Precise prediction for the light MSSM Higgs boson mass combining effective field theory and fixed-order calculations

In the Minimal Supersymmetric Standard Model heavy superparticles introduce large logarithms in the calculation of the lightest $\mathcal{CP}$-even Higgs boson mass. These logarithmic contributions can be resummed using effective field theory techniques. For light superparticles, however, fixed-order calculations are expected to be more accurate. To gain a precise prediction also for intermediate mass scales, both approaches have to be combined. Here, we report on an improvement of this method in various steps: the inclusion of electroweak contributions, of separate electroweakino and gluino thresholds, as well as resummation at the NNLL level. These improvements can lead to significant numerical effects. In most cases, the lightest $\mathcal{CP}$-even Higgs boson mass is shifted downwards by about 1 GeV. This is mainly caused by higher order corrections to the $\bar{\text{MS}}$ top-quark mass. We also describe the implementation of the new contributions in the code {\tt FeynHiggs}.