  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.
