CP-odd invariants for multi-Higgs models: applications with discrete symmetry

TL;DR

This paper develops methods to construct basis-independent CP-odd invariants for multi-Higgs models with discrete symmetries, enabling systematic analysis of CP violation in various scalar potentials.

Contribution

It introduces systematic techniques for constructing CP-odd invariants and applies them to multi-Higgs models with discrete symmetries, identifying new invariants and analyzing CP violation.

Findings

Constructed all simplest CP-odd invariants up to a given order.

Applied invariants to models with various discrete symmetries like A4, S4, Δ(27), Δ(54).

Analyzed explicit and spontaneous CP violation in multiple Higgs scenarios.

Abstract

CP-odd invariants provide a basis independent way of studying the CP properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are CP-odd or CP-even, then systematically construct all of the simplest CP-odd invariants up to a given order, finding many new ones. The CP-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 CP 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 $A_4$, $S_4$, $\Delta(27)$ or $\Delta(54)$, as well as the infinite classes of discrete symmetries $\Delta(3n^2)$ or $\Delta(6n^2)$.