Apparent Alignment and Its Protection in Two Higgs Doublet Model

With the 125 GeV boson $h^0$ belonging to a weak scalar doublet, a second doublet inspired by supersymmetry would have to be rather heavy. We show that, if the usual discrete symmetry is dropped, then apparent "alignment", that $h^0$ resembles the Standard Model Higgs boson, emerges naturally. The $H^0$, $A^0$ and $H^\pm$ bosons of the second doublet can be sub-TeV while remaining well hidden so far, with broad parameter space for search at the Large Hadron Collider. For two Higgs doublets, the alignment phenomenon seems to favor absence of discrete symmetry.