Higgs Bosons in Heavy Supersymmetry with an Intermediate $m_A$

The minimal supersymmetric standard model leads to precise predictions of the properties of the light Higgs boson degrees of freedom that depend on only a few relevant supersymmetry breaking parameters. In particular, there is an upper bound on the mass of the lightest neutral Higgs boson, which for a supersymmetric spectrum of the order of a TeV is barely above the one of the Higgs resonance recently observed at the LHC. This bound can be raised by considering a heavier supersymmetric spectrum, relaxing the tension between theory and experiment. In a previous article, we studied the predictions for the lightest CP-even Higgs mass for large values of the scalar-top and heavy Higgs boson masses. In this article we perform a similar analysis, considering also the case of a CP-odd Higgs boson mass $m_A$ of the order of the weak scale. We perform the calculation using effective theory techniques, considering a two-Higgs doublet model and a Standard Model-like theory and resumming the large logarithmic corrections that appear at scales above and below $m_A$, respectively. We calculate the mass and couplings of the lightest CP-even Higgs boson and compare our results with the ones obtained by other methods.