Seminarium "Teoria cząstek elementarnych i kosmologia"

I will discuss classifying accidental symmetries in multi-Higgs DoubletModels (nHDMs). The potentials of nHDMs contain a large number ofSU(2)_L-preserving accidental symmetries as subgroups of the symplecticgroup Sp(2n). To classify these, we introduce prime invariants andirreducible representations in bilinear field space that enable us toexplicitly construct accidentally symmetric nHDM potentials. I willshowcase the classification of the symmetries and present the relationshipbetween the theoretical parameters of the scalar potential for; (i) theTwo Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model(3HDM). I show the maximum number of 13 accidental symmetries for the 2HDMpotential and present the complete list of 40 accidental symmetries forthe 3HDM potential.Furthermore, I will present the complete set of continuous maximalsymmetries that the potential of an nHDM should satisfy for naturalStandard Model (SM) alignment. As a result, no large mass scales orfine-tuning is required for such alignment, which still persists even ifthese symmetries were broken softly by bilinear mass terms. In particular,the Maximal Symmetric HDM (MS-nHDM) can provide both natural SM alignmentand quartic coupling unification up to the Planck scale. Most remarkably,I show that the MS-2HDM is a very predictive extension of the SM governedby two only additional parameters: (i) the charged Higgs mass and (ii)tanβ, whilst the quartic coupling unification scale μX ispredicted to assume two discrete values. With these two input parameters,the entire Higgs-mass spectrum of the model can be determined.
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