AbstractWe discuss various improvements of the prediction for the light MSSM Higgs boson mass in the hybrid framework of the public code $$\texttt {FeynHiggs}$$
FeynHiggs
, which combines fixed-order and effective field theory results. First, we discuss the resummation of logarithmic contributions proportional to the bottom-Yukawa coupling including two-loop $$\Delta _b$$
Δ
b
resummation. For large $$\tan \beta $$
tan
β
, these improvements can lead to large upward shifts of the Higgs mass compared to the existing fixed-order calculations. Second, we improve the implemented EFT calculation by fully taking into account the effect of $$\mathcal{CP}$$
CP
-violating phases. As a third improvement, we discuss the inclusion of partial $$\hbox {N}^3$$
N
3
LL resummation. The presented improvements will be implemented into $$\texttt {FeynHiggs}$$
FeynHiggs
.