Natural alignment in multi-Higgs doublet models

We present the complete set of continuous maximal symmetries that the potential of an n-Higgs Doublet Model (nHDM) should satisfy for natural Standard Model (SM) alignment. As a result, no large mass scales or fine-tuning is required for such alignment, which still persists even if these symmetries were broken softly by bilinear mass terms. In particular, the Maximal Symmetric n
HDM (MS-nHDM) can provide both natural SM alignment and quartic coupling unification up to the Planck scale. Most remarkably, we show that the MS-2HDM is a very predictive extension of the SM governed by two only additional parameters: (i) the charged Higgs mass Mh± (or m212) and (ii) tanβ, whilst the quartic coupling unification scale μX is predicted to assume two discrete
values. With these two input parameters, the entire Higgs-mass spectrum of the model can be determined. Moreover, we obtain definite predictions of misalignment for the SM-like Higgs-boson couplings to the gauge bosons and to the quarks, which might be testable at future precision high-energy colliders.