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 ϵK 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.
Highlights
Observed mixings; inability to explain the origin of the observed CP violation (CPV) [5]; and incapacity to cast any light on the quark and lepton mass and mixing hierarchies
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 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
Summary
A priori, the scalar potential of such a model may have (before one uses the liberty to redefine the fields of the model) 54 independent real parameters, as opposed to the two parameters of the SM scalar potential or 14 free parameters of the general 2HDM scalar sector. The proposal by Weinberg of a 3HDM equipped with natural flavor conservation in the Yukawa sector [16], for instance, included two discrete symmetries generated by φ2 → −φ2 and, separately, φ3 → −φ3, making the symmetry group of the model Z2 × Z2. This symmetry is spontaneously broken by the vacuum expectation values (vevs) in the Higgs doublets. For the reader’s convenience and to set up the notation, we begin with a general reminder on the freedom in choosing CP transformations one has when building a model
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