Systematic construction of basis invariants in the 2HDM
Andreas Trautner
TL;DR
This paper introduces a systematic method for constructing basis invariants in the 2HDM scalar sector, enabling complete characterization of invariants and simplifying conditions for CP conservation.
Contribution
A new method using hermitian projection operators and Young tableaux to explicitly construct the full ring of basis invariants in the 2HDM.
Findings
Constructed the complete set of basis invariants for 2HDM.
Provided a simple proof of CP conservation conditions.
Demonstrated the method's potential for generalization to other models.
Abstract
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…
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