extension, the Minimal Supersymmetric SM (MSSM). The measured mass value,
having already reached the level of a precision observable with an experimental
accuracy of about 500 MeV, plays an important role in this context. In the MSSM
the mass of the light CP-even Higgs boson, M_h, can directly be predicted from
the other parameters of the model. The accuracy of this prediction should at
least match the one of the experimental result. The relatively high mass value
of about 126 GeV has led to many investigations where the scalar top quarks are
in the multi-TeV range. We improve the prediction for M_h in the MSSM by
combining the existing fixed-order result, comprising the full one-loop and
leading and subleading two-loop corrections, with a resummation of the leading
and subleading logarithmic contributions from the scalar top sector to all
orders. In this way for the first time a high-precision prediction for the mass
of the light CP-even Higgs boson in the MSSM is possible all the way up to the
multi-TeV region of the relevant supersymmetric particles. The results are
included in the code FeynHiggs.
