Higgs-Sector Predictions from Maximally Symmetric multi-Higgs Doublet Models

Maximally Symmetric $n$-Higgs Doublet Models (MS-$n$HDMs)define very economic settings that enable sharp Higgs-sector predictions beyond the Standard Model (SM) potentially testable at high-energy colliders. The scalar potential of a MS-$n$HDM obeys an $\mathrm{Sp(2}n)$ symmetry, which is softly broken by bilinear scalar masses and explicitly by hypercharge and Yukawa couplings through renormalisation-group effects. The $\mathrm{Sp(2}n)$ also ensures natural SM alignment and allows for quartic coupling unification up to the Planck scale. As typical examples, we consider maximally symmetric realisations of the Type-II 2HDM and the Type-V 3HDM. We show how in terms of a few input parameters, definite predictions for the entire scalar mass spectrum of the MS-2HDM and MS-3HDM are obtained, including the SM-like Higgs-boson couplings to the gauge bosons and fermions.