Implications of naturalness for the heavy Higgs bosons of supersymmetry

Recently, it has been argued that various measures of supersymmetric naturalness-electroweak, Higgs mass and EENZ/BG-when applied consistently, concur with one another and make very specific predictions for natural supersymmetric spectra. Highly natural spectra are characterized by light Higgsinos with mass not too far from m sub(h) and well-mixed but TeV-scale third generation squarks. We apply the unified naturalness measure to the case of heavy Higgs bosons A, H and H super(+ or -). We find that their masses are bounded from above by naturalness depending on tan beta : e.g. for 10% fine-tuning and tan beta ~ 10, we expect m sub(A) [