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We present a calculation of the light neutral CP-even Higgs boson pole mass in the real $$\text {MSSM}$$ 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.

The impact of the finite top-quark mass on the inclusive Higgs production cross section at higher perturbative orders has been an open question for almost three decades. In this paper, we report on the computation of this effect at NNLO QCD. For the purely gluonic channel, it amounts to $+0.62\%$ relative to the result obtained in the HEFT approximation. The formally sub-leading partonic channels over-compensate this shift, leading to an overall effect of $-0.26\%$ at a $pp$ collider energy of $13\,\mathrm{TeV}$, and $-0.1\%$ at $8\,\mathrm{TeV}$. This result eliminates one of the main theoretical uncertainties to inclusive Higgs production cross section at the LHC., 5 pages, 1 figure