Extending Trinity to the Scalar Sector through Discrete Flavoured Symmetries

TL;DR

This paper proposes a new multi-Higgs model based on flavoured symmetries, extending the Trinity Principle to the scalar sector, which naturally explains fermion masses, CP violation, and reduces flavor-changing neutral currents.

Contribution

It introduces the Trinity Principle with flavoured symmetries, providing minimal multi-Higgs extensions of the Standard Model that generate realistic CP violation and control flavor-changing processes.

Findings

Models satisfy the Trinity Principle with $ ext{Z}_3$ and $ ext{Z}_2 imes ext{Z}_2'$ symmetries.

Vacuum phases generate a complex CKM matrix consistent with experiments.

Strong reduction in Yukawa parameters and controlled scalar flavor-changing neutral couplings.

Abstract

We conjecture the existence of a relation between elementary scalars and fermions, making it plausible the existence of three Higgs doublets. We introduce a Trinity Principle (TP) which, given the fact that there are no massless quarks, requires the existence of a minimum of three Higgs doublets. The TP states that each line of the mass matrix of a quark of a given charge should receive the contribution from one and only one scalar doublet and furthermore a given scalar doublet should contribute to one and only one line of the mass matrix of a quark of a given charge. This principle is analogous to the Natural Flavour Conservation (NFC) of Glashow and Weinberg with the key distinction that NFC required the introduction of a flavour blind symmetry, while the TP requires a flavoured symmetry, to be implemented in a natural way. We provide two examples which satisfy the Trinity Principle based on $\mathbb{Z}_3$ and $\mathbb{Z}_2\times\mathbb{Z}_2'$ flavoured symmetries, and show that they are the minimal multi-Higgs extensions of the Standard Model where CP can be imposed as a symmetry of the full Lagrangian and broken by the vacuum, without requiring soft-breaking terms. We show that the vacuum phases are sufficient to generate a complex CKM matrix, in agreement with experiment. The above mentioned flavoured symmetries lead to a strong reduction in the number of parameters in the Yukawa interactions, enabling a control of the Scalar Flavour Changing Neutral Couplings (SFCNC). We analyse some of the other physical implications of the two models, including an estimate of the enhancement of the Baryon Asymmetry of the Universe provided by the new sources of CP violation, and a discussion of the the strength of their tree-level SFCNC.