Higgs alignment and the top quark

There is a surprising connection between the top quark and Higgs alignment in Gildener-Weinberg multi-Higgs doublet models. Were it not for the top quark and its large mass, the coupling of the 125 GeV Higgs boson $H$ to gauge bosons and fermions would be indistinguishable from those of the Standard Model Higgs. The top quark's coupling to a single Higgs doublet breaks this perfect alignment in higher orders of the Coleman-Weinberg loop expansion of the effective potential. But the effect is still small, $< {\cal{O}}(1\%)$, and probably experimentally inaccessible.