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(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-+/-. We find that their masses are bounded from above by naturalness depending on tan beta: e.g. for 10% fine-tuning and tan beta similar to 10, we expect m(A) less than or similar to 2.5 TeV whilst for 3% fine-tuning and tan beta as high as 50, then m(A) less than or similar to 8 TeV. Furthermore, the presence of light Higgsinos seriously alters the heavy Higgs boson branching ratios, thus diminishing prospects for usual searches into standard model final states, while new discovery possibilities arise due to the supersymmetric decay modes. The heavy supersymmetric decay modes tend to be H, A, H-+/- -> W, Z, or h + E-T + soft tracks so that single heavy Higgs production is characterized by the presence of high p(T) W, Z or h bosons plus missing E-T. These new heavy Higgs boson signatures seem to be challenging to extract from SM backgrounds.