The light CP-even MSSM Higgs mass including N\(^\mathbf {3}\)LO+N\(^\mathbf {3}\)LL QCD corrections

We present a calculation of the light neutral CP-even Higgs boson pole mass in the real $$\text {MSSM}$$ which combines state-of-the-art EFT and fixed-order results, including the three-loop fixed-order QCD corrections as well as the resummation of logarithmic terms in the ratio of the weak to the SUSY scale up to fourth logarithmic order. This hybrid calculation should be valid for arbitrary SUSY scales above the weak scale. Comparison to the pure fixed-order and EFT results provides an estimate of their individual validity range.