Systematic construction of basis invariants in the 2HDM

Trautner, Andreas (0000 0001 2288 6103, grid.419604.e, Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117, Heidelberg, Germany) (0000 0001 2240 3300, grid.10388.32, Bethe Center for Theoretical Physics und Physikalisches Institut der Universität Bonn, Nussallee 12, 53115, Bonn, Germany)

12 June 2019

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.

Published in: JHEP 1905 (2019) 208 DOI: 10.1007/JHEP05(2019)208
arXiv: 1812.02614
License: CC-BY-4.0

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