CP4 miracle: shaping Yukawa sector with CP symmetry of order four

TL;DR

This paper investigates a three-Higgs-doublet model with a unique CP symmetry of order 4, demonstrating its compatibility with experimental data and its potential to explain fermion masses, mixing, and CP violation.

Contribution

It introduces a novel CP4-symmetric three-Higgs-doublet model that constrains the scalar and Yukawa sectors while remaining consistent with current experimental results.

Findings

Model fits electroweak precision data and LHC Higgs results.

Reproduces fermion masses, mixing, and CP violation accurately.

Can account for meson CP-violation parameters despite flavor-changing neutral currents.

Abstract

We explore the phenomenology of a unique three-Higgs-doublet model based on the single CP symmetry of order 4 (CP4) without any accidental symmetries. The CP4 symmetry is imposed on the scalar potential and Yukawa interactions, strongly shaping both sectors of the model and leading to a very characteristic phenomenology. The scalar sector is analyzed in detail, and in the Yukawa sector we list all possible CP4-symmetric structures which do not run into immediate conflict with experiment, namely, do not lead to massless or mass-degenerate quarks nor to insufficient mixing or CP-violation in the CKM matrix. We show that the parameter space of the model, although very constrained by CP4, is large enough to comply with the electroweak precision data and the LHC results for the 125 GeV Higgs boson phenomenology, as well as to perfectly reproduce all fermion masses, mixing, and CP violation. Despite the presence of flavor changing neutral currents mediated by heavy Higgs scalars, we find through a parameter space scan many points which accurately reproduce the kaon CP-violating parameter $\epsilon_K$ as well as oscillation parameters in K and $B_{(s)}$ mesons. Thus, CP4 offers a novel minimalistic framework for building models with very few assumptions, sufficient predictive power, and rich phenomenology yet to be explored.