Dr Neda Darvishi (Royal Holloway, University of London)

I will discuss classifying accidental symmetries in multi-Higgs Doublet Models (nHDMs). The potentials of nHDMs contain a large number of SU(2)_L-preserving accidental symmetries as subgroups of the symplectic group Sp(2n). To classify these, prime invariants and irreducible representations in bilinear field space can be used that enable us to explicitly construct accidentally symmetric nHDM potentials. I will showcase the classification of the symmetries and present the relationship between the theoretical parameters of the scalar potential for; (i) the Two Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model (3HDM). In this approach, I will present the maximum number of 13 accidental symmetries for the 2HDM potential and 40 accidental symmetries for the 3HDM potential. Furthermore, I will present the complete set of continuous maximal symmetries that the potential of 2HDM and 3HDM should satisfy for the natural Standard Model (SM) alignment limit. As a result,  no large mass scales or fine-tuning is required for such alignment limit, which still persists even if these symmetries were broken softly by bilinear mass terms. In particular, the Maximal Symmetric nHDM (MS-nHDM) can provide natural SM alignment whereas exhibiting quartic coupling unification up to the Planck scale. I will show that the MS-nHDM are very predictive extensions of the SM governed only by a few BSM parameters that allow determining the entire Higgs-mass spectrum of the model.