CKM matrix and fermion masses in the dualized standard model

Abstract

A Dualized Standard Model recently proposed affords a natural explanation for the existence of Higgs fields and of exactly 3 generations of fermions, while giving at the same time the observed fermion mass hierarchy together with a tree-level CKM matrix equal to the identity matrix. It further suggests a method for generating from loop corrections the lower generation masses and nondiagonal CKM matrix elements. In this paper, the proposed calculation is carried out to 1-loop. It is found first that with the method suggested one can account readily for the masses of the second generation fermions as a 'leakage' from the highest generation. Then, with the Yukawa couplings fixed by fitting the masses of the 2 higher generations, one is left with only 2 free parameters to evaluate the CKM matrix and the masses in the lowest generation. One obtains a very good fit to the CKM matrix and sensible values for the masses of d and e, though, for a valid reason, not of u. In addition, the fitted values of the Yukawa couplings and vacuum expectation values of the dual colour Higgs fields show remarkable features perhaps indicative of a deeper significance.

Lepton transmutation in the dualized standard model

“…We notice in particular that the mass matrix m ′ after renormalization rotates with changing scale µ, which was the crucial property that gave rise in our earlier papers [21,7] to the distinctive fermion mass and mixing patterns observed in experiment.…”

“…(4.14) of [21] due to a misprint in the formula for Σ (φ1) in eq. (3.2) quoted from [20] which means that the coefficient of the last term in eq.…”

“…This is what was evaluated 2 in [21] and is all that is needed to calculate the single-particle properties such as fermion mass and mixing parameters of interest to us there. We notice in particular that the mass matrix m ′ after renormalization rotates with changing scale µ, which was the crucial property that gave rise in our earlier papers [21,7] to the distinctive fermion mass and mixing patterns observed in experiment.…”

“…(3.2) quoted from [20] which means that the coefficient of the last term in eq. (5.8) of [21] should be 3/(64π 2 ) instead of 5/(64π 2 ). Apart from the fact that the numerical values given for the parameter ρ in eq.…”

“…In order to calculate to the same loop order reaction processes by making all possible insertions, we shall need the explicit mass spectrum of the Higgs fields and their couplings to the fermions, which are deducible from (2) and (1) respectively. Following Weinberg [20] we shall work in a real representation where the remaining 9 Higgs bosons were found earlier [21] to have at tree-level the following mass values:…”