Abstract
-odd invariants provide a basis independent way of studying the properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are odd or even, then systematically construct all of the simplest -odd invariants up to a given order, finding many new ones. The -odd invariants are valid for general potentials when expressed in a standard form. We then apply our results to scalar potentials involving three (or six) Higgs fields which form irreducible triplets under a discrete symmetry, including invariants for both explicit as well as spontaneous violation. The considered cases include one triplet of Standard Model (SM) gauge singlet scalars, one triplet of SM Higgs doublets, two triplets of SM singlets, and two triplets of SM Higgs doublets. For each case, we study the potential symmetric under one of the simplest discrete symmetries with irreducible triplet representations, namely , , or , as well as the infinite classes of discrete symmetries or .
- Received 6 May 2016
DOI:https://doi.org/10.1103/PhysRevD.94.056007
© 2016 American Physical Society