Yet another extension of the standard model: Oases in the desert?

We search for conceptually simple extensions of the standard model, and describe here a candidate model which we find attractive. Our starting point is the assumption that off-diagonal CKM mixing matrix elements are directly related by lowest order perturbation theory to the quark mass matrices. This appears to be most easily and naturally implemented by assuming that all off-diagonal elements reside in the down-quark mass matrix. This assumption is in turn naturally realized by introducing three generations of heavy, electroweak-singlet down quarks which couple to the Higgs sector diagonally in flavor, while mass mixing off-diagonally with the light down quarks. Anomaly cancellation then naturally leads to inclusion of electroweak vector-doublet leptons. It is then only a short step to completing the extension to three generations of fundamental $\underset{¯}{27}$ representations of $E\left(6\right).$ Consequences of this picture include (1) the hypothesis of “Stech texture” for the down-quark mass matrix (imaginary off-diagonal elements) leads to an approximate right unitarity triangle $(\gamma \approx \pi /2),$ and a value of $\sin 2\beta$ between 0.64 and 0.80. (2) Assuming only that the third generation B couples to the Higgs sector at least as strongly as does the top quark, the mass of the B is roughly estimated to lie between 1.7 TeV and 10 TeV, with lower-generation quarks no heavier. The corresponding guess for the new leptons is a factor two lower, 0.8 TeV to 5 TeV. (3) Within the validity of the model, flavor and $\mathrm{CP}$ violation are “infrared” in nature, induced by semi-soft mass mixing terms, not Yukawa couplings. (4) The “Mexican hat” structure of the Higgs potential may be radiatively induced by the new heavy down-quark one-loop contributions to the potential. (5) A subset of the precision electroweak experiments are sensitive to the physics induced by the heavy quarks and/or leptons. (6) If the Higgs couplings of the new quarks are flavor symmetric, then there necessarily must be at least one “oasis” in the desert, induced by new radiative corrections to the top quark and Higgs coupling constants, and roughly at ${10}^3\mathrm{TeV}.$ (7) If the Higgs couplings of the new down quarks are hierarchical and equal to the usual Higgs couplings to right-handed up quarks, then, in the limit in which gauge coupling constants are set to zero, parity violation is also “infrared,” induced by semi-soft mass terms.