Uncertainties in the lightest $$CP$$ CP even Higgs boson mass prediction in the minimal supersymmetric standard model: fixed order versus effective field theory prediction

We quantify and examine the uncertainties in predictions of the lightest $$CP$$ even Higgs boson pole mass Mₕ in the Minimal Supersymmetric Standard Model ( MSSM ), utilising current spectrum generators and including some three-loop corrections. There are two broadly different approximations being used: effective field theory (EFT) where an effective Standard Model ( SM ) is used below a supersymmetric mass scale, and a fixed order calculation, where the MSSM is matched to QCD× QED at the electroweak scale. The uncertainties on the Mₕ prediction in each approach are broken down into logarithmic and finite pieces. The inferred values of the stop mass parameters are sensitively dependent upon the precision of the prediction for Mₕ . The fixed order calculation appears to be more accurate below a supersymmetry (SUSY) mass scale of MS≈ 1.2~TeV , whereas above this scale, the EFT calculation is more accurate. We also revisit the range of the lightest stop mass across fine-tuned parameter space that has an appropriate stable vacuum and is compatible with the lightest $$CP$$ even Higgs boson h being identified with the one discovered at the ATLAS and CMS experiments in 2012; we achieve a maximum value of ~ 10¹¹ GeV.