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 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.
Highlights
In order to formulate a theory and execute computations it arguably is necessary to pick a certain basis and parametrization
A basis invariant parametrization simplifies the analysis of renormalization group equations (RGE) and RGE running, both for Standard Model (SM) fermions [26,27,28] as well as for extended scalar sectors [29,30,31], and so the question of how to construct basis invariants continues to be of interest [32, 33]
For tensor products of only Y3, Z3, and Z5abcd → (Z5), the statement (ii) holds and we have confirmed this explicitly. This can be read off directly from the Plethystic logarithm (PL) (5.8), where we find that no single invariant structure of the generating set appears with multiplicity higher than one — implying that each single tensor product Z5⊗a ⊗ Y3⊗b ⊗ Z3⊗c can host at most one independent invariant
Summary
Before starting the actual discussion of this paper let us introduce the technical terms used. The maximal number of algebraically independent invariants is equal to the number of physical parameters of a theory in the usual sense Not surprisingly, this is the number of parameters which remains after all possible basis changes have been used to absorb parameters, i.e. set as many of them to zero as possible. For many applications it makes sense to go beyond the set of algebraically independent invariants This is the case, because a relation of the kind (2.1) does not guarantee that we can solve for an arbitrary invariant. For this reason, it makes sense to discuss a generating set of a ring, which consists of all invariants that cannot be written as a polynomial of other invariants, Ii = P
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
