Abstract
We derive the complete set of continuous maximal symmetries for Standard Model (SM) alignment that may occur in the tree-level scalar potential of multi-Higgs Doublet Models, with $n > 2$ Higgs doublets. Our results generalize the symmetries of SM alignment, without decoupling of large mass scales or fine-tuning, previously obtained in the context of two-Higgs Doublet Models.
Highlights
As more and more data are being collected at the CERN Large Hadron Collider (LHC), it becomes even more apparent from global analyses [1,2,3,4,5] that the observed Higgs boson h, with a mass Mh ≈ 125 GeV, interacts with the gauge bosons with coupling strengths that are very close to those predicted by the standard model (SM) [6]
The constraints deduced from the strengths of these Higgs couplings, primarily to WÆ and Z bosons, put severe limits on the actual form of a possible heavy scalar sector in the observable sub-TeV range, and so on the model structure of new physics to be anticipated at the LHC
If there are additional heavy scalars in the theory, as predicted in two-Higgs doublet models (2HDMs) [7,8,9] or nHDMs, with n > 2 Higgs doublets [10,11,12,13,14,15], there are two main strategies that are followed in the literature to avoid too large mixings of the heavy scalars to the SM Higgs boson h
Summary
As more and more data are being collected at the CERN Large Hadron Collider (LHC), it becomes even more apparent from global analyses [1,2,3,4,5] that the observed Higgs boson h, with a mass Mh ≈ 125 GeV, interacts with the gauge bosons with coupling strengths that are very close to those predicted by the standard model (SM) [6]. The second strategy, which is of interest to us, is a bit more optimistic, as it leaves open the possibility to directly probe the heavy scalar sector It assumes that the new scalars are not very heavy after all, e.g. they have masses in the sub-TeV range, but the theoretical parameters are arranged in such a way that the new scalars do not mix significantly with h. The key observation to be made here is that SM alignment is naturally achieved in multiHDMs, if the dimension-4 part of the scalar potential V containing the quartic couplings of the EWSB scalars is invariant under rotations that diagonalize their corresponding squared mass matrix of dimension 2 in V.
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