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 row 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 row 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 Z(3) and Z(2) x 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 strength of their tree-level SFCNC.

Abstract: A simple variant of a realistic flavor symmetry scheme for fermion masses and mixings provides a possible interpretation of the diphoton anomaly as an electroweak singlet “flavon.” The existence of TeV scale vectorlike T-quarks required to provide adequate values for Cabibbo-Kobayashi-Maskawa (CKM) parameters can also naturally account for the diphoton anomaly. Correlations between V-ub and V-cb with the vectorlike T-quark mass can be predicted. Should the diphoton anomaly survive in a future run, our proposed interpretation can also be tested in upcoming B and LHC studies.

Abstract: The precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the filtered neutral meson B-d states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-d-factory of entangled states, is established. This allows the identification of genuine Asymmetry Parameters in the time distribution of the asymmetries and their measurability by disentangling genuine and possible fake terms. We express the nine asymmetry parameters three different observables for each one of the three symmetries in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled B-d-meson states and we obtain a global fit to their values from the BaBar collaboration experimental results. The possible fake terms are all compatible with zero and the information content of the nine asymmetry parameters is indeed different. The non -vanishing Delta l(c)(T) = 0.687 +/- 0.020 and Delta l(c)(CP) = 0.680 +/- 0.021 are impressive separate direct evidence of Time -Reversal -violation and CP-violation in these transitions and compatible with Standard Model expectations. An intriguing 2 sigma effect for the Re(theta) parameter responsible of CPT -violation appears which, interpreted as an upper limit, leads to vertical bar M (B) over baro (B) over baro vertical bar MBoBo < 4.0 x 10(-5) eV at 95% C.L. for the diagonal flavour terms of the mass matrix. It contributes to the CP-violating Delta l(c)(CP) asymmetry parameter in an unorthodox manner – in its cos(Delta M t) time dependence-, and it is accessible in facilities with non-entangled B-d's, like the LHCb experiment.