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Systematic construction of basis invariants in the 2HDM
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A new systematic method for the explicit construction of (basis-)invariants is introduced and employed to construct the full ring of basis invariants of the Two-Higgs-Doublet-Model (2HDM) scalar sector. Co- and invariant quantities are obtained by the use of hermitian projection operators. These projection operators are constructed from Young tableaux via birdtrack diagrams and they are used in two steps. First, to extract basis-covariant quantities, and second, to combine the covariants in order to obtain the actual basis invariants. The Hilbert series and Plethystic logarithm are used to find the number and structure of the complete set of generating invariants as well as their interrelations (syzygies). Having full control over the complete ring of (CP-even and CP-odd) basis invariants, we give a new and simple proof of the necessary and sufficient conditions for explicit CP conservation in the 2HDM, confirming earlier results by Gunion and Haber. The method generalizes to other models, with the only foreseeable limitation being computing power.
Forward citations
Cited by 2 Pith papers
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GOOFy-compatible 3HDMs and beyond
A GOOFy-compatible quadratic sector requires a sign character realized in R*otimesR, and the RG stability of the 2HDM r0 relation is a unique SU(2) accident.
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The Hilbert Series and the Flavor Invariants of the 3HDM
The full multigraded Hilbert series of the 3HDM is computed in closed form, and a basis of SU(3)-invariant operators is constructed up to cubic order in the quartic couplings.
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