Doubling Up on Supersymmetry in the Higgs Sector

We explore the possibility that physics at the TeV scale possesses approximate $N = 2$ supersymmetry, which is reduced to the $N=1$ minimal supersymmetric extension of the Standard Model (MSSM) at the electroweak scale. This doubling of supersymmetry modifies the Higgs sector of the theory, with consequences for the masses, mixings and couplings of the MSSM Higgs bosons, whose phenomenological consequences we explore in this paper. The mass of the lightest neutral Higgs boson $h$ is independent of $\tan \beta$ at the tree level, and the decoupling limit is realized whatever the values of the heavy Higgs boson masses. Radiative corrections to the top quark and stop squarks dominate over those due to particles in $N=2$ gauge multiplets. We assume that these radiative corrections fix $m_h \simeq 125$ GeV, whatever the masses of the other neutral Higgs bosons $H, A$, a scenario that we term the $h$2MSSM. Since the $H, A$ bosons decouple from the $W$ and $Z$ bosons in the $h$2MSSM at tree level, only the LHC constraints on $H, A$ and $H^\pm$ couplings to fermions are applicable. These and the indirect constraints from LHC measurements of $h$ couplings are consistent with $m_A \gtrsim 200$ GeV for $\tan \beta \in (2, 8)$ in the $h$2MSSM.